TSTP Solution File: CAT026+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT026+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 17:29:55 EDT 2022
% Result : Theorem 0.85s 0.81s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT026+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 07:29:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.85/0.81 % SZS status Theorem
% 0.85/0.81 % SZS output start Proof
% 0.85/0.81 tff(r2_nattra_1_type, type, (
% 0.85/0.81 r2_nattra_1: ( $i * $i * $i * $i ) > $o)).
% 0.85/0.81 tff(k11_isocat_2_type, type, (
% 0.85/0.81 k11_isocat_2: ( $i * $i * $i * $i ) > $i)).
% 0.85/0.81 tff(tptp_fun_E_4_type, type, (
% 0.85/0.81 tptp_fun_E_4: $i)).
% 0.85/0.81 tff(tptp_fun_C_2_type, type, (
% 0.85/0.81 tptp_fun_C_2: $i)).
% 0.85/0.81 tff(tptp_fun_B_1_type, type, (
% 0.85/0.81 tptp_fun_B_1: $i)).
% 0.85/0.81 tff(tptp_fun_A_0_type, type, (
% 0.85/0.81 tptp_fun_A_0: $i)).
% 0.85/0.81 tff(tptp_fun_D_3_type, type, (
% 0.85/0.81 tptp_fun_D_3: $i)).
% 0.85/0.81 tff(k2_isocat_1_type, type, (
% 0.85/0.81 k2_isocat_1: ( $i * $i * $i * $i * $i ) > $i)).
% 0.85/0.81 tff(k16_cat_2_type, type, (
% 0.85/0.81 k16_cat_2: ( $i * $i ) > $i)).
% 0.85/0.81 tff(k11_cat_2_type, type, (
% 0.85/0.81 k11_cat_2: ( $i * $i ) > $i)).
% 0.85/0.81 tff(k8_isocat_2_type, type, (
% 0.85/0.81 k8_isocat_2: ( $i * $i ) > $i)).
% 0.85/0.81 tff(m2_cat_1_type, type, (
% 0.85/0.81 m2_cat_1: ( $i * $i * $i ) > $o)).
% 0.85/0.81 tff(v2_cat_1_type, type, (
% 0.85/0.81 v2_cat_1: $i > $o)).
% 0.85/0.81 tff(l1_cat_1_type, type, (
% 0.85/0.81 l1_cat_1: $i > $o)).
% 0.85/0.81 tff(k12_isocat_2_type, type, (
% 0.85/0.81 k12_isocat_2: ( $i * $i * $i * $i ) > $i)).
% 0.85/0.81 tff(k17_cat_2_type, type, (
% 0.85/0.81 k17_cat_2: ( $i * $i ) > $i)).
% 0.85/0.81 tff(k9_isocat_2_type, type, (
% 0.85/0.81 k9_isocat_2: ( $i * $i ) > $i)).
% 0.85/0.81 tff(1,plain,
% 0.85/0.81 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(2,plain,
% 0.85/0.81 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.85/0.81 tff(3,plain,
% 0.85/0.81 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(4,plain,
% 0.85/0.81 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[3])).
% 0.85/0.81 tff(5,plain,
% 0.85/0.81 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(6,plain,
% 0.85/0.81 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[5])).
% 0.85/0.81 tff(7,plain,
% 0.85/0.81 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/0.81 inference(transitivity,[status(thm)],[6, 4])).
% 0.85/0.81 tff(8,plain,
% 0.85/0.81 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(9,plain,
% 0.85/0.81 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[8])).
% 0.85/0.81 tff(10,plain,
% 0.85/0.81 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.81 inference(rewrite,[status(thm)],[])).
% 0.85/0.81 tff(11,plain,
% 0.85/0.81 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) <=> ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))), (![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) <=> ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), rewrite(((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(12,plain,
% 0.85/0.81 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[11])).
% 0.85/0.81 tff(13,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_isocat_2')).
% 0.85/0.81 tff(14,plain,
% 0.85/0.81 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.85/0.81 tff(15,plain,
% 0.85/0.81 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.85/0.81 tff(16,plain,(
% 0.85/0.81 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.81 inference(skolemize,[status(sab)],[15])).
% 0.85/0.81 tff(17,plain,
% 0.85/0.81 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.85/0.82 tff(18,plain,
% 0.85/0.82 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.85/0.82 tff(19,plain,
% 0.85/0.82 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.85/0.82 tff(20,plain,
% 0.85/0.82 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(21,plain,
% 0.85/0.82 (((v2_cat_1(B!1) & l1_cat_1(B!1)) & (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))) <=> (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(22,plain,
% 0.85/0.82 (((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))) <=> (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(23,plain,
% 0.85/0.82 (((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))) <=> (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(24,plain,
% 0.85/0.82 ((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) <=> (v2_cat_1(C!2) & l1_cat_1(C!2))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(25,plain,
% 0.85/0.82 (((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) & ((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))) <=> ((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[24, 23])).
% 0.85/0.82 tff(26,plain,
% 0.85/0.82 (((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) & ((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))) <=> (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(transitivity,[status(thm)],[25, 22])).
% 0.85/0.82 tff(27,plain,
% 0.85/0.82 ((~(~(v2_cat_1(B!1) & l1_cat_1(B!1)))) <=> (v2_cat_1(B!1) & l1_cat_1(B!1))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(28,plain,
% 0.85/0.82 (((~(~(v2_cat_1(B!1) & l1_cat_1(B!1)))) & ((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) & ((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))))) <=> ((v2_cat_1(B!1) & l1_cat_1(B!1)) & (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[27, 26])).
% 0.85/0.82 tff(29,plain,
% 0.85/0.82 (((~(~(v2_cat_1(B!1) & l1_cat_1(B!1)))) & ((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) & ((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))))) <=> (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(transitivity,[status(thm)],[28, 21])).
% 0.85/0.82 tff(30,plain,
% 0.85/0.82 ((~(~(v2_cat_1(A!0) & l1_cat_1(A!0)))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(31,plain,
% 0.85/0.82 (((~(~(v2_cat_1(A!0) & l1_cat_1(A!0)))) & ((~(~(v2_cat_1(B!1) & l1_cat_1(B!1)))) & ((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) & ((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))))) <=> ((v2_cat_1(A!0) & l1_cat_1(A!0)) & (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[30, 29])).
% 0.85/0.82 tff(32,plain,
% 0.85/0.82 (((~(~(v2_cat_1(A!0) & l1_cat_1(A!0)))) & ((~(~(v2_cat_1(B!1) & l1_cat_1(B!1)))) & ((~(~(v2_cat_1(C!2) & l1_cat_1(C!2)))) & ((~(~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)))) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))))),
% 0.85/0.82 inference(transitivity,[status(thm)],[31, 20])).
% 0.85/0.82 tff(33,plain,
% 0.85/0.82 ((~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C)))))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(34,plain,
% 0.85/0.82 ((~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => ![E: $i] : (m2_cat_1(E, A, k11_cat_2(B, C)) => (r2_nattra_1(A, k11_cat_2(B, C), D, E) => (r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E)))))))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C)))))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(35,axiom,(~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => ![E: $i] : (m2_cat_1(E, A, k11_cat_2(B, C)) => (r2_nattra_1(A, k11_cat_2(B, C), D, E) => (r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t38_isocat_2')).
% 0.85/0.82 tff(36,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.85/0.82 tff(37,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.85/0.82 tff(38,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.85/0.82 tff(39,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.85/0.82 tff(40,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.85/0.82 tff(41,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.85/0.82 tff(42,plain,
% 0.85/0.82 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)) | (~m2_cat_1(E, A, k11_cat_2(B, C))))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.85/0.82 tff(43,plain,
% 0.85/0.82 (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.85/0.82 tff(44,plain,
% 0.85/0.82 (l1_cat_1(A!0)),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(45,plain,
% 0.85/0.82 (v2_cat_1(A!0)),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(46,plain,
% 0.85/0.82 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(47,plain,
% 0.85/0.82 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(48,plain,
% 0.85/0.82 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.85/0.82 tff(49,plain,
% 0.85/0.82 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[48, 45, 44, 19])).
% 0.85/0.82 tff(50,plain,
% 0.85/0.82 (l1_cat_1(B!1)),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(51,plain,
% 0.85/0.82 (v2_cat_1(B!1)),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(52,plain,
% 0.85/0.82 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(53,plain,
% 0.85/0.82 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C))))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(54,plain,
% 0.85/0.82 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.85/0.82 tff(55,plain,
% 0.85/0.82 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[54, 51, 50, 49])).
% 0.85/0.82 tff(56,plain,
% 0.85/0.82 (l1_cat_1(C!2)),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(57,plain,
% 0.85/0.82 (v2_cat_1(C!2)),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(58,plain,
% 0.85/0.82 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2)))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2)))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(59,plain,
% 0.85/0.82 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2)))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(60,plain,
% 0.85/0.82 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.85/0.82 tff(61,plain,
% 0.85/0.82 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[60, 57, 56, 55])).
% 0.85/0.82 tff(62,plain,
% 0.85/0.82 (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))))),
% 0.85/0.82 inference(and_elim,[status(thm)],[43])).
% 0.85/0.82 tff(63,plain,
% 0.85/0.82 (m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))),
% 0.85/0.82 inference(or_elim,[status(thm)],[62])).
% 0.85/0.82 tff(64,plain,
% 0.85/0.82 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(65,plain,
% 0.85/0.82 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(66,plain,
% 0.85/0.82 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.85/0.82 tff(67,plain,
% 0.85/0.82 (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[66, 63, 61])).
% 0.85/0.82 tff(68,plain,
% 0.85/0.82 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, E!4)),
% 0.85/0.82 inference(symmetry,[status(thm)],[67])).
% 0.85/0.82 tff(69,plain,
% 0.85/0.82 (^[A: $i, B: $i] : refl(((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(70,plain,
% 0.85/0.82 (![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[69])).
% 0.85/0.82 tff(71,plain,
% 0.85/0.82 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(72,plain,
% 0.85/0.82 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[71])).
% 0.85/0.82 tff(73,plain,
% 0.85/0.83 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(74,plain,
% 0.85/0.83 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(75,plain,
% 0.85/0.83 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[74])).
% 0.85/0.83 tff(76,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_isocat_2')).
% 0.85/0.83 tff(77,plain,
% 0.85/0.83 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.85/0.83 tff(78,plain,
% 0.85/0.83 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.85/0.83 tff(79,plain,(
% 0.85/0.83 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.85/0.83 inference(skolemize,[status(sab)],[78])).
% 0.85/0.83 tff(80,plain,
% 0.85/0.83 (![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.85/0.83 tff(81,plain,
% 0.85/0.83 (![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.85/0.83 tff(82,plain,
% 0.85/0.83 (((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))) <=> ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(83,plain,
% 0.85/0.83 (((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(84,plain,
% 0.85/0.83 (((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2))))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[83])).
% 0.85/0.83 tff(85,plain,
% 0.85/0.83 (((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))),
% 0.85/0.83 inference(transitivity,[status(thm)],[84, 82])).
% 0.85/0.83 tff(86,plain,
% 0.85/0.83 ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(87,plain,
% 0.85/0.83 ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.85/0.83 tff(88,plain,
% 0.85/0.83 (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[87, 51, 50, 57, 56, 81])).
% 0.85/0.83 tff(89,plain,
% 0.85/0.83 (k16_cat_2(B!1, C!2) = k8_isocat_2(B!1, C!2)),
% 0.85/0.83 inference(symmetry,[status(thm)],[88])).
% 0.85/0.83 tff(90,plain,
% 0.85/0.83 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[89])).
% 0.85/0.83 tff(91,plain,
% 0.85/0.83 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, E!4)),
% 0.85/0.83 inference(transitivity,[status(thm)],[90, 68])).
% 0.85/0.83 tff(92,plain,
% 0.85/0.83 (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))),
% 0.85/0.83 inference(and_elim,[status(thm)],[43])).
% 0.85/0.83 tff(93,plain,
% 0.85/0.83 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(94,plain,
% 0.85/0.83 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(95,plain,
% 0.85/0.83 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.85/0.83 tff(96,plain,
% 0.85/0.83 (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[95, 92, 61])).
% 0.85/0.83 tff(97,plain,
% 0.85/0.83 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, D!3)),
% 0.85/0.83 inference(symmetry,[status(thm)],[96])).
% 0.85/0.83 tff(98,plain,
% 0.85/0.83 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[89])).
% 0.85/0.83 tff(99,plain,
% 0.85/0.83 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, D!3)),
% 0.85/0.83 inference(transitivity,[status(thm)],[98, 97])).
% 0.85/0.83 tff(100,plain,
% 0.85/0.83 (r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))) <=> r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[99, 91])).
% 0.85/0.83 tff(101,plain,
% 0.85/0.83 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(102,plain,
% 0.85/0.83 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[101])).
% 0.85/0.83 tff(103,plain,
% 0.85/0.83 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(104,plain,
% 0.85/0.83 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[103])).
% 0.85/0.83 tff(105,plain,
% 0.85/0.83 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.83 inference(transitivity,[status(thm)],[104, 102])).
% 0.85/0.83 tff(106,plain,
% 0.85/0.83 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))) <=> ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))), (![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))) <=> ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(107,plain,
% 0.85/0.83 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[106])).
% 0.85/0.83 tff(108,plain,
% 0.85/0.83 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(109,plain,
% 0.85/0.83 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(quant_intro(proof_bind(^[G: $i] : trans(monotonicity(rewrite(((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))) <=> ((~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))), ((m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> (m2_cat_1(G, B, C) => ((~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))), rewrite((m2_cat_1(G, B, C) => ((~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))), ((m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), (![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))), ((m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))) <=> (m2_cat_1(F, B, C) => ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), rewrite((m2_cat_1(F, B, C) => ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))) <=> ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))), ((m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))) <=> ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), (![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))) <=> ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), ((m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))) <=> (m2_cat_1(E, A, B) => ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), rewrite((m2_cat_1(E, A, B) => ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))) <=> ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), ((m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))) <=> ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), (![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))) <=> ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), ((m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))) <=> (m2_cat_1(D, A, B) => ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), rewrite((m2_cat_1(D, A, B) => ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))) <=> ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), ((m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))) <=> ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), (![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))) <=> ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))) <=> ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), rewrite(((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(110,plain,
% 0.85/0.83 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[109])).
% 0.85/0.83 tff(111,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t27_isocat_1')).
% 0.85/0.83 tff(112,plain,
% 0.85/0.83 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.85/0.83 tff(113,plain,
% 0.85/0.83 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.85/0.83 tff(114,plain,(
% 0.85/0.83 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.85/0.83 inference(skolemize,[status(sab)],[113])).
% 0.85/0.83 tff(115,plain,
% 0.85/0.83 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.85/0.83 tff(116,plain,
% 0.85/0.83 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.85/0.83 tff(117,plain,
% 0.85/0.83 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(118,plain,
% 0.85/0.84 (((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(119,plain,
% 0.85/0.84 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[118])).
% 0.85/0.84 tff(120,plain,
% 0.85/0.84 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))),
% 0.85/0.84 inference(transitivity,[status(thm)],[119, 117])).
% 0.85/0.84 tff(121,plain,
% 0.85/0.84 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(122,plain,
% 0.85/0.84 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.85/0.84 tff(123,plain,
% 0.85/0.84 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[122, 45, 44, 116])).
% 0.85/0.84 tff(124,plain,
% 0.85/0.84 (^[A: $i, B: $i] : refl(((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(125,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[124])).
% 0.85/0.84 tff(126,plain,
% 0.85/0.84 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), rewrite((v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))) <=> (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(127,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[126])).
% 0.85/0.84 tff(128,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(129,plain,
% 0.85/0.84 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(130,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[129])).
% 0.85/0.84 tff(131,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k11_cat_2')).
% 0.85/0.84 tff(132,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.85/0.84 tff(133,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.85/0.84 tff(134,plain,(
% 0.85/0.84 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.85/0.84 inference(skolemize,[status(sab)],[133])).
% 0.85/0.84 tff(135,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.85/0.84 tff(136,plain,
% 0.85/0.84 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.85/0.84 tff(137,plain,
% 0.85/0.84 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(138,plain,
% 0.85/0.84 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(139,plain,
% 0.85/0.84 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.85/0.84 tff(140,plain,
% 0.85/0.84 (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[139, 51, 50, 57, 56, 136])).
% 0.85/0.84 tff(141,plain,
% 0.85/0.84 (((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))) | l1_cat_1(k11_cat_2(B!1, C!2))),
% 0.85/0.84 inference(tautology,[status(thm)],[])).
% 0.85/0.84 tff(142,plain,
% 0.85/0.84 (l1_cat_1(k11_cat_2(B!1, C!2))),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.85/0.84 tff(143,plain,
% 0.85/0.84 (((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))) | v2_cat_1(k11_cat_2(B!1, C!2))),
% 0.85/0.84 inference(tautology,[status(thm)],[])).
% 0.85/0.84 tff(144,plain,
% 0.85/0.84 (v2_cat_1(k11_cat_2(B!1, C!2))),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.85/0.84 tff(145,plain,
% 0.85/0.84 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(146,plain,
% 0.85/0.84 (((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(147,plain,
% 0.85/0.84 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[146])).
% 0.85/0.84 tff(148,plain,
% 0.85/0.84 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))),
% 0.85/0.84 inference(transitivity,[status(thm)],[147, 145])).
% 0.85/0.84 tff(149,plain,
% 0.85/0.84 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(150,plain,
% 0.85/0.84 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.85/0.84 tff(151,plain,
% 0.85/0.84 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[150, 144, 142, 123])).
% 0.85/0.84 tff(152,plain,
% 0.85/0.84 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(153,plain,
% 0.85/0.84 (((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))) <=> ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(154,plain,
% 0.85/0.84 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[153])).
% 0.85/0.84 tff(155,plain,
% 0.85/0.84 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.85/0.85 inference(transitivity,[status(thm)],[154, 152])).
% 0.85/0.85 tff(156,plain,
% 0.85/0.85 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(157,plain,
% 0.85/0.85 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.85/0.85 tff(158,plain,
% 0.85/0.85 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[157, 51, 50, 151])).
% 0.85/0.85 tff(159,plain,
% 0.85/0.85 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(160,plain,
% 0.85/0.85 (((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) <=> ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(161,plain,
% 0.85/0.85 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.85/0.85 inference(monotonicity,[status(thm)],[160])).
% 0.85/0.85 tff(162,plain,
% 0.85/0.85 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.85/0.85 inference(transitivity,[status(thm)],[161, 159])).
% 0.85/0.85 tff(163,plain,
% 0.85/0.85 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(164,plain,
% 0.85/0.85 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.85/0.85 tff(165,plain,
% 0.85/0.85 (![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[164, 92, 158])).
% 0.85/0.85 tff(166,plain,
% 0.85/0.85 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(167,plain,
% 0.85/0.85 (((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) <=> ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(168,plain,
% 0.85/0.85 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))))),
% 0.85/0.85 inference(monotonicity,[status(thm)],[167])).
% 0.85/0.85 tff(169,plain,
% 0.85/0.85 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.85/0.86 inference(transitivity,[status(thm)],[168, 166])).
% 0.85/0.86 tff(170,plain,
% 0.85/0.86 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(171,plain,
% 0.85/0.86 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.85/0.86 tff(172,plain,
% 0.85/0.86 (![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[171, 63, 165])).
% 0.85/0.86 tff(173,plain,
% 0.85/0.86 (^[A: $i, B: $i] : refl((m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(174,plain,
% 0.85/0.86 (![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[173])).
% 0.85/0.86 tff(175,plain,
% 0.85/0.86 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(176,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[175])).
% 0.85/0.86 tff(177,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(178,plain,
% 0.85/0.86 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(179,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[178])).
% 0.85/0.86 tff(180,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k16_cat_2')).
% 0.85/0.86 tff(181,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.85/0.86 tff(182,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.85/0.86 tff(183,plain,(
% 0.85/0.86 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(skolemize,[status(sab)],[182])).
% 0.85/0.86 tff(184,plain,
% 0.85/0.86 (![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.85/0.86 tff(185,plain,
% 0.85/0.86 (![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[184, 174])).
% 0.85/0.86 tff(186,plain,
% 0.85/0.86 (((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(187,plain,
% 0.85/0.86 ((m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(188,plain,
% 0.85/0.86 (((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/0.86 inference(monotonicity,[status(thm)],[187])).
% 0.85/0.86 tff(189,plain,
% 0.85/0.86 (((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/0.86 inference(transitivity,[status(thm)],[188, 186])).
% 0.85/0.86 tff(190,plain,
% 0.85/0.86 ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(191,plain,
% 0.85/0.86 ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.85/0.86 tff(192,plain,
% 0.85/0.86 (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[191, 51, 50, 57, 56, 185])).
% 0.85/0.86 tff(193,plain,
% 0.85/0.86 (((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | ((~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) <=> ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(194,plain,
% 0.85/0.86 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | ((~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(195,plain,
% 0.85/0.86 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.85/0.86 tff(196,plain,
% 0.85/0.86 (![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[195, 192, 172])).
% 0.85/0.86 tff(197,plain,
% 0.85/0.86 (^[A: $i, B: $i] : refl((m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(198,plain,
% 0.85/0.86 (![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[197])).
% 0.85/0.86 tff(199,plain,
% 0.85/0.86 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(200,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[199])).
% 0.85/0.86 tff(201,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(202,plain,
% 0.85/0.86 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(203,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[202])).
% 0.85/0.86 tff(204,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_isocat_2')).
% 0.85/0.86 tff(205,plain,
% 0.85/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.97/0.86 tff(206,plain,
% 0.97/0.86 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.97/0.86 tff(207,plain,(
% 0.97/0.86 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.97/0.86 inference(skolemize,[status(sab)],[206])).
% 0.97/0.86 tff(208,plain,
% 0.97/0.86 (![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.97/0.86 tff(209,plain,
% 0.97/0.86 (![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[208, 198])).
% 0.97/0.86 tff(210,plain,
% 0.97/0.86 (((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(211,plain,
% 0.97/0.86 ((m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(212,plain,
% 0.97/0.86 (((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.97/0.86 inference(monotonicity,[status(thm)],[211])).
% 0.97/0.86 tff(213,plain,
% 0.97/0.86 (((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.97/0.86 inference(transitivity,[status(thm)],[212, 210])).
% 0.97/0.86 tff(214,plain,
% 0.97/0.86 ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.97/0.86 inference(quant_inst,[status(thm)],[])).
% 0.97/0.86 tff(215,plain,
% 0.97/0.86 ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.97/0.86 tff(216,plain,
% 0.97/0.86 (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.97/0.86 inference(unit_resolution,[status(thm)],[215, 51, 50, 57, 56, 209])).
% 0.97/0.86 tff(217,plain,
% 0.97/0.86 (^[A: $i, B: $i, C: $i, D: $i] : refl((r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) <=> (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))),
% 0.97/0.86 inference(bind,[status(th)],[])).
% 0.97/0.86 tff(218,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.97/0.86 inference(quant_intro,[status(thm)],[217])).
% 0.97/0.86 tff(219,plain,
% 0.97/0.86 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) <=> (~((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) <=> (~(~((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))))), rewrite((~(~((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))) <=> ((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) <=> ((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> (((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) | r2_nattra_1(A, B, C, C)))), rewrite((((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) | r2_nattra_1(A, B, C, C)) <=> (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))))),
% 0.97/0.86 inference(bind,[status(th)],[])).
% 0.97/0.86 tff(220,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> ![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.97/0.86 inference(quant_intro,[status(thm)],[219])).
% 0.97/0.86 tff(221,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(222,plain,
% 0.97/0.86 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) & m2_cat_1(C, A, B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) & m2_cat_1(C, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B)))), ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))), ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)))), (((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))), (((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))))),
% 0.97/0.86 inference(bind,[status(th)],[])).
% 0.97/0.86 tff(223,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.97/0.86 inference(quant_intro,[status(thm)],[222])).
% 0.97/0.86 tff(224,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r2_nattra_1')).
% 0.97/0.86 tff(225,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.97/0.86 tff(226,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.97/0.86 tff(227,plain,(
% 0.97/0.86 ![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.97/0.86 inference(skolemize,[status(sab)],[226])).
% 0.97/0.86 tff(228,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.97/0.86 tff(229,plain,
% 0.97/0.86 (![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.97/0.86 inference(modus_ponens,[status(thm)],[228, 218])).
% 0.97/0.86 tff(230,plain,
% 0.97/0.86 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(231,plain,
% 0.97/0.86 ((r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))) <=> ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(232,plain,
% 0.97/0.86 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))))),
% 0.97/0.86 inference(monotonicity,[status(thm)],[231])).
% 0.97/0.86 tff(233,plain,
% 0.97/0.86 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.97/0.86 inference(transitivity,[status(thm)],[232, 230])).
% 0.97/0.86 tff(234,plain,
% 0.97/0.86 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.97/0.86 inference(quant_inst,[status(thm)],[])).
% 0.97/0.86 tff(235,plain,
% 0.97/0.86 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.97/0.87 tff(236,plain,
% 0.97/0.87 (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[235, 51, 50, 229, 144, 142, 216, 192])).
% 0.97/0.87 tff(237,plain,
% 0.97/0.87 (r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)),
% 0.97/0.87 inference(or_elim,[status(thm)],[62])).
% 0.97/0.87 tff(238,plain,
% 0.97/0.87 (((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))))) <=> ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(239,plain,
% 0.97/0.87 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))))),
% 0.97/0.87 inference(quant_inst,[status(thm)],[])).
% 0.97/0.87 tff(240,plain,
% 0.97/0.87 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.97/0.87 tff(241,plain,
% 0.97/0.87 (r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[240, 237, 192, 236, 196])).
% 0.97/0.87 tff(242,plain,
% 0.97/0.87 (r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[241, 100])).
% 0.97/0.87 tff(243,plain,
% 0.97/0.87 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(244,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[243])).
% 0.97/0.87 tff(245,plain,
% 0.97/0.87 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(246,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[245])).
% 0.97/0.87 tff(247,plain,
% 0.97/0.87 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(248,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[247])).
% 0.97/0.87 tff(249,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.97/0.87 inference(transitivity,[status(thm)],[248, 246])).
% 0.97/0.87 tff(250,plain,
% 0.97/0.87 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(251,plain,
% 0.97/0.87 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[250])).
% 0.97/0.87 tff(252,plain,
% 0.97/0.87 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(253,plain,
% 0.97/0.87 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) <=> ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))), (![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) <=> ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), rewrite(((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(254,plain,
% 0.97/0.87 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[253])).
% 0.97/0.87 tff(255,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_isocat_2')).
% 0.97/0.87 tff(256,plain,
% 0.97/0.87 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.97/0.87 tff(257,plain,
% 0.97/0.87 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.97/0.87 tff(258,plain,(
% 0.97/0.87 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(skolemize,[status(sab)],[257])).
% 0.97/0.87 tff(259,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[258, 251])).
% 0.97/0.87 tff(260,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[259, 249])).
% 0.97/0.87 tff(261,plain,
% 0.97/0.87 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[260, 244])).
% 0.97/0.87 tff(262,plain,
% 0.97/0.87 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(263,plain,
% 0.97/0.87 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.97/0.87 inference(quant_inst,[status(thm)],[])).
% 0.97/0.87 tff(264,plain,
% 0.97/0.87 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.97/0.87 tff(265,plain,
% 0.97/0.87 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[264, 45, 44, 261])).
% 0.97/0.87 tff(266,plain,
% 0.97/0.87 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(267,plain,
% 0.97/0.87 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C))))))),
% 0.97/0.87 inference(quant_inst,[status(thm)],[])).
% 0.97/0.87 tff(268,plain,
% 0.97/0.87 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.97/0.87 tff(269,plain,
% 0.97/0.87 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[268, 51, 50, 265])).
% 0.97/0.87 tff(270,plain,
% 0.97/0.87 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2)))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2)))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(271,plain,
% 0.97/0.87 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2)))))),
% 0.97/0.87 inference(quant_inst,[status(thm)],[])).
% 0.97/0.87 tff(272,plain,
% 0.97/0.87 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.97/0.87 tff(273,plain,
% 0.97/0.87 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[272, 57, 56, 269])).
% 0.97/0.87 tff(274,plain,
% 0.97/0.87 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(275,plain,
% 0.97/0.87 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))))),
% 0.97/0.87 inference(quant_inst,[status(thm)],[])).
% 0.97/0.87 tff(276,plain,
% 0.97/0.87 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2)))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.97/0.87 tff(277,plain,
% 0.97/0.87 (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[276, 63, 273])).
% 0.97/0.87 tff(278,plain,
% 0.97/0.87 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, E!4)),
% 0.97/0.87 inference(symmetry,[status(thm)],[277])).
% 0.97/0.87 tff(279,plain,
% 0.97/0.87 (^[A: $i, B: $i] : refl(((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(280,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[279])).
% 0.97/0.87 tff(281,plain,
% 0.97/0.87 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(282,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[281])).
% 0.97/0.87 tff(283,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(284,plain,
% 0.97/0.87 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(285,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[284])).
% 0.97/0.87 tff(286,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k9_isocat_2')).
% 0.97/0.87 tff(287,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.97/0.87 tff(288,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.97/0.87 tff(289,plain,(
% 0.97/0.87 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.97/0.87 inference(skolemize,[status(sab)],[288])).
% 0.97/0.87 tff(290,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[289, 282])).
% 0.97/0.87 tff(291,plain,
% 0.97/0.87 (![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[290, 280])).
% 0.97/0.87 tff(292,plain,
% 0.97/0.87 (((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))) <=> ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(293,plain,
% 0.97/0.87 (((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(294,plain,
% 0.97/0.87 (((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2))))),
% 0.97/0.87 inference(monotonicity,[status(thm)],[293])).
% 0.97/0.87 tff(295,plain,
% 0.97/0.87 (((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))),
% 0.97/0.88 inference(transitivity,[status(thm)],[294, 292])).
% 0.97/0.88 tff(296,plain,
% 0.97/0.88 ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.97/0.88 inference(quant_inst,[status(thm)],[])).
% 0.97/0.88 tff(297,plain,
% 0.97/0.88 ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2))),
% 0.97/0.88 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.97/0.88 tff(298,plain,
% 0.97/0.88 (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[297, 51, 50, 57, 56, 291])).
% 0.97/0.88 tff(299,plain,
% 0.97/0.88 (k17_cat_2(B!1, C!2) = k9_isocat_2(B!1, C!2)),
% 0.97/0.88 inference(symmetry,[status(thm)],[298])).
% 0.97/0.88 tff(300,plain,
% 0.97/0.88 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))),
% 0.97/0.88 inference(monotonicity,[status(thm)],[299])).
% 0.97/0.88 tff(301,plain,
% 0.97/0.88 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, E!4)),
% 0.97/0.88 inference(transitivity,[status(thm)],[300, 278])).
% 0.97/0.88 tff(302,plain,
% 0.97/0.88 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(303,plain,
% 0.97/0.88 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))))),
% 0.97/0.88 inference(quant_inst,[status(thm)],[])).
% 0.97/0.88 tff(304,plain,
% 0.97/0.88 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2)))),
% 0.97/0.88 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.97/0.88 tff(305,plain,
% 0.97/0.88 (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[304, 92, 273])).
% 0.97/0.88 tff(306,plain,
% 0.97/0.88 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, D!3)),
% 0.97/0.88 inference(symmetry,[status(thm)],[305])).
% 0.97/0.88 tff(307,plain,
% 0.97/0.88 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))),
% 0.97/0.88 inference(monotonicity,[status(thm)],[299])).
% 0.97/0.88 tff(308,plain,
% 0.97/0.88 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, D!3)),
% 0.97/0.88 inference(transitivity,[status(thm)],[307, 306])).
% 0.97/0.88 tff(309,plain,
% 0.97/0.88 (r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))) <=> r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))),
% 0.97/0.88 inference(monotonicity,[status(thm)],[308, 301])).
% 0.97/0.88 tff(310,plain,
% 0.97/0.88 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(311,plain,
% 0.97/0.88 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(312,plain,
% 0.97/0.88 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))))),
% 0.97/0.88 inference(monotonicity,[status(thm)],[311])).
% 0.97/0.88 tff(313,plain,
% 0.97/0.88 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.97/0.88 inference(transitivity,[status(thm)],[312, 310])).
% 0.97/0.88 tff(314,plain,
% 0.97/0.88 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.97/0.88 inference(quant_inst,[status(thm)],[])).
% 0.97/0.88 tff(315,plain,
% 0.97/0.88 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.97/0.88 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.97/0.88 tff(316,plain,
% 0.97/0.88 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[315, 57, 56, 151])).
% 0.97/0.88 tff(317,plain,
% 0.97/0.88 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(318,plain,
% 0.97/0.88 (((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) <=> ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(319,plain,
% 0.97/0.89 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.97/0.89 inference(monotonicity,[status(thm)],[318])).
% 0.97/0.89 tff(320,plain,
% 0.97/0.89 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.97/0.89 inference(transitivity,[status(thm)],[319, 317])).
% 0.97/0.89 tff(321,plain,
% 0.97/0.89 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.97/0.89 inference(quant_inst,[status(thm)],[])).
% 0.97/0.89 tff(322,plain,
% 0.97/0.89 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.97/0.89 tff(323,plain,
% 0.97/0.89 (![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))),
% 0.97/0.89 inference(unit_resolution,[status(thm)],[322, 92, 316])).
% 0.97/0.89 tff(324,plain,
% 0.97/0.89 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(325,plain,
% 0.97/0.89 (((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) <=> ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(326,plain,
% 0.97/0.89 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))))),
% 0.97/0.89 inference(monotonicity,[status(thm)],[325])).
% 0.97/0.89 tff(327,plain,
% 0.97/0.89 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.97/0.89 inference(transitivity,[status(thm)],[326, 324])).
% 0.97/0.89 tff(328,plain,
% 0.97/0.89 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.97/0.89 inference(quant_inst,[status(thm)],[])).
% 0.97/0.89 tff(329,plain,
% 0.97/0.89 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.97/0.89 tff(330,plain,
% 0.97/0.89 (![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.97/0.89 inference(unit_resolution,[status(thm)],[329, 63, 323])).
% 0.97/0.89 tff(331,plain,
% 0.97/0.89 (^[A: $i, B: $i] : refl((m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(332,plain,
% 0.97/0.89 (![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[331])).
% 0.97/0.89 tff(333,plain,
% 0.97/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(334,plain,
% 0.97/0.89 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[333])).
% 0.97/0.89 tff(335,plain,
% 0.97/0.89 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(336,plain,
% 0.97/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(337,plain,
% 0.97/0.89 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[336])).
% 0.97/0.89 tff(338,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k17_cat_2')).
% 0.97/0.89 tff(339,plain,
% 0.97/0.89 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.97/0.89 tff(340,plain,
% 0.97/0.89 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[339, 335])).
% 0.97/0.89 tff(341,plain,(
% 0.97/0.89 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.97/0.89 inference(skolemize,[status(sab)],[340])).
% 0.97/0.89 tff(342,plain,
% 0.97/0.89 (![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[341, 334])).
% 0.97/0.89 tff(343,plain,
% 0.97/0.89 (![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[342, 332])).
% 0.97/0.89 tff(344,plain,
% 0.97/0.89 (((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(345,plain,
% 0.97/0.89 ((m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(346,plain,
% 0.97/0.89 (((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.97/0.89 inference(monotonicity,[status(thm)],[345])).
% 0.97/0.89 tff(347,plain,
% 0.97/0.89 (((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.97/0.89 inference(transitivity,[status(thm)],[346, 344])).
% 0.97/0.89 tff(348,plain,
% 0.97/0.89 ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.97/0.89 inference(quant_inst,[status(thm)],[])).
% 0.97/0.89 tff(349,plain,
% 0.97/0.89 ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.97/0.89 tff(350,plain,
% 0.97/0.89 (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 0.97/0.89 inference(unit_resolution,[status(thm)],[349, 51, 50, 57, 56, 343])).
% 0.97/0.89 tff(351,plain,
% 0.97/0.89 (((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | ((~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) <=> ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(352,plain,
% 0.97/0.89 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | ((~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 1.01/0.89 inference(quant_inst,[status(thm)],[])).
% 1.01/0.89 tff(353,plain,
% 1.01/0.89 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.01/0.89 tff(354,plain,
% 1.01/0.89 (![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[353, 350, 330])).
% 1.01/0.89 tff(355,plain,
% 1.01/0.89 (^[A: $i, B: $i] : refl((m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(356,plain,
% 1.01/0.89 (![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[355])).
% 1.01/0.89 tff(357,plain,
% 1.01/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(358,plain,
% 1.01/0.89 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[357])).
% 1.01/0.90 tff(359,plain,
% 1.01/0.90 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(360,plain,
% 1.01/0.90 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))))),
% 1.01/0.90 inference(bind,[status(th)],[])).
% 1.01/0.90 tff(361,plain,
% 1.01/0.90 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 1.01/0.90 inference(quant_intro,[status(thm)],[360])).
% 1.01/0.90 tff(362,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k9_isocat_2')).
% 1.01/0.90 tff(363,plain,
% 1.01/0.90 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.01/0.90 tff(364,plain,
% 1.01/0.90 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[363, 359])).
% 1.01/0.90 tff(365,plain,(
% 1.01/0.90 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 1.01/0.90 inference(skolemize,[status(sab)],[364])).
% 1.01/0.90 tff(366,plain,
% 1.01/0.90 (![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[365, 358])).
% 1.01/0.90 tff(367,plain,
% 1.01/0.90 (![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[366, 356])).
% 1.01/0.90 tff(368,plain,
% 1.01/0.90 (((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(369,plain,
% 1.01/0.90 ((m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(370,plain,
% 1.01/0.90 (((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 1.01/0.90 inference(monotonicity,[status(thm)],[369])).
% 1.01/0.90 tff(371,plain,
% 1.01/0.90 (((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 1.01/0.90 inference(transitivity,[status(thm)],[370, 368])).
% 1.01/0.90 tff(372,plain,
% 1.01/0.90 ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 1.01/0.90 inference(quant_inst,[status(thm)],[])).
% 1.01/0.90 tff(373,plain,
% 1.01/0.90 ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.01/0.90 tff(374,plain,
% 1.01/0.90 (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[373, 51, 50, 57, 56, 367])).
% 1.01/0.90 tff(375,plain,
% 1.01/0.90 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(376,plain,
% 1.01/0.90 ((r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(377,plain,
% 1.01/0.90 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))))),
% 1.01/0.90 inference(monotonicity,[status(thm)],[376])).
% 1.01/0.90 tff(378,plain,
% 1.01/0.90 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 1.01/0.90 inference(transitivity,[status(thm)],[377, 375])).
% 1.01/0.90 tff(379,plain,
% 1.01/0.90 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 1.01/0.90 inference(quant_inst,[status(thm)],[])).
% 1.01/0.90 tff(380,plain,
% 1.01/0.90 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[379, 378])).
% 1.01/0.90 tff(381,plain,
% 1.01/0.90 (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[380, 57, 56, 229, 144, 142, 374, 350])).
% 1.01/0.90 tff(382,plain,
% 1.01/0.90 (((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))))) <=> ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(383,plain,
% 1.01/0.90 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))))),
% 1.01/0.90 inference(quant_inst,[status(thm)],[])).
% 1.01/0.90 tff(384,plain,
% 1.01/0.90 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.01/0.90 tff(385,plain,
% 1.01/0.90 (r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)))),
% 1.01/0.90 inference(unit_resolution,[status(thm)],[384, 237, 350, 381, 354])).
% 1.01/0.90 tff(386,plain,
% 1.01/0.90 (r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))),
% 1.01/0.90 inference(modus_ponens,[status(thm)],[385, 309])).
% 1.01/0.90 tff(387,plain,
% 1.01/0.90 ((~(~((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))))) <=> ((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(388,plain,
% 1.01/0.90 ((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) <=> (~((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))))),
% 1.01/0.90 inference(rewrite,[status(thm)],[])).
% 1.01/0.90 tff(389,plain,
% 1.01/0.90 ((~(r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))) <=> (~(~((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))))))),
% 1.01/0.90 inference(monotonicity,[status(thm)],[388])).
% 1.01/0.90 tff(390,plain,
% 1.01/0.90 ((~(r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))) <=> ((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))))),
% 1.01/0.91 inference(transitivity,[status(thm)],[389, 387])).
% 1.01/0.91 tff(391,plain,
% 1.01/0.91 (~(r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))),
% 1.01/0.91 inference(or_elim,[status(thm)],[62])).
% 1.01/0.91 tff(392,plain,
% 1.01/0.91 ((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))),
% 1.01/0.91 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.01/0.91 tff(393,plain,
% 1.01/0.91 ($false),
% 1.01/0.91 inference(unit_resolution,[status(thm)],[392, 386, 242])).
% 1.01/0.91 % SZS output end Proof
%------------------------------------------------------------------------------