TSTP Solution File: NUM383+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Sun Sep 18 13:09:27 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 : Fri Sep 2 10:04:34 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.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(in_type, type, (
% 0.19/0.44 in: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_A_12_type, type, (
% 0.19/0.44 tptp_fun_A_12: $i)).
% 0.19/0.44 tff(element_type, type, (
% 0.19/0.44 element: ( $i * $i ) > $o)).
% 0.19/0.44 tff(powerset_type, type, (
% 0.19/0.44 powerset: $i > $i)).
% 0.19/0.44 tff(tptp_fun_B_11_type, type, (
% 0.19/0.44 tptp_fun_B_11: $i)).
% 0.19/0.44 tff(subset_type, type, (
% 0.19/0.44 subset: ( $i * $i ) > $o)).
% 0.19/0.44 tff(empty_type, type, (
% 0.19/0.44 empty: $i > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.44 tff(6,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.44 inference(skolemize,[status(sab)],[5])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!11, powerset(A!12)) <=> subset(B!11, A!12))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (element(B!11, powerset(A!12)) <=> subset(B!11, A!12)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 ((~(~(in(A!12, B!11) & subset(B!11, A!12)))) <=> (in(A!12, B!11) & subset(B!11, A!12))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))) <=> (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(12,axiom,(~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_ordinal1')).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.44 tff(20,plain,(
% 0.19/0.44 ~(~(in(A!12, B!11) & subset(B!11, A!12)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (in(A!12, B!11) & subset(B!11, A!12)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (subset(B!11, A!12)),
% 0.19/0.44 inference(and_elim,[status(thm)],[21])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((~(element(B!11, powerset(A!12)) <=> subset(B!11, A!12))) | element(B!11, powerset(A!12)) | (~subset(B!11, A!12))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((~(element(B!11, powerset(A!12)) <=> subset(B!11, A!12))) | element(B!11, powerset(A!12))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (element(B!11, powerset(A!12))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (in(A!12, B!11)),
% 0.19/0.44 inference(and_elim,[status(thm)],[21])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.44 tff(34,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.44 tff(37,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.44 inference(skolemize,[status(sab)],[36])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 ((element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12)))) <=> ((~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))),
% 0.19/0.44 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (element(A!12, A!12)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[45, 39, 26, 25])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.44 tff(54,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.44 tff(57,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[56])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (~empty(A!12)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[62, 59, 26, 25])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.44 tff(69,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.44 tff(72,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | (~element(A!12, A!12)) | in(A!12, A!12))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!12) | (~element(A!12, A!12)) | in(A!12, A!12))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 ((empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12))) <=> (empty(A!12) | (~element(A!12, A!12)) | in(A!12, A!12))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | (~element(A!12, A!12)) | in(A!12, A!12)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!12) | (~element(A!12, A!12)) | in(A!12, A!12))),
% 0.19/0.44 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!12) | (~element(A!12, A!12)) | in(A!12, A!12)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (in(A!12, A!12)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[79, 73, 63, 46])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.45 tff(86,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.45 tff(89,plain,(
% 0.19/0.45 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[88])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (((~in(A!12, A!12)) | (~in(A!12, A!12))) <=> (~in(A!12, A!12))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!12, A!12)) | (~in(A!12, A!12)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!12, A!12)) | (~in(A!12, A!12)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!12, A!12)) | (~in(A!12, A!12)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[96, 90, 80])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------