TSTP Solution File: SET931+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:08:41 EDT 2022
% Result : Theorem 0.15s 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n021.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 08:32:29 EDT 2022
% 0.09/0.31 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 tff(empty_set_type, type, (
% 0.15/0.35 empty_set: $i)).
% 0.15/0.35 tff(set_difference_type, type, (
% 0.15/0.35 set_difference: ( $i * $i ) > $i)).
% 0.15/0.35 tff(unordered_pair_type, type, (
% 0.15/0.35 unordered_pair: ( $i * $i ) > $i)).
% 0.15/0.35 tff(tptp_fun_C_2_type, type, (
% 0.15/0.35 tptp_fun_C_2: $i)).
% 0.15/0.35 tff(tptp_fun_B_3_type, type, (
% 0.15/0.35 tptp_fun_B_3: $i)).
% 0.15/0.35 tff(tptp_fun_A_4_type, type, (
% 0.15/0.35 tptp_fun_A_4: $i)).
% 0.15/0.35 tff(singleton_type, type, (
% 0.15/0.35 singleton: $i > $i)).
% 0.15/0.35 tff(subset_type, type, (
% 0.15/0.35 subset: ( $i * $i ) > $o)).
% 0.15/0.35 tff(1,assumption,(~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))), introduced(assumption)).
% 0.15/0.35 tff(2,plain,
% 0.15/0.35 (((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> ((~(A!4 = empty_set)) & (~(A!4 = singleton(B!3))) & (~(A!4 = singleton(C!2))) & (~(A!4 = unordered_pair(B!3, C!2))))) <=> ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(3,plain,
% 0.15/0.35 ((~((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> (~((~(A!4 = empty_set)) & (~(A!4 = singleton(B!3))) & (~(A!4 = singleton(C!2))) & (~(A!4 = unordered_pair(B!3, C!2))))))) <=> ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> ((~(A!4 = empty_set)) & (~(A!4 = singleton(B!3))) & (~(A!4 = singleton(C!2))) & (~(A!4 = unordered_pair(B!3, C!2)))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(4,plain,
% 0.15/0.35 ((~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))) <=> (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C)))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(5,plain,
% 0.15/0.35 ((~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((((~(A = empty_set)) & (~(A = singleton(B)))) & (~(A = singleton(C)))) & (~(A = unordered_pair(B, C))))))) <=> (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C)))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(6,axiom,(~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((((~(A = empty_set)) & (~(A = singleton(B)))) & (~(A = singleton(C)))) & (~(A = unordered_pair(B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t75_zfmisc_1')).
% 0.15/0.35 tff(7,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.15/0.35 tff(8,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.15/0.35 tff(11,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.15/0.35 tff(12,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 (~![A: $i, B: $i, C: $i] : ((set_difference(A, unordered_pair(B, C)) = empty_set) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.15/0.35 tff(14,plain,(
% 0.15/0.35 ~((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> (~((~(A!4 = empty_set)) & (~(A!4 = singleton(B!3))) & (~(A!4 = singleton(C!2))) & (~(A!4 = unordered_pair(B!3, C!2))))))),
% 0.15/0.35 inference(skolemize,[status(sab)],[13])).
% 0.15/0.35 tff(15,plain,
% 0.15/0.35 ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> ((~(A!4 = empty_set)) & (~(A!4 = singleton(B!3))) & (~(A!4 = singleton(C!2))) & (~(A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[14, 3])).
% 0.15/0.35 tff(16,plain,
% 0.15/0.35 ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.15/0.35 tff(17,plain,
% 0.15/0.35 ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) | ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))) | (~((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(18,plain,
% 0.15/0.35 ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) | ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 (set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[18, 1])).
% 0.15/0.35 tff(20,plain,
% 0.15/0.35 (^[A: $i, B: $i, C: $i] : refl((subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set))) <=> (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set))) <=> ![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[20])).
% 0.15/0.35 tff(22,plain,
% 0.15/0.35 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C)))))) <=> (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(23,plain,
% 0.15/0.35 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C)))))) <=> ![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[22])).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C)))))) <=> ![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(25,plain,
% 0.15/0.35 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, unordered_pair(B, C)) <=> (~((((~(A = empty_set)) & (~(A = singleton(B)))) & (~(A = singleton(C)))) & (~(A = unordered_pair(B, C)))))) <=> (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C)))))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(26,plain,
% 0.15/0.36 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((((~(A = empty_set)) & (~(A = singleton(B)))) & (~(A = singleton(C)))) & (~(A = unordered_pair(B, C)))))) <=> ![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[25])).
% 0.15/0.36 tff(27,axiom,(![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((((~(A = empty_set)) & (~(A = singleton(B)))) & (~(A = singleton(C)))) & (~(A = unordered_pair(B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l46_zfmisc_1')).
% 0.15/0.36 tff(28,plain,
% 0.15/0.36 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.15/0.36 tff(29,plain,
% 0.15/0.36 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.15/0.36 tff(30,plain,(
% 0.15/0.36 ![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> (~((~(A = empty_set)) & (~(A = singleton(B))) & (~(A = singleton(C))) & (~(A = unordered_pair(B, C))))))),
% 0.15/0.36 inference(skolemize,[status(sab)],[29])).
% 0.15/0.36 tff(31,plain,
% 0.15/0.36 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.15/0.36 tff(32,plain,
% 0.15/0.36 (![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.15/0.36 tff(33,plain,
% 0.15/0.36 (((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(34,plain,
% 0.15/0.36 ((subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = unordered_pair(B!3, C!2)) | (A!4 = singleton(C!2)) | (A!4 = singleton(B!3)) | (A!4 = empty_set))) <=> (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(35,plain,
% 0.15/0.36 (((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = unordered_pair(B!3, C!2)) | (A!4 = singleton(C!2)) | (A!4 = singleton(B!3)) | (A!4 = empty_set)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))))),
% 0.15/0.36 inference(monotonicity,[status(thm)],[34])).
% 0.15/0.36 tff(36,plain,
% 0.15/0.36 (((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = unordered_pair(B!3, C!2)) | (A!4 = singleton(C!2)) | (A!4 = singleton(B!3)) | (A!4 = empty_set)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))))),
% 0.15/0.36 inference(transitivity,[status(thm)],[35, 33])).
% 0.15/0.36 tff(37,plain,
% 0.15/0.36 ((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = unordered_pair(B!3, C!2)) | (A!4 = singleton(C!2)) | (A!4 = singleton(B!3)) | (A!4 = empty_set)))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(38,plain,
% 0.15/0.36 ((~![A: $i, B: $i, C: $i] : (subset(A, unordered_pair(B, C)) <=> ((A = unordered_pair(B, C)) | (A = singleton(C)) | (A = singleton(B)) | (A = empty_set)))) | (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.15/0.36 tff(39,plain,
% 0.15/0.36 (subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.15/0.36 tff(40,plain,
% 0.15/0.36 ((~(subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))) | (~subset(A!4, unordered_pair(B!3, C!2))) | ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(41,plain,
% 0.15/0.36 ((~subset(A!4, unordered_pair(B!3, C!2))) | ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.15/0.36 tff(42,plain,
% 0.15/0.36 (~subset(A!4, unordered_pair(B!3, C!2))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[41, 1])).
% 0.15/0.36 tff(43,plain,
% 0.15/0.36 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(44,plain,
% 0.15/0.36 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[43])).
% 0.15/0.36 tff(45,plain,
% 0.15/0.36 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(46,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_xboole_1')).
% 0.15/0.36 tff(47,plain,
% 0.15/0.36 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.15/0.36 tff(48,plain,(
% 0.15/0.36 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.15/0.36 inference(skolemize,[status(sab)],[47])).
% 0.15/0.36 tff(49,plain,
% 0.15/0.36 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.15/0.36 tff(50,plain,
% 0.15/0.36 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> subset(A!4, unordered_pair(B!3, C!2)))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(51,plain,
% 0.15/0.36 ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> subset(A!4, unordered_pair(B!3, C!2))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.15/0.36 tff(52,plain,
% 0.15/0.36 ((~((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> subset(A!4, unordered_pair(B!3, C!2)))) | (~(set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set)) | subset(A!4, unordered_pair(B!3, C!2))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(53,plain,
% 0.15/0.36 ((~(set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set)) | subset(A!4, unordered_pair(B!3, C!2))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.15/0.37 tff(54,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[53, 42, 19])).
% 0.15/0.37 tff(55,plain,((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(56,plain,
% 0.15/0.37 ((~(set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set)) | (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2)))) | (~((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(57,plain,
% 0.15/0.37 ((~(set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set)) | (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[56, 16])).
% 0.15/0.37 tff(58,plain,
% 0.15/0.37 (~(set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set)),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[57, 55])).
% 0.15/0.37 tff(59,plain,
% 0.15/0.37 ((~(subset(A!4, unordered_pair(B!3, C!2)) <=> ((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))) | subset(A!4, unordered_pair(B!3, C!2)) | (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(60,plain,
% 0.15/0.37 (subset(A!4, unordered_pair(B!3, C!2)) | (~((A!4 = empty_set) | (A!4 = singleton(B!3)) | (A!4 = singleton(C!2)) | (A!4 = unordered_pair(B!3, C!2))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[59, 39])).
% 0.15/0.37 tff(61,plain,
% 0.15/0.37 (subset(A!4, unordered_pair(B!3, C!2))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.15/0.37 tff(62,plain,
% 0.15/0.37 ((~((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) <=> subset(A!4, unordered_pair(B!3, C!2)))) | (set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) | (~subset(A!4, unordered_pair(B!3, C!2)))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(63,plain,
% 0.15/0.37 ((set_difference(A!4, unordered_pair(B!3, C!2)) = empty_set) | (~subset(A!4, unordered_pair(B!3, C!2)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[62, 51])).
% 0.15/0.37 tff(64,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[63, 61, 58])).
% 0.15/0.37 % SZS output end Proof
%------------------------------------------------------------------------------