%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU122+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:26:56 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU122+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:06:11 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(in_type, type, (
% 0.21/0.38 in: ( $i * $i ) > $o)).
% 0.21/0.38 tff(empty_set_type, type, (
% 0.21/0.38 empty_set: $i)).
% 0.21/0.38 tff(tptp_fun_C_0_type, type, (
% 0.21/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.38 tff(tptp_fun_A_3_type, type, (
% 0.21/0.38 tptp_fun_A_3: $i)).
% 0.21/0.38 tff(subset_type, type, (
% 0.21/0.38 subset: ( $i * $i ) > $o)).
% 0.21/0.38 tff(empty_type, type, (
% 0.21/0.38 empty: $i > $o)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.39 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.39 tff(14,plain,(
% 0.21/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(empty_set, A!3)) | ![C: $i] : ((~in(C, empty_set)) | in(C, A!3)))) | (~(subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3)))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~((~((~subset(empty_set, A!3)) | ![C: $i] : ((~in(C, empty_set)) | in(C, A!3)))) | (~(subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (((~((~subset(empty_set, A!3)) | ![C: $i] : ((~in(C, empty_set)) | in(C, A!3)))) | (~(subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3)))))) | (subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![A: $i] : subset(empty_set, A)) <=> (~![A: $i] : subset(empty_set, A))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,axiom,(~![A: $i] : subset(empty_set, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_xboole_1')).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (~![A: $i] : subset(empty_set, A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (~![A: $i] : subset(empty_set, A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (~![A: $i] : subset(empty_set, A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (~![A: $i] : subset(empty_set, A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.39 tff(27,plain,(
% 0.21/0.39 ~subset(empty_set, A!3)),
% 0.21/0.39 inference(skolemize,[status(sab)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~(subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~(subset(empty_set, A!3) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3))))) | (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (~((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (((~in(tptp_fun_C_0(A!3, empty_set), empty_set)) | in(tptp_fun_C_0(A!3, empty_set), A!3)) | in(tptp_fun_C_0(A!3, empty_set), empty_set)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (in(tptp_fun_C_0(A!3, empty_set), empty_set)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(38,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,(
% 0.21/0.39 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[39])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (empty(empty_set) <=> empty(empty_set)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(44,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (empty(empty_set)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_0(A!3, empty_set), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_0(A!3, empty_set), empty_set)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_0(A!3, empty_set), empty_set)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_0(A!3, empty_set), empty_set))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[48, 45, 42, 32])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------