%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU248+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:27:23 AM UTC 2025
% Result : Theorem 0.77s 0.96s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU248+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:28:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.77/0.96 % SZS status Theorem
% 0.77/0.96 % SZS output start Proof
% 0.77/0.96 tff(in_type, type, (
% 0.77/0.96 in: ( $i * $i ) > $o)).
% 0.77/0.96 tff(relation_rng_restriction_type, type, (
% 0.77/0.96 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.77/0.96 tff(tptp_fun_B_7_type, type, (
% 0.77/0.96 tptp_fun_B_7: $i)).
% 0.77/0.96 tff(tptp_fun_A_8_type, type, (
% 0.77/0.96 tptp_fun_A_8: $i)).
% 0.77/0.96 tff(ordered_pair_type, type, (
% 0.77/0.96 ordered_pair: ( $i * $i ) > $i)).
% 0.77/0.96 tff(tptp_fun_D_3_type, type, (
% 0.77/0.96 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.77/0.96 tff(tptp_fun_C_2_type, type, (
% 0.77/0.96 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.77/0.96 tff(relation_dom_type, type, (
% 0.77/0.96 relation_dom: $i > $i)).
% 0.77/0.96 tff(tptp_fun_C_4_type, type, (
% 0.77/0.96 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.77/0.96 tff(tptp_fun_D_5_type, type, (
% 0.77/0.96 tptp_fun_D_5: ( $i * $i ) > $i)).
% 0.77/0.96 tff(relation_type, type, (
% 0.77/0.96 relation: $i > $o)).
% 0.77/0.96 tff(subset_type, type, (
% 0.77/0.96 subset: ( $i * $i ) > $o)).
% 0.77/0.96 tff(tptp_fun_E_0_type, type, (
% 0.77/0.96 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.77/0.96 tff(tptp_fun_D_1_type, type, (
% 0.77/0.96 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.77/0.96 tff(1,plain,
% 0.77/0.96 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2,plain,
% 0.77/0.96 ((~![A: $i, B: $i] : (relation(B) => subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l29_wellord1')).
% 0.77/0.96 tff(4,plain,
% 0.77/0.96 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.77/0.96 tff(5,plain,
% 0.77/0.96 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.77/0.96 tff(6,plain,
% 0.77/0.96 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.77/0.96 tff(7,plain,
% 0.77/0.96 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.77/0.96 tff(8,plain,(
% 0.77/0.96 ~((~relation(B!7)) | subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[7])).
% 0.77/0.96 tff(9,plain,
% 0.77/0.96 (relation(B!7)),
% 0.77/0.96 inference(or_elim,[status(thm)],[8])).
% 0.77/0.96 tff(10,plain,
% 0.77/0.96 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(11,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[10])).
% 0.77/0.96 tff(12,plain,
% 0.77/0.96 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(13,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[12])).
% 0.77/0.96 tff(14,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))),
% 0.77/0.96 inference(transitivity,[status(thm)],[13, 11])).
% 0.77/0.96 tff(15,plain,
% 0.77/0.96 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A)) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))))))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(16,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A)) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[15])).
% 0.77/0.96 tff(17,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(18,plain,
% 0.77/0.96 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(19,plain,
% 0.77/0.96 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[18])).
% 0.77/0.96 tff(20,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_relat_1')).
% 0.77/0.96 tff(21,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.77/0.96 tff(22,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.77/0.96 tff(23,plain,(
% 0.77/0.96 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A)) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))),
% 0.77/0.96 inference(skolemize,[status(sab)],[22])).
% 0.77/0.96 tff(24,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.77/0.96 tff(25,plain,
% 0.77/0.96 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.77/0.96 tff(26,plain,
% 0.77/0.96 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | (~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7)))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(27,plain,
% 0.77/0.96 (((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((B = relation_dom(B!7)) | (~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7))))))))))) <=> ((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7)))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(28,plain,
% 0.77/0.96 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((B = relation_dom(B!7)) | (~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[27])).
% 0.77/0.96 tff(29,plain,
% 0.77/0.96 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((B = relation_dom(B!7)) | (~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | (~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7)))))))),
% 0.77/0.96 inference(transitivity,[status(thm)],[28, 26])).
% 0.77/0.96 tff(30,plain,
% 0.77/0.96 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((B = relation_dom(B!7)) | (~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))))))))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(31,plain,
% 0.77/0.96 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | (~relation(B!7)) | ![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.77/0.97 tff(32,plain,
% 0.77/0.97 (![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[31, 25, 9])).
% 0.77/0.97 tff(33,plain,
% 0.77/0.97 (((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(34,plain,
% 0.77/0.97 ((~(~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(35,plain,
% 0.77/0.97 (((~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(36,plain,
% 0.77/0.97 ((~$true) <=> $false),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(37,plain,
% 0.77/0.97 (((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | $true) <=> $true),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(38,plain,
% 0.77/0.97 ((relation_dom(B!7) = relation_dom(B!7)) <=> $true),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(39,plain,
% 0.77/0.97 (((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7))) <=> ((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(40,plain,
% 0.77/0.97 ((~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))) <=> (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[39])).
% 0.77/0.97 tff(41,plain,
% 0.77/0.97 (((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7))))) <=> ((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[40])).
% 0.77/0.97 tff(42,plain,
% 0.77/0.97 ((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) <=> (~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7))))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[41])).
% 0.77/0.97 tff(43,plain,
% 0.77/0.97 (((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))) <=> ((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | $true)),
% 0.77/0.97 inference(monotonicity,[status(thm)],[42, 38])).
% 0.77/0.97 tff(44,plain,
% 0.77/0.97 (((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))) <=> $true),
% 0.77/0.97 inference(transitivity,[status(thm)],[43, 37])).
% 0.77/0.97 tff(45,plain,
% 0.77/0.97 ((~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7)))) <=> (~$true)),
% 0.77/0.97 inference(monotonicity,[status(thm)],[44])).
% 0.77/0.97 tff(46,plain,
% 0.77/0.97 ((~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7)))) <=> $false),
% 0.77/0.97 inference(transitivity,[status(thm)],[45, 36])).
% 0.77/0.97 tff(47,plain,
% 0.77/0.97 ((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(48,plain,
% 0.77/0.97 (((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))))) <=> ((~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))) | $false)),
% 0.77/0.97 inference(monotonicity,[status(thm)],[47, 46])).
% 0.77/0.97 tff(49,plain,
% 0.77/0.97 (((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))),
% 0.77/0.97 inference(transitivity,[status(thm)],[48, 35])).
% 0.77/0.97 tff(50,plain,
% 0.77/0.97 ((~((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[49])).
% 0.77/0.97 tff(51,plain,
% 0.77/0.97 ((~((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7)))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))),
% 0.77/0.97 inference(transitivity,[status(thm)],[50, 34])).
% 0.77/0.97 tff(52,plain,
% 0.77/0.97 (((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | (~((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[51])).
% 0.77/0.97 tff(53,plain,
% 0.77/0.97 (((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | (~((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))),
% 0.77/0.97 inference(transitivity,[status(thm)],[52, 33])).
% 0.77/0.97 tff(54,plain,
% 0.77/0.97 ((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | (~((~((~(relation_dom(B!7) = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7)) | in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), tptp_fun_D_5(relation_dom(B!7), B!7)), B!7))) | (~((~in(tptp_fun_C_4(relation_dom(B!7), B!7), relation_dom(B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(B!7), B!7), D), B!7)))))) | (relation_dom(B!7) = relation_dom(B!7))))))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(55,plain,
% 0.77/0.97 ((~![B: $i] : (~((~((~(B = relation_dom(B!7))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), B!7)))))))) | (~((~((~(in(tptp_fun_C_4(B, B!7), B) | in(ordered_pair(tptp_fun_C_4(B, B!7), tptp_fun_D_5(B, B!7)), B!7))) | (~((~in(tptp_fun_C_4(B, B!7), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, B!7), D), B!7)))))) | (B = relation_dom(B!7))))))) | ![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.77/0.97 tff(56,plain,
% 0.77/0.97 (![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[55, 32])).
% 0.77/0.97 tff(57,plain,
% 0.77/0.97 ((~![C: $i] : (~((~((~in(C, relation_dom(B!7))) | in(ordered_pair(C, tptp_fun_D_3(C, B!7)), B!7))) | (~(in(C, relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(C, D), B!7))))))) | (~((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), B!7)), B!7))) | (~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))))))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(58,plain,
% 0.77/0.97 (~((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), B!7)), B!7))) | (~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7)))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.77/0.97 tff(59,plain,
% 0.77/0.97 (((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), B!7)), B!7))) | (~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))))) | (in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7)))),
% 0.77/0.97 inference(tautology,[status(thm)],[])).
% 0.77/0.97 tff(60,plain,
% 0.77/0.97 (in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.77/0.97 tff(61,plain,
% 0.77/0.97 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(62,plain,
% 0.77/0.97 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[61])).
% 0.77/0.97 tff(63,plain,
% 0.77/0.97 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(64,plain,
% 0.77/0.97 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[63])).
% 0.77/0.97 tff(65,plain,
% 0.77/0.97 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.77/0.97 inference(transitivity,[status(thm)],[64, 62])).
% 0.77/0.97 tff(66,plain,
% 0.77/0.97 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(67,plain,
% 0.77/0.97 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[66])).
% 0.77/0.97 tff(68,plain,
% 0.77/0.97 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(69,plain,
% 0.77/0.97 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(70,plain,
% 0.77/0.97 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[69])).
% 0.77/0.97 tff(71,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.77/0.97 tff(72,plain,
% 0.77/0.97 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.77/0.97 tff(73,plain,
% 0.77/0.97 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.77/0.97 tff(74,plain,(
% 0.77/0.97 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.77/0.97 inference(skolemize,[status(sab)],[73])).
% 0.77/0.97 tff(75,plain,
% 0.77/0.97 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.77/0.97 tff(76,plain,
% 0.77/0.97 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.77/0.97 tff(77,plain,
% 0.77/0.97 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | ![C: $i] : ((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(C, relation_dom(B!7))))) | (~(subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))))))))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(78,plain,
% 0.77/0.97 (~((~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | ![C: $i] : ((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(C, relation_dom(B!7))))) | (~(subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)))))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.77/0.97 tff(79,plain,
% 0.77/0.97 (((~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | ![C: $i] : ((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(C, relation_dom(B!7))))) | (~(subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))))))) | (subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)))))),
% 0.77/0.97 inference(tautology,[status(thm)],[])).
% 0.77/0.97 tff(80,plain,
% 0.77/0.97 (subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.77/0.97 tff(81,plain,
% 0.77/0.97 (~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))),
% 0.77/0.97 inference(or_elim,[status(thm)],[8])).
% 0.77/0.97 tff(82,plain,
% 0.77/0.97 ((~(subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)))))) | subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))))),
% 0.77/0.98 inference(tautology,[status(thm)],[])).
% 0.77/0.98 tff(83,plain,
% 0.77/0.98 ((~(subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7)) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)))))) | (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.77/0.98 tff(84,plain,
% 0.77/0.98 (~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.77/0.98 tff(85,plain,
% 0.77/0.98 (((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))) | (~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)))),
% 0.77/0.98 inference(tautology,[status(thm)],[])).
% 0.77/0.98 tff(86,plain,
% 0.77/0.98 (~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.77/0.98 tff(87,plain,
% 0.77/0.98 ((~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))),
% 0.77/0.98 inference(tautology,[status(thm)],[])).
% 0.77/0.98 tff(88,plain,
% 0.77/0.98 ((~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.77/0.98 tff(89,plain,
% 0.77/0.98 (![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[88, 60])).
% 0.77/0.98 tff(90,plain,
% 0.77/0.98 ((~![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), B!7))) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(91,plain,
% 0.77/0.98 (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.77/0.98 tff(92,plain,
% 0.77/0.98 (((~in(tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)), A!8)) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7)),
% 0.77/0.98 inference(tautology,[status(thm)],[])).
% 0.77/0.98 tff(93,plain,
% 0.77/0.98 ((~in(tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)), A!8)) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.77/0.98 tff(94,plain,
% 0.77/0.98 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.77/0.98 inference(bind,[status(th)],[])).
% 0.77/0.98 tff(95,plain,
% 0.77/0.98 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(quant_intro,[status(thm)],[94])).
% 0.77/0.98 tff(96,plain,
% 0.77/0.98 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(97,plain,
% 0.77/0.98 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.77/0.98 inference(bind,[status(th)],[])).
% 0.77/0.98 tff(98,plain,
% 0.77/0.98 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(quant_intro,[status(thm)],[97])).
% 0.77/0.98 tff(99,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.77/0.98 tff(100,plain,
% 0.77/0.98 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.77/0.98 tff(101,plain,
% 0.77/0.98 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.77/0.98 tff(102,plain,(
% 0.77/0.98 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(skolemize,[status(sab)],[101])).
% 0.77/0.98 tff(103,plain,
% 0.77/0.98 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.77/0.98 tff(104,plain,
% 0.77/0.98 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(105,plain,
% 0.77/0.98 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(106,plain,
% 0.77/0.98 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.77/0.98 tff(107,plain,
% 0.77/0.98 (relation(relation_rng_restriction(A!8, B!7))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[106, 103, 9])).
% 0.77/0.98 tff(108,plain,
% 0.77/0.98 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7))))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(109,plain,
% 0.77/0.98 (((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((B = relation_dom(relation_rng_restriction(A!8, B!7))) | (~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7)))))))))))) <=> ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7))))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(110,plain,
% 0.77/0.98 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((B = relation_dom(relation_rng_restriction(A!8, B!7))) | (~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[109])).
% 0.77/0.98 tff(111,plain,
% 0.77/0.98 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((B = relation_dom(relation_rng_restriction(A!8, B!7))) | (~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7))))))))),
% 0.77/0.98 inference(transitivity,[status(thm)],[110, 108])).
% 0.77/0.98 tff(112,plain,
% 0.77/0.98 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((B = relation_dom(relation_rng_restriction(A!8, B!7))) | (~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))))))))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(113,plain,
% 0.77/0.98 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)), A))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, A), D), A)))))))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.77/0.98 tff(114,plain,
% 0.77/0.98 (![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[113, 25, 107])).
% 0.77/0.98 tff(115,plain,
% 0.77/0.98 (((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(116,plain,
% 0.77/0.98 ((~(~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(117,plain,
% 0.77/0.98 (((~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(118,plain,
% 0.77/0.98 (((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | $true) <=> $true),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(119,plain,
% 0.77/0.98 ((relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7))) <=> $true),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(120,plain,
% 0.77/0.98 (((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7)))) <=> ((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(121,plain,
% 0.77/0.98 ((~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))) <=> (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7)))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[120])).
% 0.77/0.98 tff(122,plain,
% 0.77/0.98 (((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7)))))) <=> ((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[121])).
% 0.77/0.98 tff(123,plain,
% 0.77/0.98 ((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) <=> (~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7)))))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[122])).
% 0.77/0.98 tff(124,plain,
% 0.77/0.98 (((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) <=> ((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | $true)),
% 0.77/0.98 inference(monotonicity,[status(thm)],[123, 119])).
% 0.77/0.98 tff(125,plain,
% 0.77/0.98 (((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) <=> $true),
% 0.82/0.98 inference(transitivity,[status(thm)],[124, 118])).
% 0.82/0.98 tff(126,plain,
% 0.82/0.98 ((~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7))))) <=> (~$true)),
% 0.82/0.99 inference(monotonicity,[status(thm)],[125])).
% 0.82/0.99 tff(127,plain,
% 0.82/0.99 ((~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7))))) <=> $false),
% 0.82/0.99 inference(transitivity,[status(thm)],[126, 36])).
% 0.82/0.99 tff(128,plain,
% 0.82/0.99 ((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(129,plain,
% 0.82/0.99 (((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))))) <=> ((~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))) | $false)),
% 0.82/0.99 inference(monotonicity,[status(thm)],[128, 127])).
% 0.82/0.99 tff(130,plain,
% 0.82/0.99 (((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[129, 117])).
% 0.82/0.99 tff(131,plain,
% 0.82/0.99 ((~((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7))))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[130])).
% 0.82/0.99 tff(132,plain,
% 0.82/0.99 ((~((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7))))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[131, 116])).
% 0.82/0.99 tff(133,plain,
% 0.82/0.99 (((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | (~((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[132])).
% 0.82/0.99 tff(134,plain,
% 0.82/0.99 (((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | (~((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[133, 115])).
% 0.82/0.99 tff(135,plain,
% 0.82/0.99 ((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | (~((~((~(relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7))) | in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), relation_dom(relation_rng_restriction(A!8, B!7)))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(relation_dom(relation_rng_restriction(A!8, B!7)), relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (relation_dom(relation_rng_restriction(A!8, B!7)) = relation_dom(relation_rng_restriction(A!8, B!7)))))))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(136,plain,
% 0.82/0.99 ((~![B: $i] : (~((~((~(B = relation_dom(relation_rng_restriction(A!8, B!7)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7))))))))) | (~((~((~(in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B) | in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), tptp_fun_D_5(B, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~((~in(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_4(B, relation_rng_restriction(A!8, B!7)), D), relation_rng_restriction(A!8, B!7))))))) | (B = relation_dom(relation_rng_restriction(A!8, B!7)))))))) | ![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.82/0.99 tff(137,plain,
% 0.82/0.99 (![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[136, 114])).
% 0.82/0.99 tff(138,plain,
% 0.82/0.99 ((~![C: $i] : (~((~((~in(C, relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(C, tptp_fun_D_3(C, relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(C, relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(C, D), relation_rng_restriction(A!8, B!7)))))))) | (~((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), relation_rng_restriction(A!8, B!7)))))))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(139,plain,
% 0.82/0.99 (~((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), relation_rng_restriction(A!8, B!7))))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.82/0.99 tff(140,plain,
% 0.82/0.99 (((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~(in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), D), relation_rng_restriction(A!8, B!7)))))) | ((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(141,plain,
% 0.82/0.99 ((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.82/0.99 tff(142,plain,
% 0.82/0.99 (((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(B!7))) | in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(143,plain,
% 0.82/0.99 (in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[142, 84])).
% 0.82/0.99 tff(144,plain,
% 0.82/0.99 ((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | (~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(145,plain,
% 0.82/0.99 ((~((~in(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_dom(relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))) | in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.82/0.99 tff(146,plain,
% 0.82/0.99 (in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[145, 141])).
% 0.82/0.99 tff(147,plain,
% 0.82/0.99 ((((~in(tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)), A!8)) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7))) <=> in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))) | (~((~in(tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)), A!8)) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7)))) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(148,plain,
% 0.82/0.99 (((~in(tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)), A!8)) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7))) <=> in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[147, 146, 93])).
% 0.82/0.99 tff(149,plain,
% 0.82/0.99 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(150,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[149])).
% 0.82/0.99 tff(151,plain,
% 0.82/0.99 (^[A: $i, B: $i] : refl(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(152,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[151])).
% 0.82/0.99 tff(153,plain,
% 0.82/0.99 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(154,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[153])).
% 0.82/0.99 tff(155,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[154, 152])).
% 0.82/0.99 tff(156,plain,
% 0.82/0.99 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(157,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[156])).
% 0.82/1.00 tff(158,plain,
% 0.82/1.00 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(159,plain,
% 0.82/1.00 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) <=> ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), rewrite((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(160,plain,
% 0.82/1.00 (![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[159])).
% 0.82/1.00 tff(161,axiom,(![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_1')).
% 0.82/1.00 tff(162,plain,
% 0.82/1.00 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.82/1.00 tff(163,plain,
% 0.82/1.00 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.82/1.00 tff(164,plain,(
% 0.82/1.00 ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))),
% 0.82/1.00 inference(skolemize,[status(sab)],[163])).
% 0.82/1.00 tff(165,plain,
% 0.82/1.00 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.82/1.00 tff(166,plain,
% 0.82/1.00 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.82/1.00 tff(167,plain,
% 0.82/1.00 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[166, 150])).
% 0.82/1.00 tff(168,plain,
% 0.82/1.00 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(B!7)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(B!7)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(169,plain,
% 0.82/1.00 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(B!7)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(170,plain,
% 0.82/1.00 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(B!7)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.82/1.00 tff(171,plain,
% 0.82/1.00 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[170, 167, 9])).
% 0.82/1.00 tff(172,plain,
% 0.82/1.00 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(173,plain,
% 0.82/1.00 (((~relation(relation_rng_restriction(A!8, B!7))) | (~((~((relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), relation_rng_restriction(A!8, B!7))))) | (~((~(relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7))))))))) <=> ((~relation(relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(174,plain,
% 0.82/1.00 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | (~((~((relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), relation_rng_restriction(A!8, B!7))))) | (~((~(relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7))))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[173])).
% 0.82/1.00 tff(175,plain,
% 0.82/1.00 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | (~((~((relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), relation_rng_restriction(A!8, B!7))))) | (~((~(relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))),
% 0.82/1.00 inference(transitivity,[status(thm)],[174, 172])).
% 0.82/1.00 tff(176,plain,
% 0.82/1.00 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | (~((~((relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!8, B!7), B!7, A!8), tptp_fun_E_0(relation_rng_restriction(A!8, B!7), B!7, A!8)), relation_rng_restriction(A!8, B!7))))) | (~((~(relation_rng_restriction(A!8, B!7) = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7)))))))))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(177,plain,
% 0.82/1.00 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!8, B!7)) | (((~in(tptp_fun_E_0(C, B!7, A!8), A!8)) | (~in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), B!7))) <=> in(ordered_pair(tptp_fun_D_1(C, B!7, A!8), tptp_fun_E_0(C, B!7, A!8)), C)))) | (~((~(C = relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.82/1.00 tff(178,plain,
% 0.82/1.00 (![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7))))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[177, 107, 171])).
% 0.82/1.00 tff(179,plain,
% 0.82/1.00 ((~![D: $i, E: $i] : (~(((~in(E, A!8)) | (~in(ordered_pair(D, E), B!7))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!8, B!7))))) | (~(((~in(tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7)), A!8)) | (~in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), B!7))) <=> in(ordered_pair(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), tptp_fun_D_3(tptp_fun_C_2(relation_dom(B!7), relation_dom(relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))), relation_rng_restriction(A!8, B!7))))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(180,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[179, 178, 148])).
% 0.82/1.00 % SZS output end Proof
% 0.82/1.01 % E exiting
%------------------------------------------------------------------------------