TSTP Solution File: SET877+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 05:08:29 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 08:24:05 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.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(tptp_fun_B_3_type, type, (
% 0.12/0.38 tptp_fun_B_3: $i)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(singleton_type, type, (
% 0.12/0.38 singleton: $i > $i)).
% 0.12/0.38 tff(set_intersection2_type, type, (
% 0.12/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))) <=> (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((set_intersection2(singleton(A), singleton(B)) = singleton(A)) => (A = B))) <=> (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![A: $i, B: $i] : ((set_intersection2(singleton(A), singleton(B)) = singleton(A)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_zfmisc_1')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~(set_intersection2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.38 tff(11,plain,(
% 0.12/0.38 ~((~(set_intersection2(singleton(A!4), singleton(B!3)) = singleton(A!4))) | (A!4 = B!3))),
% 0.12/0.38 inference(skolemize,[status(sab)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (set_intersection2(singleton(A!4), singleton(B!3)) = singleton(A!4)),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(singleton(A!4), singleton(B!3)) = set_intersection2(singleton(B!3), singleton(A!4)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (set_intersection2(singleton(A!4), singleton(B!3)) = set_intersection2(singleton(B!3), singleton(A!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (set_intersection2(singleton(B!3), singleton(A!4)) = set_intersection2(singleton(A!4), singleton(B!3))),
% 0.12/0.38 inference(symmetry,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (set_intersection2(singleton(B!3), singleton(A!4)) = singleton(A!4)),
% 0.12/0.38 inference(transitivity,[status(thm)],[22, 12])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl(((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A)) <=> ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A)) <=> ![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A)) <=> ![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite(((set_intersection2(A, singleton(B)) = singleton(B)) => in(B, A)) <=> ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((set_intersection2(A, singleton(B)) = singleton(B)) => in(B, A)) <=> ![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,axiom,(![A: $i, B: $i] : ((set_intersection2(A, singleton(B)) = singleton(B)) => in(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l30_zfmisc_1')).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.38 tff(32,plain,(
% 0.12/0.38 ![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (((~![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))) | ((~(set_intersection2(singleton(B!3), singleton(A!4)) = singleton(A!4))) | in(A!4, singleton(B!3)))) <=> ((~![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))) | (~(set_intersection2(singleton(B!3), singleton(A!4)) = singleton(A!4))) | in(A!4, singleton(B!3)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))) | ((~(set_intersection2(singleton(B!3), singleton(A!4)) = singleton(A!4))) | in(A!4, singleton(B!3)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~(set_intersection2(A, singleton(B)) = singleton(B))) | in(B, A))) | (~(set_intersection2(singleton(B!3), singleton(A!4)) = singleton(A!4))) | in(A!4, singleton(B!3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (in(A!4, singleton(B!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 33, 23])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (~(A!4 = B!3)),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) | (~in(A!4, singleton(B!3))) | (A!4 = B!3)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 38, 37])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(pull_quant,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[46, 42])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(56,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.39 tff(58,plain,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~![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!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ((~![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!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)) | $false) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~$true) <=> $false),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (($true | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> ($true | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> $true),
% 0.12/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[69])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[70, 65])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((~(singleton(B!3) = singleton(B!3))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ((~(singleton(B!3) = singleton(B!3))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[74, 65])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[75])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.39 inference(transitivity,[status(thm)],[76, 73])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.12/0.39 inference(transitivity,[status(thm)],[78, 72])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> (((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)) | $false)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[79, 71])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.12/0.39 inference(transitivity,[status(thm)],[80, 64])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (~((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[81])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.39 inference(transitivity,[status(thm)],[82, 63])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (((~![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(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))) <=> ((~![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!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[83])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (((~![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(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))) <=> ((~![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!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[84, 62])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 ((~![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(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[87, 61, 40])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------