%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU253+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:27:24 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU253+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:31:01 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(tptp_fun_B_2_type, type, (
% 0.18/0.37 tptp_fun_B_2: $i > $i)).
% 0.18/0.37 tff(relation_restriction_type, type, (
% 0.18/0.37 relation_restriction: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_A_9_type, type, (
% 0.18/0.37 tptp_fun_A_9: $i)).
% 0.18/0.37 tff(tptp_fun_B_8_type, type, (
% 0.18/0.37 tptp_fun_B_8: $i)).
% 0.18/0.37 tff(tptp_fun_C_1_type, type, (
% 0.18/0.37 tptp_fun_C_1: $i > $i)).
% 0.18/0.37 tff(in_type, type, (
% 0.18/0.37 in: ( $i * $i ) > $o)).
% 0.18/0.37 tff(ordered_pair_type, type, (
% 0.18/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.18/0.37 tff(relation_field_type, type, (
% 0.18/0.37 relation_field: $i > $i)).
% 0.18/0.37 tff(connected_type, type, (
% 0.18/0.37 connected: $i > $o)).
% 0.18/0.37 tff(relation_type, type, (
% 0.18/0.37 relation: $i > $o)).
% 0.18/0.37 tff(cartesian_product2_type, type, (
% 0.18/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) <=> (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))),
% 0.18/0.37 inference(commutativity,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) <=> (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.18/0.37 inference(symmetry,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 ((~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))) <=> (~(tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 ((~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8)))) <=> (~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) <=> (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(7,axiom,(~![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_wellord1')).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.18/0.37 tff(12,plain,(
% 0.18/0.37 ~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[11])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (relation(B!8)),
% 0.18/0.37 inference(or_elim,[status(thm)],[13])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.37 tff(20,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.37 tff(23,plain,(
% 0.18/0.37 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[22])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!8)) | relation(relation_restriction(B!8, A!9)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!8)) | relation(relation_restriction(B!8, A!9)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!8)) | relation(relation_restriction(B!8, A!9)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!8)) | relation(relation_restriction(B!8, A!9))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (relation(relation_restriction(B!8, A!9))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A))))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (^[A: $i] : refl(((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[34, 32])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (^[A: $i] : rewrite(((~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))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))) <=> ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![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))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 (![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))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (^[A: $i] : trans(monotonicity(rewrite((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))))) <=> (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)))))), ((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)))))) <=> (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)))))))), rewrite((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)))))) <=> ((~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))))))), ((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)))))) <=> ((~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))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (![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))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.38 tff(41,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/sandbox/benchmark/theBenchmark.p','l4_wellord1')).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![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))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (![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))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.18/0.38 tff(44,plain,(
% 0.18/0.38 ![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))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[43])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 30])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))))) <=> ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[50, 48])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[53, 47, 28])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))) | (connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (~connected(relation_restriction(B!8, A!9))),
% 0.18/0.39 inference(or_elim,[status(thm)],[13])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (~(tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 3])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(C)) & in(A, B)) <=> (~((~in(A, relation_field(C))) | (~in(A, B))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))))), rewrite(((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))) <=> ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> (relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))))), rewrite((relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.39 tff(73,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_wellord1')).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.18/0.39 tff(76,plain,(
% 0.18/0.39 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[75])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[81, 78, 14, 65])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[85, 60])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[89, 78, 14, 86])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.18/0.40 tff(100,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_wellord1')).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.18/0.40 tff(103,plain,(
% 0.18/0.40 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[102])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[108, 105, 14])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[110, 60])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 ((((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 ((((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[113, 109])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[115])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(B, D)) | (~in(A, C))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C))))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(120,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.41 tff(122,plain,(
% 0.18/0.41 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[121])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (~(((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[127, 82])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[129, 90])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ((~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[131, 130, 128])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 ((((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))) | ((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 ((((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[134, 126])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 ((~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[136, 135, 114])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[140, 105, 14])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[142, 60])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 ((((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(145,plain,
% 0.18/0.41 ((((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[145, 141])).
% 0.18/0.41 tff(147,plain,
% 0.18/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(148,plain,
% 0.18/0.42 (~(((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[147, 124])).
% 0.18/0.42 tff(149,plain,
% 0.18/0.42 ((~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[149, 130, 128])).
% 0.18/0.42 tff(151,plain,
% 0.18/0.42 ((((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))) | ((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(152,plain,
% 0.18/0.42 ((((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[152, 148])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 ((~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[154, 153, 146])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(157,plain,
% 0.18/0.42 (((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))))) <=> ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(158,plain,
% 0.18/0.42 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[157])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[158, 156])).
% 0.18/0.42 tff(160,plain,
% 0.18/0.42 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.42 tff(162,plain,
% 0.18/0.42 (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[161, 47, 14])).
% 0.18/0.42 tff(163,plain,
% 0.18/0.42 (((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))) | ((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 ((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.18/0.42 tff(165,plain,
% 0.18/0.42 (connected(B!8)),
% 0.18/0.42 inference(or_elim,[status(thm)],[13])).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 ((~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))) | (~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 ((~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.18/0.42 tff(168,plain,
% 0.18/0.42 (![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[167, 164])).
% 0.18/0.42 tff(169,plain,
% 0.18/0.42 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(170,plain,
% 0.18/0.42 (((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8)))) <=> (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(171,plain,
% 0.18/0.43 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[170])).
% 0.18/0.43 tff(172,plain,
% 0.18/0.43 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[171, 169])).
% 0.18/0.43 tff(173,plain,
% 0.18/0.43 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(174,plain,
% 0.18/0.43 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.18/0.43 tff(175,plain,
% 0.18/0.43 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[174, 168])).
% 0.18/0.43 tff(176,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[175, 155, 137, 92, 84, 63])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------