%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET002+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 05:24:43 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SET002+3 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 03:59:55 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(subset_type, type, (
% 0.11/0.36 subset: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_B_2_type, type, (
% 0.11/0.36 tptp_fun_B_2: $i)).
% 0.11/0.36 tff(union_type, type, (
% 0.11/0.36 union: ( $i * $i ) > $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~![B: $i] : (union(B, B) = B)) <=> (~![B: $i] : (union(B, B) = B))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,axiom,(~![B: $i] : (union(B, B) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_idempotency_of_union')).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (~![B: $i] : (union(B, B) = B)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![B: $i] : (union(B, B) = B)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![B: $i] : (union(B, B) = B)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![B: $i] : (union(B, B) = B)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,(
% 0.11/0.36 ~(union(B!2, B!2) = B!2)),
% 0.11/0.36 inference(skolemize,[status(sab)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (^[B: $i, C: $i] : refl(((~subset(B, C)) | (union(B, C) = C)) <=> ((~subset(B, C)) | (union(B, C) = C)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[B: $i, C: $i] : rewrite((subset(B, C) => (union(B, C) = C)) <=> ((~subset(B, C)) | (union(B, C) = C)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.36 tff(13,axiom,(![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_union')).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.11/0.36 tff(16,plain,(
% 0.11/0.36 ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(skolemize,[status(sab)],[15])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | ((~subset(B!2, B!2)) | (union(B!2, B!2) = B!2))) <=> ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | (~subset(B!2, B!2)) | (union(B!2, B!2) = B!2))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | ((~subset(B!2, B!2)) | (union(B!2, B!2) = B!2))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | (~subset(B!2, B!2)) | (union(B!2, B!2) = B!2)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (~subset(B!2, B!2)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[20, 17, 7])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (^[B: $i] : refl(subset(B, B) <=> subset(B, B))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![B: $i] : subset(B, B) <=> ![B: $i] : subset(B, B)),
% 0.11/0.36 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (![B: $i] : subset(B, B) <=> ![B: $i] : subset(B, B)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(25,axiom,(![B: $i] : subset(B, B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_of_subset')).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (![B: $i] : subset(B, B)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.36 tff(27,plain,(
% 0.11/0.36 ![B: $i] : subset(B, B)),
% 0.11/0.36 inference(skolemize,[status(sab)],[26])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (![B: $i] : subset(B, B)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ((~![B: $i] : subset(B, B)) | subset(B!2, B!2)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------