TSTP Solution File: SEU132+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU132+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 07:27:39 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU132+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:44:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(in_type, type, (
% 0.20/0.42 in: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_A_10_type, type, (
% 0.20/0.42 tptp_fun_A_10: $i)).
% 0.20/0.42 tff(tptp_fun_D_3_type, type, (
% 0.20/0.42 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_B_9_type, type, (
% 0.20/0.42 tptp_fun_B_9: $i)).
% 0.20/0.42 tff(set_intersection2_type, type, (
% 0.20/0.42 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_C_2_type, type, (
% 0.20/0.42 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.42 tff(set_difference_type, type, (
% 0.20/0.42 set_difference: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_C_8_type, type, (
% 0.20/0.42 tptp_fun_C_8: $i)).
% 0.20/0.42 tff(tptp_fun_D_4_type, type, (
% 0.20/0.42 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(subset_type, type, (
% 0.20/0.42 subset: ( $i * $i ) > $o)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(pull_quant,[status(thm)],[])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_4(C, B, A), C)) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (((in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | $false) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 ((~$true) <=> $false),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (($true | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 ((set_difference(B!9, C!8) = set_difference(B!9, C!8)) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))) <=> ($true | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))) <=> $true),
% 0.20/0.43 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8))))) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8))))) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[30, 25])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ((~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (($false | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 ((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[34, 25])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> ($false | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[36, 33])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) <=> (~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[38, 32])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))))) <=> ((in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | $false)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[39, 31])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[40, 24])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8))))))) <=> (~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 ((~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8))))))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[42, 23])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[44, 22])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 21])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.44 tff(59,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.44 tff(62,plain,(
% 0.20/0.44 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[61])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))) | ![C: $i] : ((~in(C, set_difference(A!10, C!8))) | in(C, set_difference(B!9, C!8))))) | (~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (~((~((~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))) | ![C: $i] : ((~in(C, set_difference(A!10, C!8))) | in(C, set_difference(B!9, C!8))))) | (~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (((~((~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))) | ![C: $i] : ((~in(C, set_difference(A!10, C!8))) | in(C, set_difference(B!9, C!8))))) | (~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))))) | (subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(71,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_xboole_1')).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[75, 69])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[77, 69])).
% 0.20/0.45 tff(79,plain,(
% 0.20/0.45 ~((~subset(A!10, B!9)) | subset(set_difference(A!10, C!8), set_difference(B!9, C!8)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[78])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))),
% 0.20/0.45 inference(or_elim,[status(thm)],[79])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 ((~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 ((~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[82, 68])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 ((~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 ((~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[87, 48])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 ((~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (((in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | $false) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (($true | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 ((set_difference(A!10, C!8) = set_difference(A!10, C!8)) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))) <=> ($true | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))) <=> $true),
% 0.20/0.45 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 ((~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8))))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 ((~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8))))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[96, 25])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 ((~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (($false | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 ((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 ((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[100, 25])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> ($false | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[102, 99])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 ((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) <=> (~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[104, 98])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))))) <=> ((in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | $false)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[105, 97])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))))) <=> (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[106, 91])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 ((~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8))))))) <=> (~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8))))))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[108, 90])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[110, 89])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | (~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)) <=> ((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_4(C, B, A), C) <=> ((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)))))))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[113, 21])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[115, 83])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 ((~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) <=> ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 114])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[122, 121, 88])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[126, 119])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 ((~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)))))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (~(in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[128, 127, 125])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(133,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.46 tff(135,plain,(
% 0.20/0.46 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.46 inference(skolemize,[status(sab)],[134])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!10, B!9) = set_intersection2(B!9, A!10))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (set_intersection2(A!10, B!9) = set_intersection2(B!9, A!10)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (subset(A!10, B!9)),
% 0.20/0.46 inference(or_elim,[status(thm)],[79])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.46 tff(145,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.20/0.46 tff(148,plain,(
% 0.20/0.46 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(skolemize,[status(sab)],[147])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!10, B!9)) | (set_intersection2(A!10, B!9) = A!10))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!10, B!9)) | (set_intersection2(A!10, B!9) = A!10))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!10, B!9)) | (set_intersection2(A!10, B!9) = A!10))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!10, B!9)) | (set_intersection2(A!10, B!9) = A!10)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (set_intersection2(A!10, B!9) = A!10),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[152, 149, 139])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (A!10 = set_intersection2(A!10, B!9)),
% 0.20/0.46 inference(symmetry,[status(thm)],[153])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (A!10 = set_intersection2(B!9, A!10)),
% 0.20/0.46 inference(transitivity,[status(thm)],[154, 138])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 ((~((~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))))) | (~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (~((~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[156, 155, 129])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (((~((~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))))) | (~((A!10 = set_intersection2(B!9, A!10)) | (in(tptp_fun_D_3(A!10, A!10, B!9), A!10) <=> ((~in(tptp_fun_D_3(A!10, A!10, B!9), B!9)) | (~in(tptp_fun_D_3(A!10, A!10, B!9), A!10))))))) | ((~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ((~((~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))))) | (~((A!10 = set_intersection2(B!9, A!10)) | (in(tptp_fun_D_3(A!10, A!10, B!9), A!10) <=> ((~in(tptp_fun_D_3(A!10, A!10, B!9), B!9)) | (~in(tptp_fun_D_3(A!10, A!10, B!9), A!10))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (^[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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.46 inference(pull_quant,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (^[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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[165, 161])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (^[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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[168, 166])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (^[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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(175,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/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.47 tff(177,plain,(
% 0.20/0.47 ![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[176])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) & in(tptp_fun_D_3(C, B, A), B)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (![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_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[179, 169])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_3(C, B, A), C) <=> ((~in(tptp_fun_D_3(C, B, A), A)) | (~in(tptp_fun_D_3(C, B, A), B))))))))) | (~((~((~(A!10 = set_intersection2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10) <=> (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))))))) | (~((A!10 = set_intersection2(B!9, A!10)) | (in(tptp_fun_D_3(A!10, A!10, B!9), A!10) <=> ((~in(tptp_fun_D_3(A!10, A!10, B!9), B!9)) | (~in(tptp_fun_D_3(A!10, A!10, B!9), A!10))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[181, 180, 159])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------