%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET591+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 05:25:56 AM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET591+3 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.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 05:28:55 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(member_type, type, (
% 0.22/0.41 member: ( $i * $i ) > $o)).
% 0.22/0.41 tff(empty_set_type, type, (
% 0.22/0.41 empty_set: $i)).
% 0.22/0.41 tff(tptp_fun_D_0_type, type, (
% 0.22/0.41 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_B_3_type, type, (
% 0.22/0.41 tptp_fun_B_3: $i)).
% 0.22/0.41 tff(subset_type, type, (
% 0.22/0.41 subset: ( $i * $i ) > $o)).
% 0.22/0.41 tff(empty_type, type, (
% 0.22/0.41 empty: $i > $o)).
% 0.22/0.41 tff(tptp_fun_C_1_type, type, (
% 0.22/0.41 tptp_fun_C_1: $i > $i)).
% 0.22/0.41 tff(difference_type, type, (
% 0.22/0.41 difference: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_C_2_type, type, (
% 0.22/0.41 tptp_fun_C_2: $i)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.41 tff(11,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.41 tff(14,plain,(
% 0.22/0.41 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[13])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))) | (subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.41 tff(21,assumption,((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))))), introduced(assumption)).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.22/0.41 tff(24,plain,(~((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))))) | (subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.22/0.41 tff(27,assumption,(member(tptp_fun_D_0(empty_set, B!3), B!3)), introduced(assumption)).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B)))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 (^[B: $i] : refl((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[33, 31])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (^[B: $i] : trans(monotonicity(rewrite(((~empty(B)) | ![C: $i] : (~member(C, B))) <=> ((~empty(B)) | ![C: $i] : (~member(C, B)))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))))), rewrite((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B))) <=> ![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(38,axiom,(![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_defn')).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.42 tff(40,plain,(
% 0.22/0.42 ![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[39])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[42, 29])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(B!3) | member(tptp_fun_C_1(B!3), B!3))) | (~((~empty(B!3)) | ![C: $i] : (~member(C, B!3))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (~((~(empty(B!3) | member(tptp_fun_C_1(B!3), B!3))) | (~((~empty(B!3)) | ![C: $i] : (~member(C, B!3)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (((~(empty(B!3) | member(tptp_fun_C_1(B!3), B!3))) | (~((~empty(B!3)) | ![C: $i] : (~member(C, B!3))))) | ((~empty(B!3)) | ![C: $i] : (~member(C, B!3)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 ((~empty(B!3)) | ![C: $i] : (~member(C, B!3))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (((~(empty(B!3) | member(tptp_fun_C_1(B!3), B!3))) | (~((~empty(B!3)) | ![C: $i] : (~member(C, B!3))))) | (empty(B!3) | member(tptp_fun_C_1(B!3), B!3))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (empty(B!3) | member(tptp_fun_C_1(B!3), B!3)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.22/0.42 tff(50,assumption,(((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3)) <=> member(tptp_fun_C_1(B!3), difference(C!2, B!3))), introduced(assumption)).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(56,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_defn')).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.42 tff(58,plain,(
% 0.22/0.42 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[57])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3)) <=> member(tptp_fun_C_1(B!3), difference(C!2, B!3))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[61, 60, 50])).
% 0.22/0.42 tff(63,plain,(~(((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3)) <=> member(tptp_fun_C_1(B!3), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(64,assumption,(member(tptp_fun_C_1(B!3), B!3)), introduced(assumption)).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3)) | (~member(tptp_fun_C_1(B!3), B!3))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 ((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 ((((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3)) <=> member(tptp_fun_C_1(B!3), difference(C!2, B!3))) | (~((~member(tptp_fun_C_1(B!3), C!2)) | member(tptp_fun_C_1(B!3), B!3))) | (~member(tptp_fun_C_1(B!3), difference(C!2, B!3)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(68,plain,
% 0.22/0.42 (~member(tptp_fun_C_1(B!3), difference(C!2, B!3))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[67, 66, 63])).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~(subset(B!3, difference(C!2, B!3)) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), B!3), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), B!3), difference(C!2, B!3))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(70,plain,
% 0.22/0.42 (~((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~(subset(B!3, difference(C!2, B!3)) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), B!3), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), B!3), difference(C!2, B!3)))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[69, 16])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 (((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~(subset(B!3, difference(C!2, B!3)) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), B!3), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), B!3), difference(C!2, B!3))))))) | ((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 ((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 ((~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))) <=> (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 ((~![B: $i, C: $i] : (subset(B, difference(C, B)) => (B = empty_set))) <=> (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(75,axiom,(~![B: $i, C: $i] : (subset(B, difference(C, B)) => (B = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th50')).
% 0.22/0.42 tff(76,plain,
% 0.22/0.42 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.22/0.42 tff(77,plain,
% 0.22/0.42 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.22/0.42 tff(79,plain,
% 0.22/0.42 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[78, 73])).
% 0.22/0.42 tff(80,plain,(
% 0.22/0.42 ~((~subset(B!3, difference(C!2, B!3))) | (B!3 = empty_set))),
% 0.22/0.42 inference(skolemize,[status(sab)],[79])).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 (subset(B!3, difference(C!2, B!3))),
% 0.22/0.42 inference(or_elim,[status(thm)],[80])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 ((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(83,plain,
% 0.22/0.42 ((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[83, 72])).
% 0.22/0.42 tff(85,plain,
% 0.22/0.42 (((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | ((~member(tptp_fun_C_1(B!3), B!3)) | member(tptp_fun_C_1(B!3), difference(C!2, B!3)))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | (~member(tptp_fun_C_1(B!3), B!3)) | member(tptp_fun_C_1(B!3), difference(C!2, B!3)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 ((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | ((~member(tptp_fun_C_1(B!3), B!3)) | member(tptp_fun_C_1(B!3), difference(C!2, B!3)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(87,plain,
% 0.22/0.42 ((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | (~member(tptp_fun_C_1(B!3), B!3)) | member(tptp_fun_C_1(B!3), difference(C!2, B!3))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.22/0.42 tff(88,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[87, 84, 64, 68])).
% 0.22/0.42 tff(89,plain,(~member(tptp_fun_C_1(B!3), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(90,plain,
% 0.22/0.42 ((~(empty(B!3) | member(tptp_fun_C_1(B!3), B!3))) | empty(B!3) | member(tptp_fun_C_1(B!3), B!3)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(91,plain,
% 0.22/0.42 (empty(B!3)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[90, 89, 49])).
% 0.22/0.42 tff(92,plain,
% 0.22/0.42 ((~((~empty(B!3)) | ![C: $i] : (~member(C, B!3)))) | (~empty(B!3)) | ![C: $i] : (~member(C, B!3))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(93,plain,
% 0.22/0.42 (![C: $i] : (~member(C, B!3))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[92, 91, 47])).
% 0.22/0.42 tff(94,plain,
% 0.22/0.42 ((~![C: $i] : (~member(C, B!3))) | (~member(tptp_fun_D_0(empty_set, B!3), B!3))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(95,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[94, 93, 27])).
% 0.22/0.42 tff(96,plain,(~member(tptp_fun_D_0(empty_set, B!3), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(97,plain,
% 0.22/0.42 (((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)) | member(tptp_fun_D_0(empty_set, B!3), B!3)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(98,plain,
% 0.22/0.42 ((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.22/0.42 tff(99,plain,
% 0.22/0.42 ((~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))) | subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(100,plain,
% 0.22/0.42 ((~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))) | subset(B!3, empty_set)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.22/0.42 tff(101,plain,
% 0.22/0.42 (subset(B!3, empty_set)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[100, 26])).
% 0.22/0.42 tff(102,plain,
% 0.22/0.42 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(103,plain,
% 0.22/0.42 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.22/0.42 tff(104,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(105,plain,
% 0.22/0.42 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.22/0.42 tff(106,plain,
% 0.22/0.42 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(107,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.22/0.42 tff(108,plain,
% 0.22/0.42 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.42 tff(109,plain,(
% 0.22/0.42 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[108])).
% 0.22/0.42 tff(110,plain,
% 0.22/0.42 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.22/0.42 tff(111,plain,
% 0.22/0.42 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.22/0.42 tff(112,plain,
% 0.22/0.42 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(empty_set, B!3)) | (~subset(B!3, empty_set))) <=> (empty_set = B!3)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(113,plain,
% 0.22/0.42 (~(((~subset(empty_set, B!3)) | (~subset(B!3, empty_set))) <=> (empty_set = B!3))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.22/0.42 tff(114,plain,
% 0.22/0.42 ((empty_set = B!3) <=> (B!3 = empty_set)),
% 0.22/0.42 inference(commutativity,[status(thm)],[])).
% 0.22/0.42 tff(115,plain,
% 0.22/0.42 ((B!3 = empty_set) <=> (empty_set = B!3)),
% 0.22/0.42 inference(symmetry,[status(thm)],[114])).
% 0.22/0.42 tff(116,plain,
% 0.22/0.42 ((~(B!3 = empty_set)) <=> (~(empty_set = B!3))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[115])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 (~(B!3 = empty_set)),
% 0.22/0.43 inference(or_elim,[status(thm)],[80])).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 (~(empty_set = B!3)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 ((((~subset(empty_set, B!3)) | (~subset(B!3, empty_set))) <=> (empty_set = B!3)) | ((~subset(empty_set, B!3)) | (~subset(B!3, empty_set))) | (empty_set = B!3)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 ((~subset(empty_set, B!3)) | (~subset(B!3, empty_set))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[119, 118, 113])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 ((~((~subset(empty_set, B!3)) | (~subset(B!3, empty_set)))) | (~subset(empty_set, B!3)) | (~subset(B!3, empty_set))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 ((~subset(empty_set, B!3)) | (~subset(B!3, empty_set))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (~subset(empty_set, B!3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[122, 101])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 ((~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))))) | subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 ((~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))))) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[125, 20])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)) | member(tptp_fun_D_0(B!3, empty_set), empty_set)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 (member(tptp_fun_D_0(B!3, empty_set), empty_set)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.22/0.43 tff(129,plain,
% 0.22/0.43 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[129])).
% 0.22/0.43 tff(131,plain,
% 0.22/0.43 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(132,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.22/0.43 tff(133,plain,
% 0.22/0.43 (![B: $i] : (~member(B, empty_set))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.22/0.43 tff(134,plain,(
% 0.22/0.43 ![B: $i] : (~member(B, empty_set))),
% 0.22/0.43 inference(skolemize,[status(sab)],[133])).
% 0.22/0.43 tff(135,plain,
% 0.22/0.43 (![B: $i] : (~member(B, empty_set))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.22/0.43 tff(136,plain,
% 0.22/0.43 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!3, empty_set), empty_set))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(137,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[136, 135, 128])).
% 0.22/0.43 % SZS output end Proof
% 0.22/0.43 % E exiting
%------------------------------------------------------------------------------