TSTP Solution File: CAT033+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT033+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 17:30:01 EDT 2022
% Result : Theorem 6.75s 4.52s
% Output : Proof 6.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT033+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 : n023.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 08:09:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 6.75/4.52 % SZS status Theorem
% 6.75/4.52 % SZS output start Proof
% 6.75/4.52 tff(r1_tarski_type, type, (
% 6.75/4.52 r1_tarski: ( $i * $i ) > $o)).
% 6.75/4.52 tff(k17_ens_1_type, type, (
% 6.75/4.52 k17_ens_1: $i > $i)).
% 6.75/4.52 tff(tptp_fun_A_0_type, type, (
% 6.75/4.52 tptp_fun_A_0: $i)).
% 6.75/4.52 tff(m2_cat_1_type, type, (
% 6.75/4.52 m2_cat_1: ( $i * $i * $i ) > $o)).
% 6.75/4.52 tff(k12_ens_1_type, type, (
% 6.75/4.52 k12_ens_1: $i > $i)).
% 6.75/4.52 tff(k20_ens_1_type, type, (
% 6.75/4.52 k20_ens_1: ( $i * $i ) > $i)).
% 6.75/4.52 tff(tptp_fun_B_1_type, type, (
% 6.75/4.52 tptp_fun_B_1: $i)).
% 6.75/4.52 tff(k1_yoneda_1_type, type, (
% 6.75/4.52 k1_yoneda_1: $i > $i)).
% 6.75/4.52 tff(v2_cat_1_type, type, (
% 6.75/4.52 v2_cat_1: $i > $o)).
% 6.75/4.52 tff(l1_cat_1_type, type, (
% 6.75/4.52 l1_cat_1: $i > $o)).
% 6.75/4.52 tff(m1_subset_1_type, type, (
% 6.75/4.52 m1_subset_1: ( $i * $i ) > $o)).
% 6.75/4.52 tff(u1_cat_1_type, type, (
% 6.75/4.52 u1_cat_1: $i > $i)).
% 6.75/4.52 tff(v1_xboole_0_type, type, (
% 6.75/4.52 v1_xboole_0: $i > $o)).
% 6.75/4.52 tff(1,plain,
% 6.75/4.52 (^[A: $i] : refl(((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(2,plain,
% 6.75/4.52 (![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[1])).
% 6.75/4.52 tff(3,plain,
% 6.75/4.52 (^[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))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))), (((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(4,plain,
% 6.75/4.52 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[3])).
% 6.75/4.52 tff(5,plain,
% 6.75/4.52 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(6,plain,
% 6.75/4.52 (^[A: $i] : rewrite(((v2_cat_1(A) & l1_cat_1(A)) => (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(7,plain,
% 6.75/4.52 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[6])).
% 6.75/4.52 tff(8,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_yoneda_1')).
% 6.75/4.52 tff(9,plain,
% 6.75/4.52 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[8, 7])).
% 6.75/4.52 tff(10,plain,
% 6.75/4.52 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[9, 5])).
% 6.75/4.52 tff(11,plain,(
% 6.75/4.52 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 6.75/4.52 inference(skolemize,[status(sab)],[10])).
% 6.75/4.52 tff(12,plain,
% 6.75/4.52 (![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[11, 4])).
% 6.75/4.52 tff(13,plain,
% 6.75/4.52 (![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[12, 2])).
% 6.75/4.52 tff(14,plain,
% 6.75/4.52 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(15,plain,
% 6.75/4.52 ((~(~(v2_cat_1(A!0) & l1_cat_1(A!0)))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(16,plain,
% 6.75/4.52 (((~(~(v2_cat_1(A!0) & l1_cat_1(A!0)))) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))))) <=> ((v2_cat_1(A!0) & l1_cat_1(A!0)) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)))))),
% 6.75/4.52 inference(monotonicity,[status(thm)],[15])).
% 6.75/4.52 tff(17,plain,
% 6.75/4.52 (((~(~(v2_cat_1(A!0) & l1_cat_1(A!0)))) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)))))),
% 6.75/4.52 inference(transitivity,[status(thm)],[16, 14])).
% 6.75/4.52 tff(18,plain,
% 6.75/4.52 ((~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A)))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(19,plain,
% 6.75/4.52 ((~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : (m1_subset_1(B, u1_cat_1(A)) => m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A)))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(20,axiom,(~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : (m1_subset_1(B, u1_cat_1(A)) => m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_yoneda_1')).
% 6.75/4.52 tff(21,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[20, 19])).
% 6.75/4.52 tff(22,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[21, 18])).
% 6.75/4.52 tff(23,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[22, 18])).
% 6.75/4.52 tff(24,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[23, 18])).
% 6.75/4.52 tff(25,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[24, 18])).
% 6.75/4.52 tff(26,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[25, 18])).
% 6.75/4.52 tff(27,plain,
% 6.75/4.52 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[26, 18])).
% 6.75/4.52 tff(28,plain,
% 6.75/4.52 (v2_cat_1(A!0) & l1_cat_1(A!0) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[27, 17])).
% 6.75/4.52 tff(29,plain,
% 6.75/4.52 (l1_cat_1(A!0)),
% 6.75/4.52 inference(and_elim,[status(thm)],[28])).
% 6.75/4.52 tff(30,plain,
% 6.75/4.52 (v2_cat_1(A!0)),
% 6.75/4.52 inference(and_elim,[status(thm)],[28])).
% 6.75/4.52 tff(31,plain,
% 6.75/4.52 (((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))) <=> ((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(32,plain,
% 6.75/4.52 ((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))),
% 6.75/4.52 inference(quant_inst,[status(thm)],[])).
% 6.75/4.52 tff(33,plain,
% 6.75/4.52 ((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[32, 31])).
% 6.75/4.52 tff(34,plain,
% 6.75/4.52 (k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))),
% 6.75/4.52 inference(unit_resolution,[status(thm)],[33, 30, 29, 13])).
% 6.75/4.52 tff(35,plain,
% 6.75/4.52 (k12_ens_1(k17_ens_1(A!0)) = k1_yoneda_1(A!0)),
% 6.75/4.52 inference(symmetry,[status(thm)],[34])).
% 6.75/4.52 tff(36,plain,
% 6.75/4.52 (m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) <=> m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))),
% 6.75/4.52 inference(monotonicity,[status(thm)],[35])).
% 6.75/4.52 tff(37,plain,
% 6.75/4.52 (m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)) <=> m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 6.75/4.52 inference(symmetry,[status(thm)],[36])).
% 6.75/4.52 tff(38,plain,
% 6.75/4.52 ((~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))) <=> (~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 6.75/4.52 inference(monotonicity,[status(thm)],[37])).
% 6.75/4.52 tff(39,plain,
% 6.75/4.52 (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)))),
% 6.75/4.52 inference(and_elim,[status(thm)],[28])).
% 6.75/4.52 tff(40,plain,
% 6.75/4.52 (~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))),
% 6.75/4.52 inference(or_elim,[status(thm)],[39])).
% 6.75/4.52 tff(41,plain,
% 6.75/4.52 (~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[40, 38])).
% 6.75/4.52 tff(42,plain,
% 6.75/4.52 (^[A: $i] : refl(((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(43,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[42])).
% 6.75/4.52 tff(44,plain,
% 6.75/4.52 (^[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))))), (((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | ((~l1_cat_1(A)) | (~v2_cat_1(A)))))), rewrite(((~v1_xboole_0(k17_ens_1(A))) | ((~l1_cat_1(A)) | (~v2_cat_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))), (((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(45,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[44])).
% 6.75/4.52 tff(46,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(47,plain,
% 6.75/4.52 (^[A: $i] : rewrite(((v2_cat_1(A) & l1_cat_1(A)) => (~v1_xboole_0(k17_ens_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(48,plain,
% 6.75/4.52 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (~v1_xboole_0(k17_ens_1(A)))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[47])).
% 6.75/4.52 tff(49,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (~v1_xboole_0(k17_ens_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_ens_1')).
% 6.75/4.52 tff(50,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[49, 48])).
% 6.75/4.52 tff(51,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[50, 46])).
% 6.75/4.52 tff(52,plain,(
% 6.75/4.52 ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 6.75/4.52 inference(skolemize,[status(sab)],[51])).
% 6.75/4.52 tff(53,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[52, 45])).
% 6.75/4.52 tff(54,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[53, 43])).
% 6.75/4.52 tff(55,plain,
% 6.75/4.52 (((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))) <=> ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(56,plain,
% 6.75/4.52 (((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0))) <=> ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(57,plain,
% 6.75/4.52 (((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))) <=> ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0)))))),
% 6.75/4.52 inference(monotonicity,[status(thm)],[56])).
% 6.75/4.52 tff(58,plain,
% 6.75/4.52 (((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))) <=> ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))),
% 6.75/4.52 inference(transitivity,[status(thm)],[57, 55])).
% 6.75/4.52 tff(59,plain,
% 6.75/4.52 ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))),
% 6.75/4.52 inference(quant_inst,[status(thm)],[])).
% 6.75/4.52 tff(60,plain,
% 6.75/4.52 ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0)))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[59, 58])).
% 6.75/4.52 tff(61,plain,
% 6.75/4.52 (~v1_xboole_0(k17_ens_1(A!0))),
% 6.75/4.52 inference(unit_resolution,[status(thm)],[60, 30, 29, 54])).
% 6.75/4.52 tff(62,plain,
% 6.75/4.52 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(63,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[62])).
% 6.75/4.52 tff(64,plain,
% 6.75/4.52 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(65,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[64])).
% 6.75/4.52 tff(66,plain,
% 6.75/4.52 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(67,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[66])).
% 6.75/4.52 tff(68,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 6.75/4.52 inference(transitivity,[status(thm)],[67, 65])).
% 6.75/4.52 tff(69,plain,
% 6.75/4.52 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(70,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[69])).
% 6.75/4.52 tff(71,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.52 inference(rewrite,[status(thm)],[])).
% 6.75/4.52 tff(72,plain,
% 6.75/4.52 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))) <=> ((~r1_tarski(k17_ens_1(B), A)) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))), ((m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> (m1_subset_1(C, u1_cat_1(B)) => ((~r1_tarski(k17_ens_1(B), A)) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))), rewrite((m1_subset_1(C, u1_cat_1(B)) => ((~r1_tarski(k17_ens_1(B), A)) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))), ((m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), (![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), (((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), (((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))))),
% 6.75/4.52 inference(bind,[status(th)],[])).
% 6.75/4.52 tff(73,plain,
% 6.75/4.52 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.52 inference(quant_intro,[status(thm)],[72])).
% 6.75/4.52 tff(74,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t49_ens_1')).
% 6.75/4.52 tff(75,plain,
% 6.75/4.52 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.52 inference(modus_ponens,[status(thm)],[74, 73])).
% 6.75/4.53 tff(76,plain,
% 6.75/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[75, 71])).
% 6.75/4.53 tff(77,plain,(
% 6.75/4.53 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.53 inference(skolemize,[status(sab)],[76])).
% 6.75/4.53 tff(78,plain,
% 6.75/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[77, 70])).
% 6.75/4.53 tff(79,plain,
% 6.75/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[78, 68])).
% 6.75/4.53 tff(80,plain,
% 6.75/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[79, 63])).
% 6.75/4.53 tff(81,plain,
% 6.75/4.53 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 6.75/4.53 inference(rewrite,[status(thm)],[])).
% 6.75/4.53 tff(82,plain,
% 6.75/4.53 ((v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) <=> (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 6.75/4.53 inference(rewrite,[status(thm)],[])).
% 6.75/4.53 tff(83,plain,
% 6.75/4.53 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))))),
% 6.75/4.53 inference(monotonicity,[status(thm)],[82])).
% 6.75/4.53 tff(84,plain,
% 6.75/4.53 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 6.75/4.53 inference(transitivity,[status(thm)],[83, 81])).
% 6.75/4.53 tff(85,plain,
% 6.75/4.53 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 6.75/4.53 inference(quant_inst,[status(thm)],[])).
% 6.75/4.53 tff(86,plain,
% 6.75/4.53 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[85, 84])).
% 6.75/4.53 tff(87,plain,
% 6.75/4.53 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))),
% 6.75/4.53 inference(unit_resolution,[status(thm)],[86, 80, 61])).
% 6.75/4.53 tff(88,plain,
% 6.75/4.53 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))))),
% 6.75/4.53 inference(rewrite,[status(thm)],[])).
% 6.75/4.53 tff(89,plain,
% 6.75/4.53 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))))),
% 6.75/4.53 inference(quant_inst,[status(thm)],[])).
% 6.75/4.53 tff(90,plain,
% 6.75/4.53 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[89, 88])).
% 6.75/4.53 tff(91,plain,
% 6.75/4.53 (![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))),
% 6.75/4.53 inference(unit_resolution,[status(thm)],[90, 30, 29, 87])).
% 6.75/4.53 tff(92,plain,
% 6.75/4.53 (m1_subset_1(B!1, u1_cat_1(A!0))),
% 6.75/4.53 inference(or_elim,[status(thm)],[39])).
% 6.75/4.53 tff(93,plain,
% 6.75/4.53 (((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | (~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 6.75/4.53 inference(rewrite,[status(thm)],[])).
% 6.75/4.53 tff(94,plain,
% 6.75/4.53 (((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))) <=> ((~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 6.75/4.53 inference(rewrite,[status(thm)],[])).
% 6.75/4.53 tff(95,plain,
% 6.75/4.53 (((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))))),
% 6.75/4.53 inference(monotonicity,[status(thm)],[94])).
% 6.75/4.53 tff(96,plain,
% 6.75/4.53 (((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | (~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 6.75/4.53 inference(transitivity,[status(thm)],[95, 93])).
% 6.75/4.53 tff(97,plain,
% 6.75/4.53 ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))),
% 6.75/4.53 inference(quant_inst,[status(thm)],[])).
% 6.75/4.53 tff(98,plain,
% 6.75/4.53 ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | (~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[97, 96])).
% 6.75/4.53 tff(99,plain,
% 6.75/4.53 ((~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 6.75/4.53 inference(unit_resolution,[status(thm)],[98, 92, 91])).
% 6.75/4.53 tff(100,plain,
% 6.75/4.53 (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))),
% 6.75/4.53 inference(unit_resolution,[status(thm)],[99, 41])).
% 6.75/4.53 tff(101,plain,
% 6.75/4.53 (^[A: $i] : refl(r1_tarski(A, A) <=> r1_tarski(A, A))),
% 6.75/4.53 inference(bind,[status(th)],[])).
% 6.75/4.53 tff(102,plain,
% 6.75/4.53 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 6.75/4.53 inference(quant_intro,[status(thm)],[101])).
% 6.75/4.53 tff(103,plain,
% 6.75/4.53 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 6.75/4.53 inference(rewrite,[status(thm)],[])).
% 6.75/4.53 tff(104,plain,
% 6.75/4.53 (![A: $i, B: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 6.75/4.53 inference(elim_unused_vars,[status(thm)],[])).
% 6.75/4.53 tff(105,axiom,(![A: $i, B: $i] : r1_tarski(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 6.75/4.53 tff(106,plain,
% 6.75/4.53 (![A: $i] : r1_tarski(A, A)),
% 6.75/4.53 inference(modus_ponens,[status(thm)],[105, 104])).
% 6.75/4.56 tff(107,plain,
% 6.75/4.56 (![A: $i] : r1_tarski(A, A)),
% 6.75/4.56 inference(modus_ponens,[status(thm)],[106, 103])).
% 6.75/4.56 tff(108,plain,(
% 6.75/4.56 ![A: $i] : r1_tarski(A, A)),
% 6.75/4.56 inference(skolemize,[status(sab)],[107])).
% 6.75/4.56 tff(109,plain,
% 6.75/4.56 (![A: $i] : r1_tarski(A, A)),
% 6.75/4.56 inference(modus_ponens,[status(thm)],[108, 102])).
% 6.75/4.56 tff(110,plain,
% 6.75/4.56 ((~![A: $i] : r1_tarski(A, A)) | r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))),
% 6.75/4.56 inference(quant_inst,[status(thm)],[])).
% 6.75/4.56 tff(111,plain,
% 6.75/4.56 ($false),
% 6.75/4.56 inference(unit_resolution,[status(thm)],[110, 109, 100])).
% 6.75/4.56 % SZS output end Proof
%------------------------------------------------------------------------------