%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU139+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:27:00 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU139+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:07:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(tptp_fun_A_11_type, type, (
% 0.13/0.39 tptp_fun_A_11: $i)).
% 0.13/0.39 tff(tptp_fun_B_10_type, type, (
% 0.13/0.39 tptp_fun_B_10: $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(proper_subset_type, type, (
% 0.13/0.39 proper_subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!10, A!11)) | (~subset(A!11, B!10))) <=> (B!10 = A!11)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~(((~subset(B!10, A!11)) | (~subset(A!11, B!10))) <=> (B!10 = A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & (~(A = B))) <=> (~((~subset(A, B)) | (A = B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))), rewrite((proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))))), rewrite((~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,axiom,(![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_xboole_0')).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))) | (~(((~subset(B!10, A!11)) | (B!10 = A!11)) <=> proper_subset(B!10, A!11)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~(((~subset(B!10, A!11)) | (B!10 = A!11)) <=> proper_subset(B!10, A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))) <=> (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,axiom,(~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_xboole_1')).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.39 tff(31,plain,(
% 0.13/0.39 subset(A!11, B!10) & proper_subset(B!10, A!11)),
% 0.13/0.39 inference(skolemize,[status(sab)],[30])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (proper_subset(B!10, A!11)),
% 0.13/0.39 inference(and_elim,[status(thm)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((((~subset(B!10, A!11)) | (B!10 = A!11)) <=> proper_subset(B!10, A!11)) | (~((~subset(B!10, A!11)) | (B!10 = A!11))) | (~proper_subset(B!10, A!11))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((((~subset(B!10, A!11)) | (B!10 = A!11)) <=> proper_subset(B!10, A!11)) | (~((~subset(B!10, A!11)) | (B!10 = A!11)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (~((~subset(B!10, A!11)) | (B!10 = A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[34, 24])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (((~subset(B!10, A!11)) | (B!10 = A!11)) | (~(B!10 = A!11))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (~(B!10 = A!11)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (((~subset(B!10, A!11)) | (B!10 = A!11)) | subset(B!10, A!11)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (subset(B!10, A!11)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (subset(A!11, B!10)),
% 0.13/0.39 inference(and_elim,[status(thm)],[31])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((~((~subset(B!10, A!11)) | (~subset(A!11, B!10)))) | (~subset(B!10, A!11)) | (~subset(A!11, B!10))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~((~subset(B!10, A!11)) | (~subset(A!11, B!10)))) | (~subset(B!10, A!11))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (~((~subset(B!10, A!11)) | (~subset(A!11, B!10)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ((((~subset(B!10, A!11)) | (~subset(A!11, B!10))) <=> (B!10 = A!11)) | ((~subset(B!10, A!11)) | (~subset(A!11, B!10))) | (B!10 = A!11)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[44, 43, 37, 12])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------