TSTP Solution File: SET906+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:08:34 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 08:40:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(tptp_fun_A_7_type, type, (
% 0.20/0.39 tptp_fun_A_7: $i)).
% 0.20/0.39 tff(tptp_fun_D_0_type, type, (
% 0.20/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_B_6_type, type, (
% 0.20/0.39 tptp_fun_B_6: $i)).
% 0.20/0.39 tff(unordered_pair_type, type, (
% 0.20/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.39 tff(in_type, type, (
% 0.20/0.39 in: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_C_5_type, type, (
% 0.20/0.39 tptp_fun_C_5: $i)).
% 0.20/0.39 tff(set_union2_type, type, (
% 0.20/0.39 set_union2: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_D_1_type, type, (
% 0.20/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(subset_type, type, (
% 0.20/0.39 subset: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_C_2_type, type, (
% 0.20/0.39 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.39 inference(pull_quant,[status(thm)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), monotonicity(rewrite(((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))) <=> ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))), (((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.40 tff(18,plain,(
% 0.20/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))) <=> (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6)))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))) | ((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(skolemize,[status(sab)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 0.20/0.41 inference(symmetry,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (set_union2(unordered_pair(B!6, A!7), C!5) = set_union2(unordered_pair(A!7, B!6), C!5)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(unordered_pair(B!6, A!7), C!5)),
% 0.20/0.41 inference(symmetry,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(46,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.41 tff(48,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.41 inference(skolemize,[status(sab)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(C!5, unordered_pair(A!7, B!6)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(C!5, unordered_pair(A!7, B!6))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(A!7, B!6), C!5)),
% 0.20/0.42 inference(symmetry,[status(thm)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)),
% 0.20/0.42 inference(transitivity,[status(thm)],[52, 42])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 30])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (in(A!7, set_union2(unordered_pair(A!7, B!6), C!5)) <=> in(A!7, set_union2(C!5, unordered_pair(A!7, B!6)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[57])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) <=> (~in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (^[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))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (^[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))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.42 tff(70,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')).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.42 tff(73,plain,(
% 0.20/0.42 ![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)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[72])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~![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_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~(subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5) | (~((~in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), set_union2(unordered_pair(A!7, B!6), C!5))) | in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), C!5)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (~((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~(subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5) | (~((~in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), set_union2(unordered_pair(A!7, B!6), C!5))) | in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), C!5))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~(subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5) | (~((~in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), set_union2(unordered_pair(A!7, B!6), C!5))) | in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), C!5)))))) | ((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(unordered_pair(A, B), C), C) => in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(82,axiom,(~![A: $i, B: $i, C: $i] : (subset(set_union2(unordered_pair(A, B), C), C) => in(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t47_zfmisc_1')).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 80])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[86, 80])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 80])).
% 0.20/0.42 tff(90,plain,(
% 0.20/0.42 ~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | in(A!7, C!5))),
% 0.20/0.42 inference(skolemize,[status(sab)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)),
% 0.20/0.42 inference(or_elim,[status(thm)],[90])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 ((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 79])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (~in(A!7, C!5)),
% 0.20/0.43 inference(or_elim,[status(thm)],[90])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | ((~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5))) <=> ((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | (~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | ((~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | (~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 95, 94])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (~in(A!7, set_union2(C!5, unordered_pair(A!7, B!6)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 59])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((~(in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))) | in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) | (~(in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (~(in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 100, 56])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))) | (~in(A!7, unordered_pair(B!6, A!7)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (~in(A!7, unordered_pair(B!6, A!7))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 37])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 106, 104])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))) | ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(pull_quant,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[116, 112])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[119, 117])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.43 tff(128,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.43 tff(131,plain,(
% 0.20/0.43 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[130])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 120])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))) <=> (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 134, 110])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------