TSTP Solution File: SEU230+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 07:28:20 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 10:41:59 EDT 2022
% 0.12/0.33 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(singleton_type, type, (
% 0.12/0.39 singleton: $i > $i)).
% 0.12/0.39 tff(tptp_fun_A_12_type, type, (
% 0.12/0.39 tptp_fun_A_12: $i)).
% 0.12/0.39 tff(set_union2_type, type, (
% 0.12/0.39 set_union2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_D_1_type, type, (
% 0.12/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(succ_type, type, (
% 0.12/0.39 succ: $i > $i)).
% 0.12/0.39 tff(tptp_fun_C_0_type, type, (
% 0.12/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.39 tff(18,plain,(
% 0.12/0.39 ![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))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (((~![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)))))))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) <=> ((~![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)))))))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) <=> (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 ((((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))) | $false) <=> ((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 ((~$true) <=> $false),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (($true | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))) <=> ($true | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12)))))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 ((~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12)))))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[30, 25])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 ((~(in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) <=> ((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (($false | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) <=> (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 ((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[34, 25])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) <=> ($false | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) <=> (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[36, 33])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) <=> (~(in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ((~((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) <=> ((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[38, 32])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))))) <=> (((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[39, 31])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (((~((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))))) <=> ((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[40, 24])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~((~((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12)))))))) <=> (~((~in(A!12, set_union2(A!12, singleton(A!12)))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~((~((~(set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12)))))))) <=> (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[42, 23])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (((~![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(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))))))) <=> ((~![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)))))))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((~![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(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))))))) <=> ((~![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)))))))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[44, 22])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~![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(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12)))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))))) | (~((set_union2(A!12, singleton(A!12)) = set_union2(A!12, singleton(A!12))) | ((~in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), set_union2(A!12, singleton(A!12)))) <=> (in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), A!12) | in(tptp_fun_D_1(set_union2(A!12, singleton(A!12)), singleton(A!12), A!12), singleton(A!12))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~![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)))))))) | (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 21])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(52,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.41 tff(54,plain,(
% 0.19/0.41 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(A!12) = set_union2(A!12, singleton(A!12)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (succ(A!12) = set_union2(A!12, singleton(A!12))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (set_union2(A!12, singleton(A!12)) = succ(A!12)),
% 0.19/0.41 inference(symmetry,[status(thm)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (in(A!12, set_union2(A!12, singleton(A!12))) <=> in(A!12, succ(A!12))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (in(A!12, succ(A!12)) <=> in(A!12, set_union2(A!12, singleton(A!12)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~in(A!12, succ(A!12))) <=> (~in(A!12, set_union2(A!12, singleton(A!12))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((~![A: $i] : in(A, succ(A))) <=> (~![A: $i] : in(A, succ(A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(63,axiom,(~![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 62])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 62])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 62])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 62])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (~![A: $i] : in(A, succ(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.41 tff(71,plain,(
% 0.19/0.41 ~in(A!12, succ(A!12))),
% 0.19/0.41 inference(skolemize,[status(sab)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (~in(A!12, set_union2(A!12, singleton(A!12)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~(in(A!12, set_union2(A!12, singleton(A!12))) <=> (in(A!12, A!12) | in(A!12, singleton(A!12))))) | in(A!12, set_union2(A!12, singleton(A!12))) | (~(in(A!12, A!12) | in(A!12, singleton(A!12))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (~(in(A!12, A!12) | in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 72, 48])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 ((in(A!12, A!12) | in(A!12, singleton(A!12))) | (~in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (~in(A!12, singleton(A!12))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(pull_quant,[status(thm)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[82, 78])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(92,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.41 tff(94,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!12, singleton(A!12))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~(~in(A!12, singleton(A!12)))) <=> in(A!12, singleton(A!12))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~in(A!12, singleton(A!12))) | $false) <=> (~in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (($true | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((singleton(A!12) = singleton(A!12)) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))) <=> $true),
% 0.19/0.41 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))) <=> (~$true)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))) <=> $false),
% 0.19/0.41 inference(transitivity,[status(thm)],[105, 25])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) <=> (~in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))) <=> ((~in(A!12, singleton(A!12))) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))) <=> (~in(A!12, singleton(A!12)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[108, 100])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))) <=> (~(~in(A!12, singleton(A!12))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))) <=> in(A!12, singleton(A!12))),
% 0.19/0.41 inference(transitivity,[status(thm)],[110, 99])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!12, singleton(A!12)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!12, singleton(A!12)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[112, 98])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!12) = singleton(A!12))) | (in(A!12, singleton(A!12)) <=> (A!12 = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | ((~in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12))) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!12, singleton(A!12))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[115, 97, 76])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------