TSTP Solution File: SET012-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:04:43 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 01:03:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(member_type, type, (
% 0.20/0.42 member: ( $i * $i ) > $o)).
% 0.20/0.42 tff(complement_type, type, (
% 0.20/0.42 complement: $i > $i)).
% 0.20/0.42 tff(as_type, type, (
% 0.20/0.42 as: $i)).
% 0.20/0.42 tff(f1_type, type, (
% 0.20/0.42 f1: ( $i * $i ) > $i)).
% 0.20/0.42 tff(little_set_type, type, (
% 0.20/0.42 little_set: $i > $o)).
% 0.20/0.42 tff(cs_type, type, (
% 0.20/0.42 cs: $i)).
% 0.20/0.42 tff(1,assumption,(~member(f1(as, complement(complement(as))), complement(complement(as)))), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 ((~(as = cs)) <=> (~(as = complement(complement(as))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 ((~(as = cs)) <=> (~(as = cs))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(4,axiom,(~(as = cs)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_a_equals_c')).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (~(as = cs)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (~(as = complement(complement(as)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (^[Y: $i, X: $i] : refl((little_set(f1(X, Y)) | (X = Y)) <=> (little_set(f1(X, Y)) | (X = Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(10,axiom,(![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','extensionality1')).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.42 tff(12,plain,(
% 0.20/0.42 ![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.20/0.42 inference(skolemize,[status(sab)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | (little_set(f1(as, complement(complement(as)))) | (as = complement(complement(as))))) <=> ((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | little_set(f1(as, complement(complement(as)))) | (as = complement(complement(as))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | (little_set(f1(as, complement(complement(as)))) | (as = complement(complement(as))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 ((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | little_set(f1(as, complement(complement(as)))) | (as = complement(complement(as)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (little_set(f1(as, complement(complement(as))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[16, 13, 6])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[Z: $i, X: $i] : refl((member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (^[Z: $i, X: $i] : trans(monotonicity(rewrite((member(Z, complement(X)) | (~little_set(Z))) <=> (member(Z, complement(X)) | (~little_set(Z)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)))), rewrite(((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.42 tff(23,axiom,(![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','complement2')).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.42 tff(26,plain,(
% 0.20/0.42 ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), complement(complement(as))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((member(f1(as, complement(complement(as))), complement(as)) | member(f1(as, complement(complement(as))), complement(complement(as))) | (~little_set(f1(as, complement(complement(as)))))) <=> (member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | member(f1(as, complement(complement(as))), complement(complement(as))) | (~little_set(f1(as, complement(complement(as))))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), complement(complement(as)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | member(f1(as, complement(complement(as))), complement(complement(as))) | (~little_set(f1(as, complement(complement(as))))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | member(f1(as, complement(complement(as))), complement(complement(as))) | (~little_set(f1(as, complement(complement(as))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), complement(complement(as)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (member(f1(as, complement(complement(as))), complement(as))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 27, 17, 1])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl(((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : rewrite(((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y)) <=> ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.43 tff(40,axiom,(![Y: $i, X: $i] : ((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','extensionality2')).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.43 tff(43,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[42])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((as = complement(complement(as))) | member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (as = complement(complement(as))) | member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (((as = complement(complement(as))) | member(f1(as, complement(complement(as))), complement(complement(as))) | member(f1(as, complement(complement(as))), as)) <=> ((as = complement(complement(as))) | member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((as = complement(complement(as))) | member(f1(as, complement(complement(as))), complement(complement(as))) | member(f1(as, complement(complement(as))), as))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((as = complement(complement(as))) | member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((as = complement(complement(as))) | member(f1(as, complement(complement(as))), complement(complement(as))) | member(f1(as, complement(complement(as))), as))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (as = complement(complement(as))) | member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((as = complement(complement(as))) | member(f1(as, complement(complement(as))), complement(complement(as))) | member(f1(as, complement(complement(as))), as))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (as = complement(complement(as))) | member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(complement(as)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[50, 44, 6])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (member(f1(as, complement(complement(as))), as)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[51, 1])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.43 tff(58,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','complement1')).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.43 tff(61,plain,(
% 0.20/0.43 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[60])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(as, complement(complement(as))), as)) | (~member(f1(as, complement(complement(as))), complement(as))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(as, complement(complement(as))), as)) | (~member(f1(as, complement(complement(as))), complement(as))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(as, complement(complement(as))), as)) | (~member(f1(as, complement(complement(as))), complement(as))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(as, complement(complement(as))), as)) | (~member(f1(as, complement(complement(as))), complement(as)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 62, 52, 34])).
% 0.20/0.43 tff(67,plain,(member(f1(as, complement(complement(as))), complement(complement(as)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(as, complement(complement(as))), complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(as, complement(complement(as))), complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(as, complement(complement(as))), complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(as, complement(complement(as))), complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (~member(f1(as, complement(complement(as))), complement(as))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 62, 67])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl(((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : rewrite((((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y)) <=> ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.43 tff(77,axiom,(![Y: $i, X: $i] : (((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','extensionality3')).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.43 tff(80,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((as = complement(complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))) | (~member(f1(as, complement(complement(as))), as)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (as = complement(complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))) | (~member(f1(as, complement(complement(as))), as)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((as = complement(complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))) | (~member(f1(as, complement(complement(as))), as)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (as = complement(complement(as))) | (~member(f1(as, complement(complement(as))), complement(complement(as)))) | (~member(f1(as, complement(complement(as))), as))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~member(f1(as, complement(complement(as))), complement(complement(as)))) | (~member(f1(as, complement(complement(as))), as))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 81, 6])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (~member(f1(as, complement(complement(as))), as)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[85, 67])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), as))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), as))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as)))))) <=> (member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), as))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), as)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), as))),
% 0.20/0.44 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(as, complement(complement(as))), as) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(as, complement(complement(as))), complement(as)) | (~little_set(f1(as, complement(complement(as))))) | member(f1(as, complement(complement(as))), as)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 27, 17, 86, 71])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------