%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET604+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:25:58 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET604+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 Jun 20 05:29:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_B_2_type, type, (
% 0.12/0.37 tptp_fun_B_2: $i)).
% 0.12/0.37 tff(empty_set_type, type, (
% 0.12/0.37 empty_set: $i)).
% 0.12/0.37 tff(difference_type, type, (
% 0.12/0.37 difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl(((difference(B, C) = empty_set) <=> subset(B, C)) <=> ((difference(B, C) = empty_set) <=> subset(B, C)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C)) <=> ![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C)) <=> ![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_empty_set')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))) | ((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 ((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~![B: $i] : (difference(empty_set, B) = empty_set)) <=> (~![B: $i] : (difference(empty_set, B) = empty_set))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(11,axiom,(~![B: $i] : (difference(empty_set, B) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_no_difference_with_empty_set')).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.37 tff(16,plain,(
% 0.12/0.37 ~(difference(empty_set, B!2) = empty_set)),
% 0.12/0.37 inference(skolemize,[status(sab)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2))) | (difference(empty_set, B!2) = empty_set) | (~subset(empty_set, B!2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2))) | (~subset(empty_set, B!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (~subset(empty_set, B!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[18, 9])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (^[B: $i] : refl(subset(empty_set, B) <=> subset(empty_set, B))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,axiom,(![B: $i] : subset(empty_set, B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_subset')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![B: $i] : subset(empty_set, B)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,(
% 0.12/0.37 ![B: $i] : subset(empty_set, B)),
% 0.12/0.37 inference(skolemize,[status(sab)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![B: $i] : subset(empty_set, B)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~![B: $i] : subset(empty_set, B)) | subset(empty_set, B!2)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[27, 26, 19])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------