%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU242+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:27:22 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU242+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:28:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(relation_field_type, type, (
% 0.19/0.38 relation_field: $i > $i)).
% 0.19/0.38 tff(tptp_fun_A_3_type, type, (
% 0.19/0.38 tptp_fun_A_3: $i)).
% 0.19/0.38 tff(tptp_fun_C_1_type, type, (
% 0.19/0.38 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.19/0.38 tff(set_union2_type, type, (
% 0.19/0.38 set_union2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(relation_rng_type, type, (
% 0.19/0.38 relation_rng: $i > $i)).
% 0.19/0.38 tff(relation_dom_type, type, (
% 0.19/0.38 relation_dom: $i > $i)).
% 0.19/0.38 tff(relation_type, type, (
% 0.19/0.38 relation: $i > $o)).
% 0.19/0.38 tff(ordered_pair_type, type, (
% 0.19/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_B_5_type, type, (
% 0.19/0.38 tptp_fun_B_5: $i)).
% 0.19/0.38 tff(tptp_fun_C_4_type, type, (
% 0.19/0.38 tptp_fun_C_4: $i)).
% 0.19/0.38 tff(connected_type, type, (
% 0.19/0.38 connected: $i > $o)).
% 0.19/0.38 tff(tptp_fun_D_0_type, type, (
% 0.19/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(is_connected_in_type, type, (
% 0.19/0.38 is_connected_in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((relation(A!3) & ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))))) <=> (relation(A!3) & (connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) <=> (connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3))))) <=> ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 ((relation(A!3) & ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))))) <=> (relation(A!3) & ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 ((relation(A!3) & ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))))) <=> (relation(A!3) & (connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))) <=> (~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 ((~![A: $i] : (relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A))))))) <=> (~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(8,axiom,(~![A: $i] : (relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l4_wellord1')).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (relation(A!3) & (connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) & ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (relation(A!3)),
% 0.19/0.38 inference(and_elim,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.38 tff(20,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_relat_1')).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.38 tff(23,plain,(
% 0.19/0.38 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[22])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)) <=> in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))),
% 0.19/0.38 inference(symmetry,[status(thm)],[29])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (set_union2(relation_dom(A!3), relation_rng(A!3)) = relation_field(A!3)),
% 0.19/0.38 inference(symmetry,[status(thm)],[28])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> is_connected_in(A!3, relation_field(A!3))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (is_connected_in(A!3, relation_field(A!3)) <=> is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.38 inference(symmetry,[status(thm)],[32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~is_connected_in(A!3, relation_field(A!3))) <=> (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.38 tff(35,assumption,(~((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3))), introduced(assumption)).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (~in(ordered_pair(C!4, B!5), A!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)) | (~in(ordered_pair(B!5, C!4), A!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (~in(ordered_pair(B!5, C!4), A!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)) | (~(B!5 = C!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~(B!5 = C!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)) | in(C!4, relation_field(A!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (in(C!4, relation_field(A!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 35])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)) | in(B!5, relation_field(A!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (in(B!5, relation_field(A!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 35])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) <=> (~is_connected_in(A!3, relation_field(A!3)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(B!5, relation_field(A!3))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (in(B!5, relation_field(A!3)) <=> in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[47])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 48])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(C!4, relation_field(A!3))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (in(C!4, relation_field(A!3)) <=> in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[43, 51])).
% 0.19/0.39 tff(53,assumption,(in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))), introduced(assumption)).
% 0.19/0.39 tff(54,assumption,(in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))), introduced(assumption)).
% 0.19/0.39 tff(55,assumption,(![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))), introduced(assumption)).
% 0.19/0.39 tff(56,assumption,(~in(ordered_pair(C!4, B!5), A!3)), introduced(assumption)).
% 0.19/0.39 tff(57,assumption,(~in(ordered_pair(B!5, C!4), A!3)), introduced(assumption)).
% 0.19/0.39 tff(58,assumption,(~(B!5 = C!4)), introduced(assumption)).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))))) <=> ((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3))))) <=> ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))))) <=> ((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))))) <=> ((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[64, 58, 57, 56, 55, 54, 53])).
% 0.19/0.39 tff(66,plain,((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 41, 39, 37, 52, 49])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_connected_in(A, B)) | ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))) & (is_connected_in(A, B) | (in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))) & (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) & (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_connected_in(A, B)) | ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))) & (is_connected_in(A, B) | (in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))) & (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) & (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A))))) <=> (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))), (![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A))))) <=> ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))), ((relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A)))))) <=> (relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A)))))))), rewrite((relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A)))))) <=> ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))), ((relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A)))))) <=> ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![A: $i] : (relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.40 tff(78,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_relat_2')).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.40 tff(81,plain,(
% 0.19/0.40 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_connected_in(A, B)) | ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))) & (is_connected_in(A, B) | (in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))) & (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) & (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | (~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A!3) | in(ordered_pair(C, D), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) <=> ((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A!3) | in(ordered_pair(C, D), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A!3) | in(ordered_pair(C, D), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | (~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[86, 84])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A!3) | in(ordered_pair(C, D), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), A) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) | in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) | (~relation(A!3)) | ![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[89, 83, 14])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))))))) <=> ((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))))) <=> (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))) <=> ((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))) <=> ((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ((~![B: $i] : (~((~((~is_connected_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A!3, B) | (~((~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))) | (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (~((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 ((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[101, 67])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (~is_connected_in(A!3, relation_field(A!3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 46])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (^[A: $i] : refl(((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (^[A: $i] : rewrite((relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.42 tff(109,axiom,(![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d14_relat_2')).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.19/0.42 tff(112,plain,(
% 0.19/0.42 ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[111])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | ((~relation(A!3)) | (connected(A!3) <=> is_connected_in(A!3, relation_field(A!3))))) <=> ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | (~relation(A!3)) | (connected(A!3) <=> is_connected_in(A!3, relation_field(A!3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | ((~relation(A!3)) | (connected(A!3) <=> is_connected_in(A!3, relation_field(A!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | (~relation(A!3)) | (connected(A!3) <=> is_connected_in(A!3, relation_field(A!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (connected(A!3) <=> is_connected_in(A!3, relation_field(A!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[116, 113, 14])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((~(connected(A!3) <=> is_connected_in(A!3, relation_field(A!3)))) | (~connected(A!3)) | is_connected_in(A!3, relation_field(A!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~connected(A!3)) | is_connected_in(A!3, relation_field(A!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (~connected(A!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 103])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ((connected(A!3) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) <=> (connected(A!3) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 ((connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))) <=> (connected(A!3) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (connected(A!3) | ![B: $i, C: $i] : (~(in(B, relation_field(A!3)) & in(C, relation_field(A!3)) & (~(B = C)) & (~in(ordered_pair(B, C), A!3)) & (~in(ordered_pair(C, B), A!3))))),
% 0.19/0.42 inference(and_elim,[status(thm)],[13])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (connected(A!3) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (connected(A!3) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 120])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | ((B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[129, 126, 45, 43, 41, 39, 37])).
% 0.19/0.42 tff(131,plain,((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))) <=> ((~connected(A!3)) | (~((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 ((~connected(A!3)) | (in(B!5, relation_field(A!3)) & in(C!4, relation_field(A!3)) & (~(B!5 = C!4)) & (~in(ordered_pair(B!5, C!4), A!3)) & (~in(ordered_pair(C!4, B!5), A!3)))),
% 0.19/0.42 inference(and_elim,[status(thm)],[13])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~connected(A!3)) | (~((~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (~connected(A!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~(connected(A!3) <=> is_connected_in(A!3, relation_field(A!3)))) | connected(A!3) | (~is_connected_in(A!3, relation_field(A!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (connected(A!3) | (~is_connected_in(A!3, relation_field(A!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[136, 117])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (~is_connected_in(A!3, relation_field(A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[138, 34])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (((~((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 ((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[140, 97])).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 ((~((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))) | (~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 ((~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (~((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[143, 139])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[146, 30])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)) <=> in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[148])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[150, 144])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 149])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[153, 144])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[155, 144])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (~(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 144])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[125, 135])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | (in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 (((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)))) <=> (in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | ((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | (in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.44 tff(163,plain,
% 0.19/0.44 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | ((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[162, 160])).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | ((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 ((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[165, 159, 158, 156, 154])).
% 0.19/0.44 tff(167,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[166, 152, 147])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------