%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET632+3 : TPTP v9.0.0. Released v2.2.0.
% 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 05:26:04 AM UTC 2025
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET632+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.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 05:32:26 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 tff(member_type, type, (
% 0.21/0.50 member: ( $i * $i ) > $o)).
% 0.21/0.50 tff(tptp_fun_B_5_type, type, (
% 0.21/0.50 tptp_fun_B_5: $i)).
% 0.21/0.50 tff(tptp_fun_D_0_type, type, (
% 0.21/0.50 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.21/0.50 tff(empty_set_type, type, (
% 0.21/0.50 empty_set: $i)).
% 0.21/0.50 tff(subset_type, type, (
% 0.21/0.50 subset: ( $i * $i ) > $o)).
% 0.21/0.50 tff(empty_type, type, (
% 0.21/0.50 empty: $i > $o)).
% 0.21/0.50 tff(tptp_fun_C_2_type, type, (
% 0.21/0.50 tptp_fun_C_2: $i > $i)).
% 0.21/0.50 tff(disjoint_type, type, (
% 0.21/0.50 disjoint: ( $i * $i ) > $o)).
% 0.21/0.50 tff(tptp_fun_D_3_type, type, (
% 0.21/0.50 tptp_fun_D_3: $i)).
% 0.21/0.50 tff(tptp_fun_C_4_type, type, (
% 0.21/0.50 tptp_fun_C_4: $i)).
% 0.21/0.50 tff(intersect_type, type, (
% 0.21/0.50 intersect: ( $i * $i ) > $o)).
% 0.21/0.50 tff(tptp_fun_D_1_type, type, (
% 0.21/0.50 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.21/0.50 tff(1,plain,
% 0.21/0.50 (^[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))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(2,plain,
% 0.21/0.50 (![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)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.50 tff(3,plain,
% 0.21/0.50 (^[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))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(4,plain,
% 0.21/0.50 (![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)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.50 tff(5,plain,
% 0.21/0.50 (![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)))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.50 tff(6,plain,
% 0.21/0.50 (^[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)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(7,plain,
% 0.21/0.51 (![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)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.51 tff(8,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(9,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(10,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.51 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')).
% 0.21/0.51 tff(12,plain,
% 0.21/0.51 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.51 tff(13,plain,
% 0.21/0.51 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.51 tff(14,plain,(
% 0.21/0.51 ![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)))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[13])).
% 0.21/0.51 tff(15,plain,
% 0.21/0.51 (![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)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (![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)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.51 tff(17,plain,
% 0.21/0.51 ((~![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!5, empty_set)) | ![D: $i] : ((~member(D, B!5)) | member(D, empty_set)))) | (~(subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set)))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(18,plain,
% 0.21/0.51 (~((~((~subset(B!5, empty_set)) | ![D: $i] : ((~member(D, B!5)) | member(D, empty_set)))) | (~(subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.51 tff(19,plain,
% 0.21/0.51 (((~((~subset(B!5, empty_set)) | ![D: $i] : ((~member(D, B!5)) | member(D, empty_set)))) | (~(subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set)))))) | (subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(20,plain,
% 0.21/0.51 (subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.51 tff(21,assumption,(member(tptp_fun_C_2(empty_set), empty_set)), introduced(assumption)).
% 0.21/0.51 tff(22,plain,
% 0.21/0.51 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(23,plain,
% 0.21/0.51 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.51 tff(24,plain,
% 0.21/0.51 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(25,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.21/0.51 tff(26,plain,
% 0.21/0.51 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.51 tff(27,plain,(
% 0.21/0.51 ![B: $i] : (~member(B, empty_set))),
% 0.21/0.51 inference(skolemize,[status(sab)],[26])).
% 0.21/0.51 tff(28,plain,
% 0.21/0.51 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.51 tff(29,plain,
% 0.21/0.51 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_C_2(empty_set), empty_set))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(30,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.21/0.51 tff(31,plain,(~member(tptp_fun_C_2(empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(33,plain,
% 0.21/0.51 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.51 tff(34,plain,
% 0.21/0.51 (^[B: $i] : refl((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(35,plain,
% 0.21/0.51 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.51 tff(36,plain,
% 0.21/0.51 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(37,plain,
% 0.21/0.51 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.51 tff(38,plain,
% 0.21/0.51 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.51 tff(39,plain,
% 0.21/0.51 (^[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_2(B), B))) <=> (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))))), rewrite((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(40,plain,
% 0.21/0.51 (![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.51 tff(41,plain,
% 0.21/0.51 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B))) <=> ![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(42,axiom,(![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_defn')).
% 0.21/0.51 tff(43,plain,
% 0.21/0.51 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.51 tff(44,plain,(
% 0.21/0.51 ![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[43])).
% 0.21/0.51 tff(45,plain,
% 0.21/0.51 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.21/0.51 tff(46,plain,
% 0.21/0.51 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.51 tff(47,plain,
% 0.21/0.51 (![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[46, 33])).
% 0.21/0.51 tff(48,plain,
% 0.21/0.51 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(49,plain,
% 0.21/0.51 (~((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.51 tff(50,plain,
% 0.21/0.51 (((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))))) | (empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(51,plain,
% 0.21/0.51 (empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.51 tff(52,plain,
% 0.21/0.51 ((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(53,plain,
% 0.21/0.51 (empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.51 tff(54,plain,
% 0.21/0.51 (empty(empty_set)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[53, 31])).
% 0.21/0.51 tff(55,plain,
% 0.21/0.51 (((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))))) | ((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(56,plain,
% 0.21/0.51 ((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.21/0.51 tff(57,plain,
% 0.21/0.51 ((~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set)))) | (~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(58,plain,
% 0.21/0.51 ((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.51 tff(59,plain,
% 0.21/0.51 (![C: $i] : (~member(C, empty_set))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.21/0.51 tff(60,assumption,(member(tptp_fun_D_0(B!5, empty_set), empty_set)), introduced(assumption)).
% 0.21/0.51 tff(61,assumption,(![C: $i] : (~member(C, empty_set))), introduced(assumption)).
% 0.21/0.51 tff(62,plain,
% 0.21/0.51 ((~![C: $i] : (~member(C, empty_set))) | (~member(tptp_fun_D_0(B!5, empty_set), empty_set))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(63,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[62, 61, 60])).
% 0.21/0.51 tff(64,plain,((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | (~![C: $i] : (~member(C, empty_set)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(65,plain,
% 0.21/0.51 (~member(tptp_fun_D_0(B!5, empty_set), empty_set)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.21/0.51 tff(66,plain,
% 0.21/0.51 (((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)) | member(tptp_fun_D_0(B!5, empty_set), empty_set)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(67,plain,
% 0.21/0.51 ((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.21/0.51 tff(68,assumption,((~((~subset(empty_set, B!5)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!5)))) | (~(subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)))))), introduced(assumption)).
% 0.21/0.51 tff(69,plain,
% 0.21/0.51 ((~![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!5)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!5)))) | (~(subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(70,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[69, 16, 68])).
% 0.21/0.51 tff(71,plain,(~((~((~subset(empty_set, B!5)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!5)))) | (~(subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(72,plain,
% 0.21/0.51 (((~((~subset(empty_set, B!5)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!5)))) | (~(subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)))))) | (subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(73,plain,
% 0.21/0.51 (subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.51 tff(74,plain,
% 0.21/0.51 ((~(subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5))))) | subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(75,plain,
% 0.21/0.51 (subset(empty_set, B!5) | (~((~member(tptp_fun_D_0(B!5, empty_set), empty_set)) | member(tptp_fun_D_0(B!5, empty_set), B!5)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.51 tff(76,plain,
% 0.21/0.51 (subset(empty_set, B!5)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[75, 67])).
% 0.21/0.51 tff(77,plain,
% 0.21/0.51 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(78,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.51 tff(79,plain,
% 0.21/0.51 (^[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)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(80,plain,
% 0.21/0.51 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.51 tff(81,plain,
% 0.21/0.51 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(82,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.21/0.51 tff(83,plain,
% 0.21/0.51 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.51 tff(84,plain,(
% 0.21/0.51 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[83])).
% 0.21/0.51 tff(85,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.51 tff(86,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(empty_set, B!5)) | (~subset(B!5, empty_set))) <=> (empty_set = B!5)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (~(((~subset(empty_set, B!5)) | (~subset(B!5, empty_set))) <=> (empty_set = B!5))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.21/0.51 tff(89,plain,
% 0.21/0.51 ((empty_set = B!5) <=> (B!5 = empty_set)),
% 0.21/0.51 inference(commutativity,[status(thm)],[])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 ((B!5 = empty_set) <=> (empty_set = B!5)),
% 0.21/0.51 inference(symmetry,[status(thm)],[89])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 ((~(B!5 = empty_set)) <=> (~(empty_set = B!5))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 ((~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 ((~![B: $i, C: $i, D: $i] : (((subset(B, C) & subset(B, D)) & disjoint(C, D)) => (B = empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(94,axiom,(~![B: $i, C: $i, D: $i] : (((subset(B, C) & subset(B, D)) & disjoint(C, D)) => (B = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th114')).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & disjoint(C, D))) | (B = empty_set))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[97, 92])).
% 0.21/0.51 tff(99,plain,(
% 0.21/0.51 ~((~(subset(B!5, C!4) & subset(B!5, D!3) & disjoint(C!4, D!3))) | (B!5 = empty_set))),
% 0.21/0.51 inference(skolemize,[status(sab)],[98])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (~(B!5 = empty_set)),
% 0.21/0.51 inference(or_elim,[status(thm)],[99])).
% 0.21/0.51 tff(101,plain,
% 0.21/0.51 (~(empty_set = B!5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[100, 91])).
% 0.21/0.51 tff(102,plain,
% 0.21/0.51 ((((~subset(empty_set, B!5)) | (~subset(B!5, empty_set))) <=> (empty_set = B!5)) | ((~subset(empty_set, B!5)) | (~subset(B!5, empty_set))) | (empty_set = B!5)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 ((~subset(empty_set, B!5)) | (~subset(B!5, empty_set))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[102, 101, 88])).
% 0.21/0.51 tff(104,plain,
% 0.21/0.51 ((~((~subset(empty_set, B!5)) | (~subset(B!5, empty_set)))) | (~subset(empty_set, B!5)) | (~subset(B!5, empty_set))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(105,plain,
% 0.21/0.51 ((~subset(empty_set, B!5)) | (~subset(B!5, empty_set))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.51 tff(106,plain,
% 0.21/0.51 (~subset(B!5, empty_set)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[105, 76])).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 ((~(subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set))))) | subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 ((~(subset(B!5, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set))))) | (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 (~((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[108, 20])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 (((~member(tptp_fun_D_0(empty_set, B!5), B!5)) | member(tptp_fun_D_0(empty_set, B!5), empty_set)) | member(tptp_fun_D_0(empty_set, B!5), B!5)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 (member(tptp_fun_D_0(empty_set, B!5), B!5)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[112])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_1(C, B), B) & member(tptp_fun_D_1(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))), ((((~intersect(B, C)) | (member(tptp_fun_D_1(C, B), B) & member(tptp_fun_D_1(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_1(C, B), B) & member(tptp_fun_D_1(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_1(C, B), B) & member(tptp_fun_D_1(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(120,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersect_defn')).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.51 tff(122,plain,(
% 0.21/0.51 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_1(C, B), B) & member(tptp_fun_D_1(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[121])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 ((~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, D!3)) | (~member(D, B!5))))))) <=> (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, D!3)) | (~member(D, B!5)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.52 tff(128,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, D!3)) | (~member(D, B!5)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.52 tff(129,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, D!3)) | (~member(D, B!5)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(130,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.52 tff(131,plain,
% 0.21/0.52 (~((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[130, 124])).
% 0.21/0.52 tff(132,plain,
% 0.21/0.52 (((~((~intersect(B!5, D!3)) | (~((~member(tptp_fun_D_1(D!3, B!5), B!5)) | (~member(tptp_fun_D_1(D!3, B!5), D!3)))))) | (~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))) | (intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(133,plain,
% 0.21/0.52 (intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.52 tff(134,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(135,plain,
% 0.21/0.52 ((~((~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), D!3)) | (~member(tptp_fun_D_1(B!5, D!3), B!5)))))) | (~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))))) <=> (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(136,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), D!3)) | (~member(tptp_fun_D_1(B!5, D!3), B!5)))))) | (~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[135])).
% 0.21/0.52 tff(137,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), D!3)) | (~member(tptp_fun_D_1(B!5, D!3), B!5)))))) | (~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[136, 134])).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), D!3)) | (~member(tptp_fun_D_1(B!5, D!3), B!5)))))) | (~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (~((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[139, 124])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (((~(intersect(D!3, B!5) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | (~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))))))) | ((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 ((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.21/0.52 tff(143,assumption,(~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))), introduced(assumption)).
% 0.21/0.52 tff(144,plain,
% 0.21/0.52 (((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))) | member(tptp_fun_D_1(B!5, D!3), D!3)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (member(tptp_fun_D_1(B!5, D!3), D!3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3)))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(147,plain,
% 0.21/0.52 ((~((~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), D!3)) | (~member(tptp_fun_D_1(C!4, D!3), C!4)))))) | (~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))))) <=> (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), D!3)) | (~member(tptp_fun_D_1(C!4, D!3), C!4)))))) | (~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), D!3)) | (~member(tptp_fun_D_1(C!4, D!3), C!4)))))) | (~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), D!3)) | (~member(tptp_fun_D_1(C!4, D!3), C!4)))))) | (~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_1(C, B), B)) | (~member(tptp_fun_D_1(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (~((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3)))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[151, 124])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 (((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | (~((~intersect(D!3, C!4)) | (~((~member(tptp_fun_D_1(C!4, D!3), C!4)) | (~member(tptp_fun_D_1(C!4, D!3), D!3))))))) | (intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 (intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.52 tff(155,plain,
% 0.21/0.52 (^[B: $i, C: $i] : refl((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(156,plain,
% 0.21/0.52 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.52 tff(157,plain,
% 0.21/0.52 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(158,plain,
% 0.21/0.52 (^[B: $i, C: $i] : trans(rewrite((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), rewrite((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), ((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(159,plain,
% 0.21/0.52 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.52 tff(160,axiom,(![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','disjoint_defn')).
% 0.21/0.52 tff(161,plain,
% 0.21/0.52 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.52 tff(162,plain,
% 0.21/0.52 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.21/0.52 tff(163,plain,(
% 0.21/0.52 ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[162])).
% 0.21/0.52 tff(164,plain,
% 0.21/0.52 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.21/0.52 tff(165,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))) | (~(intersect(C!4, D!3) <=> disjoint(C!4, D!3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(166,plain,
% 0.21/0.52 (~(intersect(C!4, D!3) <=> disjoint(C!4, D!3))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.21/0.52 tff(167,plain,
% 0.21/0.52 (subset(B!5, C!4) & subset(B!5, D!3) & disjoint(C!4, D!3)),
% 0.21/0.52 inference(or_elim,[status(thm)],[99])).
% 0.21/0.52 tff(168,plain,
% 0.21/0.52 (disjoint(C!4, D!3)),
% 0.21/0.52 inference(and_elim,[status(thm)],[167])).
% 0.21/0.52 tff(169,plain,
% 0.21/0.52 ((intersect(C!4, D!3) <=> disjoint(C!4, D!3)) | (~intersect(C!4, D!3)) | (~disjoint(C!4, D!3))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(170,plain,
% 0.21/0.52 ((intersect(C!4, D!3) <=> disjoint(C!4, D!3)) | (~intersect(C!4, D!3))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.52 tff(171,plain,
% 0.21/0.52 (~intersect(C!4, D!3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[170, 166])).
% 0.21/0.52 tff(172,plain,
% 0.21/0.52 (^[B: $i, C: $i] : refl(((~intersect(B, C)) | intersect(C, B)) <=> ((~intersect(B, C)) | intersect(C, B)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(173,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B)) <=> ![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[172])).
% 0.21/0.52 tff(174,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B)) <=> ![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(175,plain,
% 0.21/0.52 (^[B: $i, C: $i] : rewrite((intersect(B, C) => intersect(C, B)) <=> ((~intersect(B, C)) | intersect(C, B)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(176,plain,
% 0.21/0.52 (![B: $i, C: $i] : (intersect(B, C) => intersect(C, B)) <=> ![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.52 tff(177,axiom,(![B: $i, C: $i] : (intersect(B, C) => intersect(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_of_intersect')).
% 0.21/0.52 tff(178,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.52 tff(179,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.21/0.52 tff(180,plain,(
% 0.21/0.52 ![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(skolemize,[status(sab)],[179])).
% 0.21/0.52 tff(181,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.21/0.52 tff(182,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | ((~intersect(D!3, C!4)) | intersect(C!4, D!3))) <=> ((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | (~intersect(D!3, C!4)) | intersect(C!4, D!3))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(183,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | ((~intersect(D!3, C!4)) | intersect(C!4, D!3))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(184,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | (~intersect(D!3, C!4)) | intersect(C!4, D!3)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.52 tff(185,plain,
% 0.21/0.52 (~intersect(D!3, C!4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[184, 181, 171])).
% 0.21/0.52 tff(186,plain,
% 0.21/0.52 ((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(187,plain,
% 0.21/0.52 ((~(intersect(D!3, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3))))) | ![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.21/0.52 tff(188,plain,
% 0.21/0.52 (![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[187, 154])).
% 0.21/0.52 tff(189,plain,
% 0.21/0.52 (((~![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))) | ((~member(tptp_fun_D_1(B!5, D!3), C!4)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))) <=> ((~![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))) | (~member(tptp_fun_D_1(B!5, D!3), C!4)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(190,plain,
% 0.21/0.52 ((~![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))) | ((~member(tptp_fun_D_1(B!5, D!3), C!4)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(191,plain,
% 0.21/0.52 ((~![D: $i] : ((~member(D, C!4)) | (~member(D, D!3)))) | (~member(tptp_fun_D_1(B!5, D!3), C!4)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.52 tff(192,plain,
% 0.21/0.52 (~member(tptp_fun_D_1(B!5, D!3), C!4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[191, 188, 145])).
% 0.21/0.52 tff(193,plain,
% 0.21/0.52 (((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))) | member(tptp_fun_D_1(B!5, D!3), B!5)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(194,plain,
% 0.21/0.52 (member(tptp_fun_D_1(B!5, D!3), B!5)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[193, 143])).
% 0.21/0.52 tff(195,plain,
% 0.21/0.52 ((~![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!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(196,plain,
% 0.21/0.52 (~((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[195, 16])).
% 0.21/0.52 tff(197,plain,
% 0.21/0.52 (((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4)))))) | ((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(198,plain,
% 0.21/0.52 ((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.52 tff(199,plain,
% 0.21/0.52 (subset(B!5, C!4)),
% 0.21/0.52 inference(and_elim,[status(thm)],[167])).
% 0.21/0.52 tff(200,plain,
% 0.21/0.52 ((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(201,plain,
% 0.21/0.52 ((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.21/0.52 tff(202,plain,
% 0.21/0.52 (![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[201, 198])).
% 0.21/0.52 tff(203,plain,
% 0.21/0.52 (((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | ((~member(tptp_fun_D_1(B!5, D!3), B!5)) | member(tptp_fun_D_1(B!5, D!3), C!4))) <=> ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | (~member(tptp_fun_D_1(B!5, D!3), B!5)) | member(tptp_fun_D_1(B!5, D!3), C!4))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(204,plain,
% 0.21/0.52 ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | ((~member(tptp_fun_D_1(B!5, D!3), B!5)) | member(tptp_fun_D_1(B!5, D!3), C!4))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(205,plain,
% 0.21/0.52 ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | (~member(tptp_fun_D_1(B!5, D!3), B!5)) | member(tptp_fun_D_1(B!5, D!3), C!4)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.52 tff(206,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[205, 202, 194, 192])).
% 0.21/0.52 tff(207,plain,((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(208,plain,
% 0.21/0.52 ((~((~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3)))))) | (~intersect(D!3, B!5)) | (~((~member(tptp_fun_D_1(B!5, D!3), B!5)) | (~member(tptp_fun_D_1(B!5, D!3), D!3))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(209,plain,
% 0.21/0.52 (~intersect(D!3, B!5)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[208, 207, 142])).
% 0.21/0.52 tff(210,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | ((~intersect(B!5, D!3)) | intersect(D!3, B!5))) <=> ((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | (~intersect(B!5, D!3)) | intersect(D!3, B!5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(211,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | ((~intersect(B!5, D!3)) | intersect(D!3, B!5))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(212,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : ((~intersect(B, C)) | intersect(C, B))) | (~intersect(B!5, D!3)) | intersect(D!3, B!5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.21/0.52 tff(213,plain,
% 0.21/0.52 (~intersect(B!5, D!3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[212, 181, 209])).
% 0.21/0.52 tff(214,plain,
% 0.21/0.52 ((~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(215,plain,
% 0.21/0.52 ((~(intersect(B!5, D!3) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3))))) | ![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.21/0.52 tff(216,plain,
% 0.21/0.52 (![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[215, 133])).
% 0.21/0.53 tff(217,assumption,(member(tptp_fun_C_2(B!5), B!5)), introduced(assumption)).
% 0.21/0.53 tff(218,plain,
% 0.21/0.53 (((~![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))) | ((~member(tptp_fun_C_2(B!5), B!5)) | (~member(tptp_fun_C_2(B!5), D!3)))) <=> ((~![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))) | (~member(tptp_fun_C_2(B!5), B!5)) | (~member(tptp_fun_C_2(B!5), D!3)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(219,plain,
% 0.21/0.53 ((~![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))) | ((~member(tptp_fun_C_2(B!5), B!5)) | (~member(tptp_fun_C_2(B!5), D!3)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(220,plain,
% 0.21/0.53 ((~![D: $i] : ((~member(D, B!5)) | (~member(D, D!3)))) | (~member(tptp_fun_C_2(B!5), B!5)) | (~member(tptp_fun_C_2(B!5), D!3))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.53 tff(221,plain,
% 0.21/0.53 (~member(tptp_fun_C_2(B!5), D!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[220, 217, 216])).
% 0.21/0.53 tff(222,plain,
% 0.21/0.53 ((~![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!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~(subset(B!5, D!3) | (~((~member(tptp_fun_D_0(D!3, B!5), B!5)) | member(tptp_fun_D_0(D!3, B!5), D!3)))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(223,plain,
% 0.21/0.53 (~((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~(subset(B!5, D!3) | (~((~member(tptp_fun_D_0(D!3, B!5), B!5)) | member(tptp_fun_D_0(D!3, B!5), D!3))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[222, 16])).
% 0.21/0.53 tff(224,plain,
% 0.21/0.53 (((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~(subset(B!5, D!3) | (~((~member(tptp_fun_D_0(D!3, B!5), B!5)) | member(tptp_fun_D_0(D!3, B!5), D!3)))))) | ((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(225,plain,
% 0.21/0.53 ((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.21/0.53 tff(226,plain,
% 0.21/0.53 (subset(B!5, D!3)),
% 0.21/0.53 inference(and_elim,[status(thm)],[167])).
% 0.21/0.53 tff(227,plain,
% 0.21/0.53 ((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(228,plain,
% 0.21/0.53 ((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.21/0.53 tff(229,plain,
% 0.21/0.53 (![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.21/0.53 tff(230,plain,
% 0.21/0.53 (((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | ((~member(tptp_fun_C_2(B!5), B!5)) | member(tptp_fun_C_2(B!5), D!3))) <=> ((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | (~member(tptp_fun_C_2(B!5), B!5)) | member(tptp_fun_C_2(B!5), D!3))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(231,plain,
% 0.21/0.53 ((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | ((~member(tptp_fun_C_2(B!5), B!5)) | member(tptp_fun_C_2(B!5), D!3))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(232,plain,
% 0.21/0.53 ((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | (~member(tptp_fun_C_2(B!5), B!5)) | member(tptp_fun_C_2(B!5), D!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.53 tff(233,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[232, 229, 217, 221])).
% 0.21/0.53 tff(234,plain,(~member(tptp_fun_C_2(B!5), B!5)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(235,plain,
% 0.21/0.53 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(B!5) | member(tptp_fun_C_2(B!5), B!5))) | (~((~empty(B!5)) | ![C: $i] : (~member(C, B!5))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(236,plain,
% 0.21/0.53 (~((~(empty(B!5) | member(tptp_fun_C_2(B!5), B!5))) | (~((~empty(B!5)) | ![C: $i] : (~member(C, B!5)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[235, 47])).
% 0.21/0.53 tff(237,plain,
% 0.21/0.53 (((~(empty(B!5) | member(tptp_fun_C_2(B!5), B!5))) | (~((~empty(B!5)) | ![C: $i] : (~member(C, B!5))))) | (empty(B!5) | member(tptp_fun_C_2(B!5), B!5))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(238,plain,
% 0.21/0.53 (empty(B!5) | member(tptp_fun_C_2(B!5), B!5)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.21/0.53 tff(239,plain,
% 0.21/0.53 ((~(empty(B!5) | member(tptp_fun_C_2(B!5), B!5))) | empty(B!5) | member(tptp_fun_C_2(B!5), B!5)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(240,plain,
% 0.21/0.53 (empty(B!5) | member(tptp_fun_C_2(B!5), B!5)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.21/0.53 tff(241,plain,
% 0.21/0.53 (empty(B!5)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[240, 234])).
% 0.21/0.53 tff(242,plain,
% 0.21/0.53 (((~(empty(B!5) | member(tptp_fun_C_2(B!5), B!5))) | (~((~empty(B!5)) | ![C: $i] : (~member(C, B!5))))) | ((~empty(B!5)) | ![C: $i] : (~member(C, B!5)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(243,plain,
% 0.21/0.53 ((~empty(B!5)) | ![C: $i] : (~member(C, B!5))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[242, 236])).
% 0.21/0.53 tff(244,plain,
% 0.21/0.53 ((~((~empty(B!5)) | ![C: $i] : (~member(C, B!5)))) | (~empty(B!5)) | ![C: $i] : (~member(C, B!5))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(245,plain,
% 0.21/0.53 ((~empty(B!5)) | ![C: $i] : (~member(C, B!5))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.21/0.53 tff(246,plain,
% 0.21/0.53 (![C: $i] : (~member(C, B!5))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[245, 241])).
% 0.21/0.53 tff(247,plain,
% 0.21/0.53 ((~![C: $i] : (~member(C, B!5))) | (~member(tptp_fun_D_0(empty_set, B!5), B!5))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(248,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[247, 246, 111])).
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------