TSTP Solution File: SEU011+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU011+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 20 07:27:16 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU011+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 08:54:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(tptp_fun_C_10_type, type, (
% 0.21/0.46 tptp_fun_C_10: ( $i * $i ) > $i)).
% 0.21/0.46 tff(set_intersection2_type, type, (
% 0.21/0.46 set_intersection2: ( $i * $i ) > $i)).
% 0.21/0.46 tff(tptp_fun_A_12_type, type, (
% 0.21/0.46 tptp_fun_A_12: $i)).
% 0.21/0.46 tff(tptp_fun_B_11_type, type, (
% 0.21/0.46 tptp_fun_B_11: $i)).
% 0.21/0.46 tff(relation_composition_type, type, (
% 0.21/0.46 relation_composition: ( $i * $i ) > $i)).
% 0.21/0.46 tff(identity_relation_type, type, (
% 0.21/0.46 identity_relation: $i > $i)).
% 0.21/0.46 tff(apply_type, type, (
% 0.21/0.46 apply: ( $i * $i ) > $i)).
% 0.21/0.46 tff(in_type, type, (
% 0.21/0.46 in: ( $i * $i ) > $o)).
% 0.21/0.46 tff(relation_dom_type, type, (
% 0.21/0.46 relation_dom: $i > $i)).
% 0.21/0.46 tff(tptp_fun_D_0_type, type, (
% 0.21/0.46 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.21/0.46 tff(function_type, type, (
% 0.21/0.46 function: $i > $o)).
% 0.21/0.46 tff(relation_type, type, (
% 0.21/0.46 relation: $i > $o)).
% 0.21/0.46 tff(1,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(2,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(pull_quant,[status(thm)],[])).
% 0.21/0.46 tff(4,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.46 tff(6,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[5, 3])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[6, 2])).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[9, 7])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), rewrite(((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(14,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(16,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.46 tff(18,plain,(
% 0.21/0.46 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[17])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), A!12)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), B!11))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (~((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), A!12)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), B!11)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11)) | (in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> ((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), A!12)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), B!11, A!12), B!11))))))) | ((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 ((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(31,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_funct_1')).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.47 tff(33,plain,(
% 0.21/0.47 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[32])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))) | function(identity_relation(A!12))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 (function(identity_relation(A!12))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(43,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (![A: $i] : relation(identity_relation(A))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.47 tff(45,plain,(
% 0.21/0.47 ![A: $i] : relation(identity_relation(A))),
% 0.21/0.47 inference(skolemize,[status(sab)],[44])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![A: $i] : relation(identity_relation(A))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!12))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (relation(identity_relation(A!12))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.47 tff(63,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t34_funct_1')).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.47 tff(65,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.47 tff(66,plain,(
% 0.21/0.47 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[65])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[68, 55])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[69, 50])).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 ((~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))) <=> (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[74, 72])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[76, 71])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[79, 70, 48, 39])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 (((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))) | (relation_dom(identity_relation(A!12)) = A!12)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 (relation_dom(identity_relation(A!12)) = A!12),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 (A!12 = relation_dom(identity_relation(A!12))),
% 0.21/0.48 inference(symmetry,[status(thm)],[82])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (set_intersection2(A!12, B!11) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 (set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11)),
% 0.21/0.48 inference(symmetry,[status(thm)],[84])).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 ((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))))) | (~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 ((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))))) | (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[87, 25])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(92,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.48 tff(94,plain,(
% 0.21/0.48 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.48 inference(skolemize,[status(sab)],[93])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!12, B!11) = set_intersection2(B!11, A!12))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (set_intersection2(A!12, B!11) = set_intersection2(B!11, A!12)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 (set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12)),
% 0.21/0.48 inference(transitivity,[status(thm)],[85, 97])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[98])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12)) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))),
% 0.21/0.48 inference(symmetry,[status(thm)],[99])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (~((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[101, 35])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11)))) | function(identity_relation(B!11))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (function(identity_relation(B!11))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(B!11))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (relation(identity_relation(B!11))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[105, 46])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (^[A: $i, B: $i] : refl(((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & relation(B) & function(B)) <=> (~((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> (~(~((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))))), rewrite((~(~((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))), rewrite((relation(relation_composition(A, B)) & function(relation_composition(A, B))) <=> (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> (((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))), rewrite((((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & relation(B)) <=> (relation(A) & function(A) & relation(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> ((relation(A) & function(A) & relation(B)) & function(B)))), rewrite(((relation(A) & function(A) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B)))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))))), rewrite(((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[112])).
% 0.21/0.48 tff(114,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_funct_1')).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.21/0.48 tff(117,plain,(
% 0.21/0.48 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[116])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 (((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 ((~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))) <=> (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[125, 120])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(128,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[128, 119])).
% 0.21/0.49 tff(130,plain,
% 0.21/0.49 (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[129, 39, 106, 104, 48])).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 (((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | function(relation_composition(identity_relation(B!11), identity_relation(A!12)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(132,plain,
% 0.21/0.49 (function(relation_composition(identity_relation(B!11), identity_relation(A!12)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.21/0.49 tff(133,plain,
% 0.21/0.49 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B))) <=> (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(134,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(A)) | (~relation(B))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(A)) | (~relation(B))))))), rewrite((~(~((~relation(A)) | (~relation(B))))) <=> ((~relation(A)) | (~relation(B)))), ((~(relation(A) & relation(B))) <=> ((~relation(A)) | (~relation(B))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(A)) | (~relation(B)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(A)) | (~relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(136,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(138,plain,
% 0.21/0.49 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.49 tff(140,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.49 tff(142,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.21/0.49 tff(143,plain,(
% 0.21/0.49 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[142])).
% 0.21/0.49 tff(144,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.21/0.49 tff(146,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 ((relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12)))) <=> ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[151, 145])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 (relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[152, 48, 106])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[156, 70, 153, 132])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 (((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))) | ((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 ((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.21/0.49 tff(160,plain,
% 0.21/0.49 (^[A: $i, B: $i] : refl(((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B))) <=> ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B))) <=> ![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), (((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> (((~relation(B)) | (~function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))))), rewrite((((~relation(B)) | (~function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))), (((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 (^[A: $i, B: $i] : rewrite(((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.49 tff(167,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_funct_1')).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.21/0.49 tff(170,plain,(
% 0.21/0.49 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[169])).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | ((relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))) <=> ((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | ((relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 ((relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[176, 39, 48])).
% 0.21/0.50 tff(178,plain,
% 0.21/0.50 (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12)),
% 0.21/0.50 inference(transitivity,[status(thm)],[177, 85, 97])).
% 0.21/0.50 tff(179,plain,
% 0.21/0.50 (set_intersection2(B!11, A!12) = set_intersection2(A!12, B!11)),
% 0.21/0.50 inference(symmetry,[status(thm)],[97])).
% 0.21/0.50 tff(180,plain,
% 0.21/0.50 (identity_relation(set_intersection2(B!11, A!12)) = identity_relation(set_intersection2(A!12, B!11))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[179])).
% 0.21/0.50 tff(181,plain,
% 0.21/0.50 ((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) <=> (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.50 tff(182,plain,
% 0.21/0.50 ((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11))) <=> (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[181])).
% 0.21/0.50 tff(183,plain,
% 0.21/0.50 ((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11)))) <=> (~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[182])).
% 0.21/0.50 tff(184,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))) <=> (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(185,axiom,(~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_funct_1')).
% 0.21/0.50 tff(186,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.21/0.50 tff(187,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[186, 184])).
% 0.21/0.50 tff(188,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.21/0.50 tff(189,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.21/0.50 tff(190,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[189, 184])).
% 0.21/0.50 tff(191,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[190, 184])).
% 0.21/0.50 tff(192,plain,
% 0.21/0.50 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.21/0.50 tff(193,plain,(
% 0.21/0.50 ~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[192])).
% 0.21/0.50 tff(194,plain,
% 0.21/0.50 (~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[193, 183])).
% 0.21/0.50 tff(195,plain,
% 0.21/0.50 ((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(196,plain,
% 0.21/0.50 (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[195, 194, 178, 159])).
% 0.21/0.50 tff(197,plain,
% 0.21/0.50 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))) | in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.50 tff(199,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[198, 100])).
% 0.21/0.50 tff(200,plain,
% 0.21/0.50 ((~(in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(201,plain,
% 0.21/0.50 (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[200, 199, 88])).
% 0.21/0.50 tff(202,plain,
% 0.21/0.50 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))) | in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(203,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.21/0.50 tff(204,plain,
% 0.21/0.50 (((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))) | ![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(205,plain,
% 0.21/0.50 (![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[204, 80])).
% 0.21/0.50 tff(206,plain,
% 0.21/0.50 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) <=> ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(207,plain,
% 0.21/0.50 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.50 tff(209,plain,
% 0.21/0.50 (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[208, 205, 203])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12))) | in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(211,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[210, 201])).
% 0.21/0.50 tff(212,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(213,plain,
% 0.21/0.50 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))) <=> ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(214,plain,
% 0.21/0.50 ((~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))) <=> (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(215,plain,
% 0.21/0.50 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))))))) <=> ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[214])).
% 0.21/0.50 tff(216,plain,
% 0.21/0.50 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))))))) <=> ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[215, 213])).
% 0.21/0.50 tff(217,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[216])).
% 0.21/0.50 tff(218,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[217, 212])).
% 0.21/0.50 tff(219,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[220, 70, 106, 104])).
% 0.21/0.50 tff(222,plain,
% 0.21/0.50 (((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))) | ![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(223,plain,
% 0.21/0.50 (![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.21/0.50 tff(224,plain,
% 0.21/0.50 (((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) <=> ((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(225,plain,
% 0.21/0.50 ((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(226,plain,
% 0.21/0.50 ((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.50 tff(227,plain,
% 0.21/0.50 (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[226, 223, 211])).
% 0.21/0.50 tff(228,plain,
% 0.21/0.50 (apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))) = apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[227])).
% 0.21/0.50 tff(229,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[178])).
% 0.21/0.50 tff(230,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12)) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[229])).
% 0.21/0.50 tff(231,plain,
% 0.21/0.50 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[198, 230])).
% 0.21/0.50 tff(232,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(233,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[232])).
% 0.21/0.50 tff(234,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(235,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[234])).
% 0.21/0.50 tff(236,plain,
% 0.21/0.50 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.50 inference(pull_quant,[status(thm)],[])).
% 0.21/0.50 tff(237,plain,
% 0.21/0.50 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(238,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[237])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[238, 236])).
% 0.21/0.51 tff(240,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[239, 235])).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[241])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[242, 240])).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | ((~relation(C)) | (~function(C)))))), rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | ((~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[244])).
% 0.21/0.51 tff(246,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))) <=> ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[247])).
% 0.21/0.51 tff(249,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_funct_1')).
% 0.21/0.51 tff(250,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.21/0.51 tff(251,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.21/0.51 tff(252,plain,(
% 0.21/0.51 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[251])).
% 0.21/0.51 tff(253,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[252, 245])).
% 0.21/0.51 tff(254,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[253, 243])).
% 0.21/0.51 tff(255,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[254, 233])).
% 0.21/0.51 tff(256,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(257,plain,
% 0.21/0.51 (((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11)))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(258,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[257])).
% 0.21/0.51 tff(259,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[258, 256])).
% 0.21/0.51 tff(260,plain,
% 0.21/0.51 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(261,plain,
% 0.21/0.51 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.21/0.51 tff(262,plain,
% 0.21/0.51 ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[261, 255, 48, 39, 106, 104])).
% 0.21/0.51 tff(263,plain,
% 0.21/0.51 (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[262, 231])).
% 0.21/0.51 tff(264,plain,
% 0.21/0.51 (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))),
% 0.21/0.51 inference(transitivity,[status(thm)],[263, 228, 209])).
% 0.21/0.51 tff(265,plain,
% 0.21/0.51 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))) | (~(apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(266,plain,
% 0.21/0.51 (~(apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[265, 196])).
% 0.21/0.51 tff(267,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[266, 264])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------