%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU187+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:10 AM UTC 2025
% Result : Theorem 13.86s 14.05s
% Output : Proof 13.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU187+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:14:32 EDT 2025
% 0.13/0.35 % CPUTime :
% 13.86/14.05 % SZS status Theorem
% 13.86/14.05 % SZS output start Proof
% 13.86/14.05 tff(in_type, type, (
% 13.86/14.05 in: ( $i * $i ) > $o)).
% 13.86/14.05 tff(empty_set_type, type, (
% 13.86/14.05 empty_set: $i)).
% 13.86/14.05 tff(tptp_fun_C_4_type, type, (
% 13.86/14.05 tptp_fun_C_4: ( $i * $i ) > $i)).
% 13.86/14.05 tff(ordered_pair_type, type, (
% 13.86/14.05 ordered_pair: ( $i * $i ) > $i)).
% 13.86/14.05 tff(tptp_fun_D_5_type, type, (
% 13.86/14.05 tptp_fun_D_5: ( $i * $i ) > $i)).
% 13.86/14.05 tff(empty_type, type, (
% 13.86/14.05 empty: $i > $o)).
% 13.86/14.05 tff(relation_rng_type, type, (
% 13.86/14.05 relation_rng: $i > $i)).
% 13.86/14.05 tff(tptp_fun_D_3_type, type, (
% 13.86/14.05 tptp_fun_D_3: ( $i * $i ) > $i)).
% 13.86/14.05 tff(relation_type, type, (
% 13.86/14.05 relation: $i > $o)).
% 13.86/14.05 tff(relation_dom_type, type, (
% 13.86/14.05 relation_dom: $i > $i)).
% 13.86/14.05 tff(tptp_fun_A_7_type, type, (
% 13.86/14.05 tptp_fun_A_7: $i)).
% 13.86/14.05 tff(tptp_fun_C_1_type, type, (
% 13.86/14.05 tptp_fun_C_1: ( $i * $i ) > $i)).
% 13.86/14.05 tff(tptp_fun_D_2_type, type, (
% 13.86/14.05 tptp_fun_D_2: ( $i * $i ) > $i)).
% 13.86/14.05 tff(tptp_fun_D_0_type, type, (
% 13.86/14.05 tptp_fun_D_0: ( $i * $i ) > $i)).
% 13.86/14.05 tff(1,assumption,(in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)), introduced(assumption)).
% 13.86/14.05 tff(2,plain,
% 13.86/14.05 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 13.86/14.05 inference(bind,[status(th)],[])).
% 13.86/14.05 tff(3,plain,
% 13.86/14.05 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 13.86/14.05 inference(quant_intro,[status(thm)],[2])).
% 13.86/14.05 tff(4,plain,
% 13.86/14.05 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 13.86/14.05 inference(bind,[status(th)],[])).
% 13.86/14.05 tff(5,plain,
% 13.86/14.05 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 13.86/14.05 inference(quant_intro,[status(thm)],[4])).
% 13.86/14.05 tff(6,plain,
% 13.86/14.05 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 13.86/14.05 inference(rewrite,[status(thm)],[])).
% 13.86/14.05 tff(7,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 13.86/14.05 tff(8,plain,
% 13.86/14.05 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[7, 6])).
% 13.86/14.05 tff(9,plain,(
% 13.86/14.05 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 13.86/14.05 inference(skolemize,[status(sab)],[8])).
% 13.86/14.05 tff(10,plain,
% 13.86/14.05 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[9, 5])).
% 13.86/14.05 tff(11,plain,
% 13.86/14.05 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[10, 3])).
% 13.86/14.05 tff(12,plain,
% 13.86/14.05 (empty(empty_set) <=> empty(empty_set)),
% 13.86/14.05 inference(rewrite,[status(thm)],[])).
% 13.86/14.05 tff(13,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 13.86/14.05 tff(14,plain,
% 13.86/14.05 (empty(empty_set)),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[13, 12])).
% 13.86/14.05 tff(15,plain,
% 13.86/14.05 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)))),
% 13.86/14.05 inference(rewrite,[status(thm)],[])).
% 13.86/14.05 tff(16,plain,
% 13.86/14.05 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)))),
% 13.86/14.05 inference(quant_inst,[status(thm)],[])).
% 13.86/14.05 tff(17,plain,
% 13.86/14.05 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[16, 15])).
% 13.86/14.05 tff(18,plain,
% 13.86/14.05 ($false),
% 13.86/14.05 inference(unit_resolution,[status(thm)],[17, 14, 11, 1])).
% 13.86/14.05 tff(19,plain,(~in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 13.86/14.05 tff(20,plain,
% 13.86/14.05 (relation(empty_set) <=> relation(empty_set)),
% 13.86/14.05 inference(rewrite,[status(thm)],[])).
% 13.86/14.05 tff(21,axiom,(empty(empty_set) & relation(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_relat_1')).
% 13.86/14.05 tff(22,plain,
% 13.86/14.05 (relation(empty_set)),
% 13.86/14.05 inference(and_elim,[status(thm)],[21])).
% 13.86/14.05 tff(23,plain,
% 13.86/14.05 (relation(empty_set)),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[22, 20])).
% 13.86/14.05 tff(24,plain,
% 13.86/14.05 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))))),
% 13.86/14.05 inference(bind,[status(th)],[])).
% 13.86/14.05 tff(25,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))),
% 13.86/14.05 inference(quant_intro,[status(thm)],[24])).
% 13.86/14.05 tff(26,plain,
% 13.86/14.05 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))))),
% 13.86/14.05 inference(bind,[status(th)],[])).
% 13.86/14.05 tff(27,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))),
% 13.86/14.05 inference(quant_intro,[status(thm)],[26])).
% 13.86/14.05 tff(28,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))),
% 13.86/14.05 inference(transitivity,[status(thm)],[27, 25])).
% 13.86/14.05 tff(29,plain,
% 13.86/14.05 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A)) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))))))))),
% 13.86/14.05 inference(bind,[status(th)],[])).
% 13.86/14.05 tff(30,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A)) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))),
% 13.86/14.05 inference(quant_intro,[status(thm)],[29])).
% 13.86/14.05 tff(31,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 13.86/14.05 inference(rewrite,[status(thm)],[])).
% 13.86/14.05 tff(32,plain,
% 13.86/14.05 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))))),
% 13.86/14.05 inference(bind,[status(th)],[])).
% 13.86/14.05 tff(33,plain,
% 13.86/14.05 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 13.86/14.05 inference(quant_intro,[status(thm)],[32])).
% 13.86/14.05 tff(34,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_relat_1')).
% 13.86/14.05 tff(35,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[34, 33])).
% 13.86/14.05 tff(36,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 13.86/14.05 inference(modus_ponens,[status(thm)],[35, 31])).
% 13.86/14.05 tff(37,plain,(
% 13.86/14.05 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A)) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))),
% 13.86/14.05 inference(skolemize,[status(sab)],[36])).
% 13.86/14.05 tff(38,plain,
% 13.86/14.05 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[37, 30])).
% 13.86/14.06 tff(39,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[38, 28])).
% 13.86/14.06 tff(40,plain,
% 13.86/14.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | ((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | (~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set)))))))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(41,plain,
% 13.86/14.06 (((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((B = relation_rng(empty_set)) | (~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set))))))))))) <=> ((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set)))))))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(42,plain,
% 13.86/14.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | ((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((B = relation_rng(empty_set)) | (~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | ((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set))))))))),
% 13.86/14.06 inference(monotonicity,[status(thm)],[41])).
% 13.86/14.06 tff(43,plain,
% 13.86/14.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | ((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((B = relation_rng(empty_set)) | (~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | (~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set)))))))),
% 13.86/14.06 inference(transitivity,[status(thm)],[42, 40])).
% 13.86/14.06 tff(44,plain,
% 13.86/14.06 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | ((~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((B = relation_rng(empty_set)) | (~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))))))))),
% 13.86/14.06 inference(quant_inst,[status(thm)],[])).
% 13.86/14.06 tff(45,plain,
% 13.86/14.06 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_D_5(B, A), tptp_fun_C_4(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, A)), A)))))))))))) | (~relation(empty_set)) | ![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set))))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[44, 43])).
% 13.86/14.06 tff(46,plain,
% 13.86/14.06 (![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set))))))),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[45, 39, 23])).
% 13.86/14.06 tff(47,plain,
% 13.86/14.06 ((~![B: $i] : (~((~((~(B = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(B, empty_set), B) | in(ordered_pair(tptp_fun_D_5(B, empty_set), tptp_fun_C_4(B, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(B, empty_set), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(B, empty_set)), empty_set)))))) | (B = relation_rng(empty_set))))))) | (~((~((~(empty_set = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, empty_set)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, empty_set) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set))))))),
% 13.86/14.06 inference(quant_inst,[status(thm)],[])).
% 13.86/14.06 tff(48,plain,
% 13.86/14.06 (~((~((~(empty_set = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, empty_set)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, empty_set) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set)))))),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[47, 46])).
% 13.86/14.06 tff(49,plain,
% 13.86/14.06 (((~((~(empty_set = relation_rng(empty_set))) | ![C: $i] : (~((~((~in(C, empty_set)) | in(ordered_pair(tptp_fun_D_3(C, empty_set), C), empty_set))) | (~(in(C, empty_set) | ![D: $i] : (~in(ordered_pair(D, C), empty_set)))))))) | (~((~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set))))) | ((~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set)))),
% 13.86/14.06 inference(tautology,[status(thm)],[])).
% 13.86/14.06 tff(50,plain,
% 13.86/14.06 ((~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set))),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[49, 48])).
% 13.86/14.06 tff(51,plain,
% 13.86/14.06 ((empty_set = relation_rng(empty_set)) <=> (relation_rng(empty_set) = empty_set)),
% 13.86/14.06 inference(commutativity,[status(thm)],[])).
% 13.86/14.06 tff(52,plain,
% 13.86/14.06 ((relation_rng(empty_set) = empty_set) <=> (empty_set = relation_rng(empty_set))),
% 13.86/14.06 inference(symmetry,[status(thm)],[51])).
% 13.86/14.06 tff(53,plain,
% 13.86/14.06 ((~(relation_rng(empty_set) = empty_set)) <=> (~(empty_set = relation_rng(empty_set)))),
% 13.86/14.06 inference(monotonicity,[status(thm)],[52])).
% 13.86/14.06 tff(54,plain,
% 13.86/14.06 ((empty_set = relation_dom(empty_set)) <=> (relation_dom(empty_set) = empty_set)),
% 13.86/14.06 inference(commutativity,[status(thm)],[])).
% 13.86/14.06 tff(55,plain,
% 13.86/14.06 (^[A: $i, B: $i] : refl(((A = B) | (~empty(B)) | (~empty(A))) <=> ((A = B) | (~empty(B)) | (~empty(A))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(56,plain,
% 13.86/14.06 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[55])).
% 13.86/14.06 tff(57,plain,
% 13.86/14.06 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(B)) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(B)) | (~empty(A))))))), rewrite((~(~((A = B) | (~empty(B)) | (~empty(A))))) <=> ((A = B) | (~empty(B)) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(B)) | (~empty(A)))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(58,plain,
% 13.86/14.06 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[57])).
% 13.86/14.06 tff(59,plain,
% 13.86/14.06 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(60,plain,
% 13.86/14.06 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(61,plain,
% 13.86/14.06 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[60])).
% 13.86/14.06 tff(62,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 13.86/14.06 tff(63,plain,
% 13.86/14.06 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[62, 61])).
% 13.86/14.06 tff(64,plain,
% 13.86/14.06 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[63, 59])).
% 13.86/14.06 tff(65,plain,(
% 13.86/14.06 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 13.86/14.06 inference(skolemize,[status(sab)],[64])).
% 13.86/14.06 tff(66,plain,
% 13.86/14.06 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[65, 58])).
% 13.86/14.06 tff(67,plain,
% 13.86/14.06 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[66, 56])).
% 13.86/14.06 tff(68,plain,
% 13.86/14.06 (?[A: $i] : (empty(A) & relation(A)) <=> ?[A: $i] : (empty(A) & relation(A))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(69,axiom,(?[A: $i] : (empty(A) & relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_relat_1')).
% 13.86/14.06 tff(70,plain,
% 13.86/14.06 (?[A: $i] : (empty(A) & relation(A))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[69, 68])).
% 13.86/14.06 tff(71,plain,(
% 13.86/14.06 empty(A!7) & relation(A!7)),
% 13.86/14.06 inference(skolemize,[status(sab)],[70])).
% 13.86/14.06 tff(72,plain,
% 13.86/14.06 (empty(A!7)),
% 13.86/14.06 inference(and_elim,[status(thm)],[71])).
% 13.86/14.06 tff(73,plain,
% 13.86/14.06 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7)))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(74,plain,
% 13.86/14.06 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7)))),
% 13.86/14.06 inference(quant_inst,[status(thm)],[])).
% 13.86/14.06 tff(75,plain,
% 13.86/14.06 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[74, 73])).
% 13.86/14.06 tff(76,plain,
% 13.86/14.06 (A!7 = empty_set),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[75, 14, 72, 67])).
% 13.86/14.06 tff(77,plain,
% 13.86/14.06 (empty_set = A!7),
% 13.86/14.06 inference(symmetry,[status(thm)],[76])).
% 13.86/14.06 tff(78,plain,
% 13.86/14.06 (relation_dom(empty_set) = relation_dom(A!7)),
% 13.86/14.06 inference(monotonicity,[status(thm)],[77])).
% 13.86/14.06 tff(79,plain,
% 13.86/14.06 (relation_dom(A!7) = relation_dom(empty_set)),
% 13.86/14.06 inference(symmetry,[status(thm)],[78])).
% 13.86/14.06 tff(80,plain,
% 13.86/14.06 ((empty_set = relation_dom(A!7)) <=> (empty_set = relation_dom(empty_set))),
% 13.86/14.06 inference(monotonicity,[status(thm)],[79])).
% 13.86/14.06 tff(81,plain,
% 13.86/14.06 ((empty_set = relation_dom(A!7)) <=> (relation_dom(empty_set) = empty_set)),
% 13.86/14.06 inference(transitivity,[status(thm)],[80, 54])).
% 13.86/14.06 tff(82,assumption,(in(tptp_fun_C_1(empty_set, A!7), empty_set)), introduced(assumption)).
% 13.86/14.06 tff(83,plain,
% 13.86/14.06 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_1(empty_set, A!7), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_1(empty_set, A!7), empty_set)))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(84,plain,
% 13.86/14.06 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_1(empty_set, A!7), empty_set)))),
% 13.86/14.06 inference(quant_inst,[status(thm)],[])).
% 13.86/14.06 tff(85,plain,
% 13.86/14.06 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_1(empty_set, A!7), empty_set))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[84, 83])).
% 13.86/14.06 tff(86,plain,
% 13.86/14.06 ($false),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[85, 14, 11, 82])).
% 13.86/14.06 tff(87,plain,(~in(tptp_fun_C_1(empty_set, A!7), empty_set)), inference(lemma,lemma(discharge,[]))).
% 13.86/14.06 tff(88,plain,
% 13.86/14.06 (in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set) <=> in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7)),
% 13.86/14.06 inference(monotonicity,[status(thm)],[77])).
% 13.86/14.06 tff(89,plain,
% 13.86/14.06 (in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7) <=> in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set)),
% 13.86/14.06 inference(symmetry,[status(thm)],[88])).
% 13.86/14.06 tff(90,assumption,(in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7)), introduced(assumption)).
% 13.86/14.06 tff(91,plain,
% 13.86/14.06 (in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set)),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[90, 89])).
% 13.86/14.06 tff(92,plain,
% 13.86/14.06 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set)))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(93,plain,
% 13.86/14.06 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set)))),
% 13.86/14.06 inference(quant_inst,[status(thm)],[])).
% 13.86/14.06 tff(94,plain,
% 13.86/14.06 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[93, 92])).
% 13.86/14.06 tff(95,plain,
% 13.86/14.06 (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), empty_set)),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[94, 14, 11])).
% 13.86/14.06 tff(96,plain,
% 13.86/14.06 ($false),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[95, 91])).
% 13.86/14.06 tff(97,plain,(~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7)), inference(lemma,lemma(discharge,[]))).
% 13.86/14.06 tff(98,plain,
% 13.86/14.06 ((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7)),
% 13.86/14.06 inference(tautology,[status(thm)],[])).
% 13.86/14.06 tff(99,plain,
% 13.86/14.06 (~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[98, 97, 87])).
% 13.86/14.06 tff(100,plain,
% 13.86/14.06 (((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7))))) | (in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))),
% 13.86/14.06 inference(tautology,[status(thm)],[])).
% 13.86/14.06 tff(101,plain,
% 13.86/14.06 ((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7))))),
% 13.86/14.06 inference(unit_resolution,[status(thm)],[100, 99])).
% 13.86/14.06 tff(102,plain,
% 13.86/14.06 (relation(A!7)),
% 13.86/14.06 inference(and_elim,[status(thm)],[71])).
% 13.86/14.06 tff(103,plain,
% 13.86/14.06 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(104,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[103])).
% 13.86/14.06 tff(105,plain,
% 13.86/14.06 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(106,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[105])).
% 13.86/14.06 tff(107,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 13.86/14.06 inference(transitivity,[status(thm)],[106, 104])).
% 13.86/14.06 tff(108,plain,
% 13.86/14.06 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(109,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[108])).
% 13.86/14.06 tff(110,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(111,plain,
% 13.86/14.06 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))))),
% 13.86/14.06 inference(bind,[status(th)],[])).
% 13.86/14.06 tff(112,plain,
% 13.86/14.06 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 13.86/14.06 inference(quant_intro,[status(thm)],[111])).
% 13.86/14.06 tff(113,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relat_1')).
% 13.86/14.06 tff(114,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[113, 112])).
% 13.86/14.06 tff(115,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[114, 110])).
% 13.86/14.06 tff(116,plain,(
% 13.86/14.06 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))),
% 13.86/14.06 inference(skolemize,[status(sab)],[115])).
% 13.86/14.06 tff(117,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[116, 109])).
% 13.86/14.06 tff(118,plain,
% 13.86/14.06 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 13.86/14.06 inference(modus_ponens,[status(thm)],[117, 107])).
% 13.86/14.06 tff(119,plain,
% 13.86/14.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7)))))))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(120,plain,
% 13.86/14.06 (((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((B = relation_dom(A!7)) | (~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7))))))))))) <=> ((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7)))))))),
% 13.86/14.06 inference(rewrite,[status(thm)],[])).
% 13.86/14.06 tff(121,plain,
% 13.86/14.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((B = relation_dom(A!7)) | (~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7))))))))),
% 13.86/14.07 inference(monotonicity,[status(thm)],[120])).
% 13.86/14.07 tff(122,plain,
% 13.86/14.07 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((B = relation_dom(A!7)) | (~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7)))))))),
% 13.86/14.07 inference(transitivity,[status(thm)],[121, 119])).
% 13.86/14.07 tff(123,plain,
% 13.86/14.07 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((B = relation_dom(A!7)) | (~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))))))))),
% 13.86/14.07 inference(quant_inst,[status(thm)],[])).
% 13.86/14.07 tff(124,plain,
% 13.86/14.07 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(A!7)) | ![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7))))))),
% 13.86/14.07 inference(modus_ponens,[status(thm)],[123, 122])).
% 13.86/14.07 tff(125,plain,
% 13.86/14.07 (![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7))))))),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[124, 118, 102])).
% 13.86/14.07 tff(126,plain,
% 13.86/14.07 ((~![B: $i] : (~((~((~(B = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(B, A!7), B) | in(ordered_pair(tptp_fun_C_1(B, A!7), tptp_fun_D_2(B, A!7)), A!7))) | (~((~in(tptp_fun_C_1(B, A!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A!7), D), A!7)))))) | (B = relation_dom(A!7))))))) | (~((~((~(empty_set = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, empty_set)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, empty_set) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7))))))),
% 13.86/14.07 inference(quant_inst,[status(thm)],[])).
% 13.86/14.07 tff(127,plain,
% 13.86/14.07 (~((~((~(empty_set = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, empty_set)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, empty_set) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7)))))),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[126, 125])).
% 13.86/14.07 tff(128,plain,
% 13.86/14.07 (((~((~(empty_set = relation_dom(A!7))) | ![C: $i] : (~((~((~in(C, empty_set)) | in(ordered_pair(C, tptp_fun_D_0(C, A!7)), A!7))) | (~(in(C, empty_set) | ![D: $i] : (~in(ordered_pair(C, D), A!7)))))))) | (~((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7))))) | ((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7)))),
% 13.86/14.07 inference(tautology,[status(thm)],[])).
% 13.86/14.07 tff(129,plain,
% 13.86/14.07 ((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7))),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[128, 127])).
% 13.86/14.07 tff(130,plain,
% 13.86/14.07 ((~((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7)))) | (~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7))),
% 13.86/14.07 inference(tautology,[status(thm)],[])).
% 13.86/14.07 tff(131,plain,
% 13.86/14.07 ((~((~(in(tptp_fun_C_1(empty_set, A!7), empty_set) | in(ordered_pair(tptp_fun_C_1(empty_set, A!7), tptp_fun_D_2(empty_set, A!7)), A!7))) | (~((~in(tptp_fun_C_1(empty_set, A!7), empty_set)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(empty_set, A!7), D), A!7)))))) | (empty_set = relation_dom(A!7))),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[130, 129])).
% 13.86/14.07 tff(132,plain,
% 13.86/14.07 (empty_set = relation_dom(A!7)),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[131, 101])).
% 13.86/14.07 tff(133,plain,
% 13.86/14.07 (relation_dom(empty_set) = empty_set),
% 13.86/14.07 inference(modus_ponens,[status(thm)],[132, 81])).
% 13.86/14.07 tff(134,plain,
% 13.86/14.07 ((~(~((~(relation_dom(empty_set) = empty_set)) | (~(relation_rng(empty_set) = empty_set))))) <=> ((~(relation_dom(empty_set) = empty_set)) | (~(relation_rng(empty_set) = empty_set)))),
% 13.86/14.07 inference(rewrite,[status(thm)],[])).
% 13.86/14.07 tff(135,plain,
% 13.86/14.07 (((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set)) <=> (~((~(relation_dom(empty_set) = empty_set)) | (~(relation_rng(empty_set) = empty_set))))),
% 13.86/14.07 inference(rewrite,[status(thm)],[])).
% 13.86/14.07 tff(136,plain,
% 13.86/14.07 ((~((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set))) <=> (~(~((~(relation_dom(empty_set) = empty_set)) | (~(relation_rng(empty_set) = empty_set)))))),
% 13.86/14.07 inference(monotonicity,[status(thm)],[135])).
% 13.86/14.07 tff(137,plain,
% 13.86/14.07 ((~((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set))) <=> ((~(relation_dom(empty_set) = empty_set)) | (~(relation_rng(empty_set) = empty_set)))),
% 13.86/14.07 inference(transitivity,[status(thm)],[136, 134])).
% 13.86/14.07 tff(138,plain,
% 13.86/14.07 ((~((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set))) <=> (~((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set)))),
% 13.86/14.07 inference(rewrite,[status(thm)],[])).
% 13.86/14.07 tff(139,axiom,(~((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_relat_1')).
% 13.86/14.07 tff(140,plain,
% 13.86/14.07 (~((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set))),
% 13.86/14.07 inference(modus_ponens,[status(thm)],[139, 138])).
% 13.86/14.07 tff(141,plain,
% 13.86/14.07 ((~(relation_dom(empty_set) = empty_set)) | (~(relation_rng(empty_set) = empty_set))),
% 13.86/14.07 inference(modus_ponens,[status(thm)],[140, 137])).
% 13.86/14.07 tff(142,plain,
% 13.86/14.07 (~(relation_rng(empty_set) = empty_set)),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[141, 133])).
% 13.86/14.07 tff(143,plain,
% 13.86/14.07 (~(empty_set = relation_rng(empty_set))),
% 13.86/14.07 inference(modus_ponens,[status(thm)],[142, 53])).
% 13.86/14.07 tff(144,plain,
% 13.86/14.07 ((~((~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set)))) | (~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))) | (empty_set = relation_rng(empty_set))),
% 13.86/14.07 inference(tautology,[status(thm)],[])).
% 13.86/14.07 tff(145,plain,
% 13.86/14.07 (~((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set)))))),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[144, 143, 50])).
% 13.86/14.07 tff(146,plain,
% 13.86/14.07 (((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | (~((~in(tptp_fun_C_4(empty_set, empty_set), empty_set)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_4(empty_set, empty_set)), empty_set))))) | (in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))),
% 13.86/14.07 inference(tautology,[status(thm)],[])).
% 13.86/14.07 tff(147,plain,
% 13.86/14.07 (in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[146, 145])).
% 13.86/14.07 tff(148,plain,
% 13.86/14.07 ((~(in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set))) | in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)),
% 13.86/14.07 inference(tautology,[status(thm)],[])).
% 13.86/14.07 tff(149,plain,
% 13.86/14.07 (in(tptp_fun_C_4(empty_set, empty_set), empty_set) | in(ordered_pair(tptp_fun_D_5(empty_set, empty_set), tptp_fun_C_4(empty_set, empty_set)), empty_set)),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[148, 147])).
% 13.86/14.07 tff(150,plain,
% 13.86/14.07 (in(tptp_fun_C_4(empty_set, empty_set), empty_set)),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[149, 19])).
% 13.86/14.07 tff(151,plain,
% 13.86/14.07 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_4(empty_set, empty_set), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_4(empty_set, empty_set), empty_set)))),
% 13.86/14.07 inference(rewrite,[status(thm)],[])).
% 13.86/14.07 tff(152,plain,
% 13.86/14.07 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_4(empty_set, empty_set), empty_set)))),
% 13.86/14.07 inference(quant_inst,[status(thm)],[])).
% 13.86/14.07 tff(153,plain,
% 13.86/14.07 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_4(empty_set, empty_set), empty_set))),
% 13.86/14.07 inference(modus_ponens,[status(thm)],[152, 151])).
% 13.86/14.07 tff(154,plain,
% 13.86/14.07 ($false),
% 13.86/14.07 inference(unit_resolution,[status(thm)],[153, 14, 11, 150])).
% 13.86/14.07 % SZS output end Proof
% 13.86/14.08 % E exiting
%------------------------------------------------------------------------------