%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET063+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:25:03 AM UTC 2025
% Result : Theorem 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET063+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 04:09:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.39 % SZS status Theorem
% 0.22/0.39 % SZS output start Proof
% 0.22/0.39 tff(subset_type, type, (
% 0.22/0.39 subset: ( $i * $i ) > $o)).
% 0.22/0.39 tff(tptp_fun_B_2_type, type, (
% 0.22/0.39 tptp_fun_B_2: $i)).
% 0.22/0.39 tff(empty_set_type, type, (
% 0.22/0.39 empty_set: $i)).
% 0.22/0.39 tff(1,plain,
% 0.22/0.39 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(2,plain,
% 0.22/0.39 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.39 tff(3,plain,
% 0.22/0.39 (^[B: $i, C: $i] : trans(trans(monotonicity(rewrite((subset(B, C) & subset(C, B)) <=> (~((~subset(B, C)) | (~subset(C, B))))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))), rewrite(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))), rewrite((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(4,plain,
% 0.22/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.39 tff(5,plain,
% 0.22/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(6,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.22/0.39 tff(7,plain,
% 0.22/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.39 tff(8,plain,(
% 0.22/0.39 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[7])).
% 0.22/0.39 tff(9,plain,
% 0.22/0.39 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.22/0.39 tff(10,plain,
% 0.22/0.39 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.39 tff(11,plain,
% 0.22/0.39 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))) <=> (B!2 = empty_set)))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(12,plain,
% 0.22/0.39 (~(((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))) <=> (B!2 = empty_set))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.22/0.39 tff(13,plain,
% 0.22/0.39 ((~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))) <=> (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(14,plain,
% 0.22/0.39 ((~![B: $i] : (subset(B, empty_set) => (B = empty_set))) <=> (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(15,axiom,(~![B: $i] : (subset(B, empty_set) => (B = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_subset_of_empty_set_is_empty_set')).
% 0.22/0.39 tff(16,plain,
% 0.22/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.39 tff(17,plain,
% 0.22/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.22/0.39 tff(18,plain,
% 0.22/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.22/0.39 tff(19,plain,
% 0.22/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.22/0.39 tff(20,plain,(
% 0.22/0.39 ~((~subset(B!2, empty_set)) | (B!2 = empty_set))),
% 0.22/0.39 inference(skolemize,[status(sab)],[19])).
% 0.22/0.39 tff(21,plain,
% 0.22/0.39 (~(B!2 = empty_set)),
% 0.22/0.39 inference(or_elim,[status(thm)],[20])).
% 0.22/0.39 tff(22,plain,
% 0.22/0.39 ((((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))) <=> (B!2 = empty_set)) | ((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))) | (B!2 = empty_set)),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 ((((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))) <=> (B!2 = empty_set)) | ((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 ((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 (subset(B!2, empty_set)),
% 0.22/0.40 inference(or_elim,[status(thm)],[20])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 ((~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))) | (~subset(B!2, empty_set)) | (~subset(empty_set, B!2))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 ((~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))) | (~subset(empty_set, B!2))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 (~subset(empty_set, B!2)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 (^[B: $i] : refl(subset(empty_set, B) <=> subset(empty_set, B))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.22/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(32,axiom,(![B: $i] : subset(empty_set, B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_subset')).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 (![B: $i] : subset(empty_set, B)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.40 tff(34,plain,(
% 0.22/0.40 ![B: $i] : subset(empty_set, B)),
% 0.22/0.40 inference(skolemize,[status(sab)],[33])).
% 0.22/0.40 tff(35,plain,
% 0.22/0.40 (![B: $i] : subset(empty_set, B)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.22/0.40 tff(36,plain,
% 0.22/0.40 ((~![B: $i] : subset(empty_set, B)) | subset(empty_set, B!2)),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(37,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.22/0.40 % SZS output end Proof
% 0.22/0.40 % E exiting
%------------------------------------------------------------------------------