TSTP Solution File: SEU242+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Tue Sep 20 07:28:27 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.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 : Sat Sep 3 11:13:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(in_type, type, (
% 0.12/0.37 in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(relation_field_type, type, (
% 0.12/0.37 relation_field: $i > $i)).
% 0.12/0.37 tff(tptp_fun_A_3_type, type, (
% 0.12/0.37 tptp_fun_A_3: $i)).
% 0.12/0.37 tff(tptp_fun_C_1_type, type, (
% 0.12/0.37 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.12/0.37 tff(set_union2_type, type, (
% 0.12/0.37 set_union2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(relation_rng_type, type, (
% 0.12/0.37 relation_rng: $i > $i)).
% 0.12/0.37 tff(relation_dom_type, type, (
% 0.12/0.37 relation_dom: $i > $i)).
% 0.12/0.37 tff(relation_type, type, (
% 0.12/0.37 relation: $i > $o)).
% 0.12/0.37 tff(ordered_pair_type, type, (
% 0.12/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_B_5_type, type, (
% 0.12/0.37 tptp_fun_B_5: $i)).
% 0.12/0.37 tff(tptp_fun_C_4_type, type, (
% 0.12/0.37 tptp_fun_C_4: $i)).
% 0.12/0.37 tff(connected_type, type, (
% 0.12/0.37 connected: $i > $o)).
% 0.12/0.37 tff(tptp_fun_D_0_type, type, (
% 0.12/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(is_connected_in_type, type, (
% 0.12/0.37 is_connected_in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((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)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (((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)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~(~relation(A!3))) <=> relation(A!3)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (((~(~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))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (((~(~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)))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 ((~![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)))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 ((~![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)))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 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')).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (~![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))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (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))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (relation(A!3)),
% 0.12/0.37 inference(and_elim,[status(thm)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.37 tff(23,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')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.37 tff(26,plain,(
% 0.12/0.37 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[25])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (((~![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))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~![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))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((~![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (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)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (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))),
% 0.12/0.37 inference(symmetry,[status(thm)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (set_union2(relation_dom(A!3), relation_rng(A!3)) = relation_field(A!3)),
% 0.12/0.37 inference(symmetry,[status(thm)],[31])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> is_connected_in(A!3, relation_field(A!3))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (is_connected_in(A!3, relation_field(A!3)) <=> is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.37 inference(symmetry,[status(thm)],[35])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~is_connected_in(A!3, relation_field(A!3))) <=> (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[36])).
% 0.12/0.38 tff(38,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)).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (((~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))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (~in(ordered_pair(C!4, B!5), A!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~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(B!5, C!4), A!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (~in(ordered_pair(B!5, C!4), A!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (((~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)) | (~(B!5 = C!4))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (~(B!5 = C!4)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((~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(C!4, relation_field(A!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (in(C!4, relation_field(A!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 38])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (((~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(B!5, relation_field(A!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (in(B!5, relation_field(A!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 38])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) <=> (~is_connected_in(A!3, relation_field(A!3)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[35])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(B!5, relation_field(A!3))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (in(B!5, relation_field(A!3)) <=> in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(C!4, relation_field(A!3))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (in(C!4, relation_field(A!3)) <=> in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[53])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[46, 54])).
% 0.12/0.38 tff(56,assumption,(in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))), introduced(assumption)).
% 0.12/0.38 tff(57,assumption,(in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))), introduced(assumption)).
% 0.12/0.38 tff(58,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)).
% 0.12/0.38 tff(59,assumption,(~in(ordered_pair(C!4, B!5), A!3)), introduced(assumption)).
% 0.12/0.38 tff(60,assumption,(~in(ordered_pair(B!5, C!4), A!3)), introduced(assumption)).
% 0.12/0.38 tff(61,assumption,(~(B!5 = C!4)), introduced(assumption)).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (((~![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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (((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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (((~![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))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[63])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 (((~![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)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[64, 62])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 ((~![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)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 ((~![C: $i, D: $i] : ((C = D) | in(ordered_pair(C, D), A!3) | in(ordered_pair(D, C), A!3) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[67, 61, 60, 59, 58, 57, 56])).
% 0.12/0.38 tff(69,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,[]))).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 (~![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)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[69, 44, 42, 40, 55, 52])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[71])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[74, 72])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[76])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (^[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] : (~(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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 (![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] : (~(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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[78])).
% 0.12/0.38 tff(80,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.12/0.38 tff(83,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')).
% 0.12/0.38 tff(84,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.38 tff(85,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.12/0.38 tff(86,plain,(
% 0.12/0.38 ![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))))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[85])).
% 0.12/0.38 tff(87,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.12/0.38 tff(88,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.12/0.38 tff(89,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[88, 75])).
% 0.12/0.38 tff(90,plain,
% 0.12/0.38 (((~![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))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(91,plain,
% 0.12/0.38 (((~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))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(92,plain,
% 0.12/0.38 (((~![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)))))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[91])).
% 0.12/0.38 tff(93,plain,
% 0.12/0.38 (((~![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))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[92, 90])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 ((~![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))))))))) | ((~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))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 ((~![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))))))))) | (~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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[95, 89, 17])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 ((~![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)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (~((~((~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))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (((~((~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))))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 ((~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)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 ((~((~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)))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 ((~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)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[102, 70])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 (~is_connected_in(A!3, relation_field(A!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[103, 49])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.39 tff(110,axiom,(![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d14_relat_2')).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.12/0.39 tff(113,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[112])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(117,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.39 tff(118,plain,
% 0.12/0.39 (connected(A!3) <=> is_connected_in(A!3, relation_field(A!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[117, 114, 17])).
% 0.12/0.39 tff(119,plain,
% 0.12/0.39 ((~(connected(A!3) <=> is_connected_in(A!3, relation_field(A!3)))) | (~connected(A!3)) | is_connected_in(A!3, relation_field(A!3))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 ((~connected(A!3)) | is_connected_in(A!3, relation_field(A!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.12/0.39 tff(121,plain,
% 0.12/0.39 (~connected(A!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[120, 104])).
% 0.12/0.39 tff(122,plain,
% 0.12/0.39 ((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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(123,plain,
% 0.12/0.39 ((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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(124,plain,
% 0.12/0.39 (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))))),
% 0.12/0.39 inference(and_elim,[status(thm)],[16])).
% 0.12/0.39 tff(125,plain,
% 0.12/0.39 (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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.12/0.39 tff(126,plain,
% 0.12/0.39 (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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.12/0.39 tff(127,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[126, 121])).
% 0.12/0.39 tff(128,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(129,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(130,plain,
% 0.12/0.39 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | (B!5 = C!4) | in(ordered_pair(B!5, C!4), A!3) | in(ordered_pair(C!4, B!5), A!3) | (~in(B!5, relation_field(A!3))) | (~in(C!4, relation_field(A!3)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.12/0.39 tff(131,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[130, 127, 48, 46, 44, 42, 40])).
% 0.12/0.39 tff(132,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,[]))).
% 0.12/0.39 tff(133,plain,
% 0.12/0.39 (((~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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(134,plain,
% 0.12/0.39 ((~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)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[16])).
% 0.12/0.39 tff(135,plain,
% 0.12/0.39 ((~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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.12/0.39 tff(136,plain,
% 0.12/0.39 (~connected(A!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.12/0.39 tff(137,plain,
% 0.12/0.39 ((~(connected(A!3) <=> is_connected_in(A!3, relation_field(A!3)))) | connected(A!3) | (~is_connected_in(A!3, relation_field(A!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(138,plain,
% 0.12/0.39 (connected(A!3) | (~is_connected_in(A!3, relation_field(A!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[137, 118])).
% 0.12/0.39 tff(139,plain,
% 0.12/0.39 (~is_connected_in(A!3, relation_field(A!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[138, 136])).
% 0.12/0.39 tff(140,plain,
% 0.12/0.39 (~is_connected_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[139, 37])).
% 0.12/0.39 tff(141,plain,
% 0.12/0.39 (((~((~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))) | (~((~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))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(142,plain,
% 0.12/0.39 (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)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[141, 98])).
% 0.12/0.39 tff(143,plain,
% 0.12/0.39 ((~(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))) | (~((~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)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(144,plain,
% 0.12/0.39 (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)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.12/0.39 tff(145,plain,
% 0.12/0.39 (~((~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))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[144, 140])).
% 0.12/0.40 tff(146,plain,
% 0.12/0.40 (((~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)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(147,plain,
% 0.12/0.40 (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)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.12/0.40 tff(148,plain,
% 0.12/0.40 (in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[147, 33])).
% 0.12/0.40 tff(149,plain,
% 0.12/0.40 (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)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.12/0.40 tff(150,plain,
% 0.12/0.40 (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))),
% 0.12/0.40 inference(symmetry,[status(thm)],[149])).
% 0.12/0.40 tff(151,plain,
% 0.12/0.40 (((~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)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(152,plain,
% 0.12/0.40 (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)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[151, 145])).
% 0.12/0.40 tff(153,plain,
% 0.12/0.40 (in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[152, 150])).
% 0.12/0.40 tff(154,plain,
% 0.12/0.40 (((~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))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(155,plain,
% 0.12/0.40 (~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)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[154, 145])).
% 0.12/0.40 tff(156,plain,
% 0.12/0.40 (((~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))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(157,plain,
% 0.12/0.40 (~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)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[156, 145])).
% 0.12/0.40 tff(158,plain,
% 0.12/0.40 (((~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)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(159,plain,
% 0.12/0.40 (~(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))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[158, 145])).
% 0.12/0.40 tff(160,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[126, 136])).
% 0.12/0.40 tff(161,plain,
% 0.12/0.40 (((~![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))))) | (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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(162,plain,
% 0.12/0.40 ((~![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))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(163,plain,
% 0.12/0.40 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(B, C), A!3) | in(ordered_pair(C, B), A!3) | (~in(B, relation_field(A!3))) | (~in(C, relation_field(A!3))))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.12/0.40 tff(164,plain,
% 0.12/0.40 ((~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), relation_field(A!3)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[163, 160, 159, 157, 155])).
% 0.12/0.40 tff(165,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[164, 153, 148])).
% 0.12/0.40 % SZS output end Proof
%------------------------------------------------------------------------------