%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU180+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:09 AM UTC 2025
% Result : Theorem 120.72s 120.88s
% Output : Proof 120.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU180+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:13:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 120.72/120.88 % SZS status Theorem
% 120.72/120.88 % SZS output start Proof
% 120.72/120.88 tff(in_type, type, (
% 120.72/120.88 in: ( $i * $i ) > $o)).
% 120.72/120.88 tff(relation_field_type, type, (
% 120.72/120.88 relation_field: $i > $i)).
% 120.72/120.88 tff(tptp_fun_C_37_type, type, (
% 120.72/120.88 tptp_fun_C_37: $i)).
% 120.72/120.88 tff(tptp_fun_B_38_type, type, (
% 120.72/120.88 tptp_fun_B_38: $i)).
% 120.72/120.88 tff(set_union2_type, type, (
% 120.72/120.88 set_union2: ( $i * $i ) > $i)).
% 120.72/120.88 tff(relation_rng_type, type, (
% 120.72/120.88 relation_rng: $i > $i)).
% 120.72/120.88 tff(relation_dom_type, type, (
% 120.72/120.88 relation_dom: $i > $i)).
% 120.72/120.88 tff(relation_type, type, (
% 120.72/120.88 relation: $i > $o)).
% 120.72/120.88 tff(ordered_pair_type, type, (
% 120.72/120.88 ordered_pair: ( $i * $i ) > $i)).
% 120.72/120.88 tff(tptp_fun_A_39_type, type, (
% 120.72/120.88 tptp_fun_A_39: $i)).
% 120.72/120.88 tff(subset_type, type, (
% 120.72/120.88 subset: ( $i * $i ) > $o)).
% 120.72/120.88 tff(tptp_fun_C_16_type, type, (
% 120.72/120.88 tptp_fun_C_16: ( $i * $i ) > $i)).
% 120.72/120.88 tff(1,plain,
% 120.72/120.88 ((~((in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37))) | (~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)))) <=> (~((in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37))) | (~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(2,plain,
% 120.72/120.88 ((~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))) <=> (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(3,plain,
% 120.72/120.88 ((~![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(4,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_relat_1')).
% 120.72/120.88 tff(5,plain,
% 120.72/120.88 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[4, 3])).
% 120.72/120.88 tff(6,plain,
% 120.72/120.88 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[5, 2])).
% 120.72/120.88 tff(7,plain,
% 120.72/120.88 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[6, 2])).
% 120.72/120.88 tff(8,plain,
% 120.72/120.88 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[7, 2])).
% 120.72/120.88 tff(9,plain,(
% 120.72/120.88 ~((in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37))) | (~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)))),
% 120.72/120.88 inference(skolemize,[status(sab)],[8])).
% 120.72/120.88 tff(10,plain,
% 120.72/120.88 (~((in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37))) | (~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[9, 1])).
% 120.72/120.88 tff(11,plain,
% 120.72/120.88 (relation(C!37)),
% 120.72/120.88 inference(or_elim,[status(thm)],[10])).
% 120.72/120.88 tff(12,plain,
% 120.72/120.88 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(13,plain,
% 120.72/120.88 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[12])).
% 120.72/120.88 tff(14,plain,
% 120.72/120.88 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(15,plain,
% 120.72/120.88 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(16,plain,
% 120.72/120.88 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[15])).
% 120.72/120.88 tff(17,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 120.72/120.88 tff(18,plain,
% 120.72/120.88 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[17, 16])).
% 120.72/120.88 tff(19,plain,
% 120.72/120.88 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[18, 14])).
% 120.72/120.88 tff(20,plain,(
% 120.72/120.88 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(skolemize,[status(sab)],[19])).
% 120.72/120.88 tff(21,plain,
% 120.72/120.88 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[20, 13])).
% 120.72/120.88 tff(22,plain,
% 120.72/120.88 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(C!37)) | (relation_field(C!37) = set_union2(relation_dom(C!37), relation_rng(C!37))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(C!37)) | (relation_field(C!37) = set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(23,plain,
% 120.72/120.88 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(C!37)) | (relation_field(C!37) = set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(24,plain,
% 120.72/120.88 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(C!37)) | (relation_field(C!37) = set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[23, 22])).
% 120.72/120.88 tff(25,plain,
% 120.72/120.88 (relation_field(C!37) = set_union2(relation_dom(C!37), relation_rng(C!37))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 120.72/120.88 tff(26,plain,
% 120.72/120.88 (set_union2(relation_dom(C!37), relation_rng(C!37)) = relation_field(C!37)),
% 120.72/120.88 inference(symmetry,[status(thm)],[25])).
% 120.72/120.88 tff(27,plain,
% 120.72/120.88 (in(B!38, set_union2(relation_dom(C!37), relation_rng(C!37))) <=> in(B!38, relation_field(C!37))),
% 120.72/120.88 inference(monotonicity,[status(thm)],[26])).
% 120.72/120.88 tff(28,plain,
% 120.72/120.88 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(29,plain,
% 120.72/120.88 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[28])).
% 120.72/120.88 tff(30,plain,
% 120.72/120.88 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(31,plain,
% 120.72/120.88 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[30])).
% 120.72/120.88 tff(32,plain,
% 120.72/120.88 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 120.72/120.88 inference(transitivity,[status(thm)],[31, 29])).
% 120.72/120.88 tff(33,plain,
% 120.72/120.88 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(34,plain,
% 120.72/120.88 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[33])).
% 120.72/120.88 tff(35,plain,
% 120.72/120.88 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(36,plain,
% 120.72/120.88 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(37,plain,
% 120.72/120.88 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[36])).
% 120.72/120.88 tff(38,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 120.72/120.88 tff(39,plain,
% 120.72/120.88 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[38, 37])).
% 120.72/120.88 tff(40,plain,
% 120.72/120.88 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[39, 35])).
% 120.72/120.88 tff(41,plain,(
% 120.72/120.88 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))),
% 120.72/120.88 inference(skolemize,[status(sab)],[40])).
% 120.72/120.88 tff(42,plain,
% 120.72/120.88 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[41, 34])).
% 120.72/120.88 tff(43,plain,
% 120.72/120.88 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[42, 32])).
% 120.72/120.88 tff(44,plain,
% 120.72/120.88 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))) | (~((~((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~(subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) | (~((~in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_rng(C!37)), relation_rng(C!37))) | in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_rng(C!37)), set_union2(relation_dom(C!37), relation_rng(C!37)))))))))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(45,plain,
% 120.72/120.88 (~((~((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~(subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) | (~((~in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_rng(C!37)), relation_rng(C!37))) | in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_rng(C!37)), set_union2(relation_dom(C!37), relation_rng(C!37))))))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[44, 43])).
% 120.72/120.88 tff(46,plain,
% 120.72/120.88 (((~((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~(subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) | (~((~in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_rng(C!37)), relation_rng(C!37))) | in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_rng(C!37)), set_union2(relation_dom(C!37), relation_rng(C!37)))))))) | ((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))),
% 120.72/120.88 inference(tautology,[status(thm)],[])).
% 120.72/120.88 tff(47,plain,
% 120.72/120.88 ((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[46, 45])).
% 120.72/120.88 tff(48,plain,
% 120.72/120.88 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(49,plain,
% 120.72/120.88 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[48])).
% 120.72/120.88 tff(50,plain,
% 120.72/120.88 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(51,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 120.72/120.88 tff(52,plain,
% 120.72/120.88 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[51, 50])).
% 120.72/120.88 tff(53,plain,(
% 120.72/120.88 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 120.72/120.88 inference(skolemize,[status(sab)],[52])).
% 120.72/120.88 tff(54,plain,
% 120.72/120.88 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[53, 49])).
% 120.72/120.88 tff(55,plain,
% 120.72/120.88 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(relation_dom(C!37), relation_rng(C!37)) = set_union2(relation_rng(C!37), relation_dom(C!37)))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(56,plain,
% 120.72/120.88 (set_union2(relation_dom(C!37), relation_rng(C!37)) = set_union2(relation_rng(C!37), relation_dom(C!37))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[55, 54])).
% 120.72/120.88 tff(57,plain,
% 120.72/120.88 (subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) <=> subset(relation_rng(C!37), set_union2(relation_rng(C!37), relation_dom(C!37)))),
% 120.72/120.88 inference(monotonicity,[status(thm)],[56])).
% 120.72/120.88 tff(58,plain,
% 120.72/120.88 (subset(relation_rng(C!37), set_union2(relation_rng(C!37), relation_dom(C!37))) <=> subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(symmetry,[status(thm)],[57])).
% 120.72/120.88 tff(59,plain,
% 120.72/120.88 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(60,plain,
% 120.72/120.88 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[59])).
% 120.72/120.88 tff(61,plain,
% 120.72/120.88 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(62,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 120.72/120.88 tff(63,plain,
% 120.72/120.88 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[62, 61])).
% 120.72/120.88 tff(64,plain,(
% 120.72/120.88 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 120.72/120.88 inference(skolemize,[status(sab)],[63])).
% 120.72/120.88 tff(65,plain,
% 120.72/120.88 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[64, 60])).
% 120.72/120.88 tff(66,plain,
% 120.72/120.88 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(relation_rng(C!37), set_union2(relation_rng(C!37), relation_dom(C!37)))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(67,plain,
% 120.72/120.88 (subset(relation_rng(C!37), set_union2(relation_rng(C!37), relation_dom(C!37)))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[66, 65])).
% 120.72/120.88 tff(68,plain,
% 120.72/120.88 (subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[67, 58])).
% 120.72/120.88 tff(69,plain,
% 120.72/120.88 ((~((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(tautology,[status(thm)],[])).
% 120.72/120.88 tff(70,plain,
% 120.72/120.88 ((~((~subset(relation_rng(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | ![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[69, 68])).
% 120.72/120.88 tff(71,plain,
% 120.72/120.88 (![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[70, 47])).
% 120.72/120.88 tff(72,plain,
% 120.72/120.88 (in(ordered_pair(A!39, B!38), C!37)),
% 120.72/120.88 inference(or_elim,[status(thm)],[10])).
% 120.72/120.88 tff(73,plain,
% 120.72/120.88 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(74,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[73])).
% 120.72/120.88 tff(75,plain,
% 120.72/120.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(76,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[75])).
% 120.72/120.88 tff(77,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(78,plain,
% 120.72/120.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 120.72/120.88 inference(bind,[status(th)],[])).
% 120.72/120.88 tff(79,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(quant_intro,[status(thm)],[78])).
% 120.72/120.88 tff(80,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_relat_1')).
% 120.72/120.88 tff(81,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[80, 79])).
% 120.72/120.88 tff(82,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[81, 77])).
% 120.72/120.88 tff(83,plain,(
% 120.72/120.88 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 120.72/120.88 inference(skolemize,[status(sab)],[82])).
% 120.72/120.88 tff(84,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[83, 76])).
% 120.72/120.88 tff(85,plain,
% 120.72/120.88 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[84, 74])).
% 120.72/120.88 tff(86,plain,
% 120.72/120.88 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)) | (~((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)) | (~((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37))))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(87,plain,
% 120.72/120.88 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)) | (~((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37))))))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(88,plain,
% 120.72/120.88 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(C!37)) | (~in(ordered_pair(A!39, B!38), C!37)) | (~((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37)))))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[87, 86])).
% 120.72/120.88 tff(89,plain,
% 120.72/120.88 (~((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[88, 85, 11, 72])).
% 120.72/120.88 tff(90,plain,
% 120.72/120.88 (((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37)))) | in(B!38, relation_rng(C!37))),
% 120.72/120.88 inference(tautology,[status(thm)],[])).
% 120.72/120.88 tff(91,plain,
% 120.72/120.88 (in(B!38, relation_rng(C!37))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[90, 89])).
% 120.72/120.88 tff(92,plain,
% 120.72/120.88 (((~![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | ((~in(B!38, relation_rng(C!37))) | in(B!38, set_union2(relation_dom(C!37), relation_rng(C!37))))) <=> ((~![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | (~in(B!38, relation_rng(C!37))) | in(B!38, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(93,plain,
% 120.72/120.88 ((~![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | ((~in(B!38, relation_rng(C!37))) | in(B!38, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(94,plain,
% 120.72/120.88 ((~![C: $i] : ((~in(C, relation_rng(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | (~in(B!38, relation_rng(C!37))) | in(B!38, set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[93, 92])).
% 120.72/120.88 tff(95,plain,
% 120.72/120.88 (in(B!38, set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[94, 91, 71])).
% 120.72/120.88 tff(96,plain,
% 120.72/120.88 (in(B!38, relation_field(C!37))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[95, 27])).
% 120.72/120.88 tff(97,plain,
% 120.72/120.88 (in(A!39, set_union2(relation_dom(C!37), relation_rng(C!37))) <=> in(A!39, relation_field(C!37))),
% 120.72/120.88 inference(monotonicity,[status(thm)],[26])).
% 120.72/120.88 tff(98,plain,
% 120.72/120.88 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))) | (~((~((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~(subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) | (~((~in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_dom(C!37)), relation_dom(C!37))) | in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_dom(C!37)), set_union2(relation_dom(C!37), relation_rng(C!37)))))))))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(99,plain,
% 120.72/120.88 (~((~((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~(subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) | (~((~in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_dom(C!37)), relation_dom(C!37))) | in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_dom(C!37)), set_union2(relation_dom(C!37), relation_rng(C!37))))))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[98, 43])).
% 120.72/120.88 tff(100,plain,
% 120.72/120.88 (((~((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~(subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37))) | (~((~in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_dom(C!37)), relation_dom(C!37))) | in(tptp_fun_C_16(set_union2(relation_dom(C!37), relation_rng(C!37)), relation_dom(C!37)), set_union2(relation_dom(C!37), relation_rng(C!37)))))))) | ((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))),
% 120.72/120.88 inference(tautology,[status(thm)],[])).
% 120.72/120.88 tff(101,plain,
% 120.72/120.88 ((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[100, 99])).
% 120.72/120.88 tff(102,plain,
% 120.72/120.88 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(103,plain,
% 120.72/120.88 (subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[102, 65])).
% 120.72/120.88 tff(104,plain,
% 120.72/120.88 ((~((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | (~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(tautology,[status(thm)],[])).
% 120.72/120.88 tff(105,plain,
% 120.72/120.88 ((~((~subset(relation_dom(C!37), set_union2(relation_dom(C!37), relation_rng(C!37)))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37)))))) | ![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[104, 103])).
% 120.72/120.88 tff(106,plain,
% 120.72/120.88 (![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[105, 101])).
% 120.72/120.88 tff(107,plain,
% 120.72/120.88 (((~in(A!39, relation_dom(C!37))) | (~in(B!38, relation_rng(C!37)))) | in(A!39, relation_dom(C!37))),
% 120.72/120.88 inference(tautology,[status(thm)],[])).
% 120.72/120.88 tff(108,plain,
% 120.72/120.88 (in(A!39, relation_dom(C!37))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[107, 89])).
% 120.72/120.88 tff(109,plain,
% 120.72/120.88 (((~![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | ((~in(A!39, relation_dom(C!37))) | in(A!39, set_union2(relation_dom(C!37), relation_rng(C!37))))) <=> ((~![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | (~in(A!39, relation_dom(C!37))) | in(A!39, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(110,plain,
% 120.72/120.88 ((~![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | ((~in(A!39, relation_dom(C!37))) | in(A!39, set_union2(relation_dom(C!37), relation_rng(C!37))))),
% 120.72/120.88 inference(quant_inst,[status(thm)],[])).
% 120.72/120.88 tff(111,plain,
% 120.72/120.88 ((~![C: $i] : ((~in(C, relation_dom(C!37))) | in(C, set_union2(relation_dom(C!37), relation_rng(C!37))))) | (~in(A!39, relation_dom(C!37))) | in(A!39, set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[110, 109])).
% 120.72/120.88 tff(112,plain,
% 120.72/120.88 (in(A!39, set_union2(relation_dom(C!37), relation_rng(C!37)))),
% 120.72/120.88 inference(unit_resolution,[status(thm)],[111, 108, 106])).
% 120.72/120.88 tff(113,plain,
% 120.72/120.88 (in(A!39, relation_field(C!37))),
% 120.72/120.88 inference(modus_ponens,[status(thm)],[112, 97])).
% 120.72/120.88 tff(114,plain,
% 120.72/120.88 ((~(~((~in(A!39, relation_field(C!37))) | (~in(B!38, relation_field(C!37)))))) <=> ((~in(A!39, relation_field(C!37))) | (~in(B!38, relation_field(C!37))))),
% 120.72/120.88 inference(rewrite,[status(thm)],[])).
% 120.72/120.88 tff(115,plain,
% 120.72/120.88 ((in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37))) <=> (~((~in(A!39, relation_field(C!37))) | (~in(B!38, relation_field(C!37)))))),
% 120.77/121.00 inference(rewrite,[status(thm)],[])).
% 120.77/121.00 tff(116,plain,
% 120.77/121.00 ((~(in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37)))) <=> (~(~((~in(A!39, relation_field(C!37))) | (~in(B!38, relation_field(C!37))))))),
% 120.77/121.00 inference(monotonicity,[status(thm)],[115])).
% 120.77/121.00 tff(117,plain,
% 120.77/121.00 ((~(in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37)))) <=> ((~in(A!39, relation_field(C!37))) | (~in(B!38, relation_field(C!37))))),
% 120.77/121.00 inference(transitivity,[status(thm)],[116, 114])).
% 120.77/121.00 tff(118,plain,
% 120.77/121.00 (~(in(A!39, relation_field(C!37)) & in(B!38, relation_field(C!37)))),
% 120.77/121.00 inference(or_elim,[status(thm)],[10])).
% 120.77/121.00 tff(119,plain,
% 120.77/121.00 ((~in(A!39, relation_field(C!37))) | (~in(B!38, relation_field(C!37)))),
% 120.77/121.00 inference(modus_ponens,[status(thm)],[118, 117])).
% 120.77/121.00 tff(120,plain,
% 120.77/121.00 (~in(B!38, relation_field(C!37))),
% 120.77/121.00 inference(unit_resolution,[status(thm)],[119, 113])).
% 120.77/121.00 tff(121,plain,
% 120.77/121.00 ($false),
% 120.77/121.00 inference(unit_resolution,[status(thm)],[120, 96])).
% 120.77/121.00 % SZS output end Proof
% 121.06/121.24 % E exiting
%------------------------------------------------------------------------------