%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU223+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:27:18 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU223+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:24:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(relation_type, type, (
% 0.20/0.48 relation: $i > $o)).
% 0.20/0.48 tff(relation_dom_restriction_type, type, (
% 0.20/0.48 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tptp_fun_A_78_type, type, (
% 0.20/0.48 tptp_fun_A_78: $i)).
% 0.20/0.48 tff(tptp_fun_C_76_type, type, (
% 0.20/0.48 tptp_fun_C_76: $i)).
% 0.20/0.48 tff(function_type, type, (
% 0.20/0.48 function: $i > $o)).
% 0.20/0.48 tff(in_type, type, (
% 0.20/0.48 in: ( $i * $i ) > $o)).
% 0.20/0.48 tff(relation_dom_type, type, (
% 0.20/0.48 relation_dom: $i > $i)).
% 0.20/0.48 tff(tptp_fun_B_77_type, type, (
% 0.20/0.48 tptp_fun_B_77: $i)).
% 0.20/0.48 tff(apply_type, type, (
% 0.20/0.48 apply: ( $i * $i ) > $i)).
% 0.20/0.48 tff(set_intersection2_type, type, (
% 0.20/0.48 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tptp_fun_D_75_type, type, (
% 0.20/0.48 tptp_fun_D_75: ( $i * $i ) > $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))))) <=> (~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A)))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, relation_dom(relation_dom_restriction(C, A))) => (apply(relation_dom_restriction(C, A), B) = apply(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(4,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, relation_dom(relation_dom_restriction(C, A))) => (apply(relation_dom_restriction(C, A), B) = apply(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t70_funct_1')).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, relation_dom(relation_dom_restriction(C, A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.48 tff(9,plain,(
% 0.20/0.48 ~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[8])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (relation(C!76) & function(C!76)),
% 0.20/0.48 inference(or_elim,[status(thm)],[10])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (relation(C!76)),
% 0.20/0.48 inference(and_elim,[status(thm)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.48 tff(18,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.48 tff(21,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[20])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!76)) | relation(relation_dom_restriction(C!76, A!78)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!76)) | relation(relation_dom_restriction(C!76, A!78)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!76)) | relation(relation_dom_restriction(C!76, A!78)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!76)) | relation(relation_dom_restriction(C!76, A!78))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (relation(relation_dom_restriction(C!76, A!78))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (function(C!76)),
% 0.20/0.48 inference(and_elim,[status(thm)],[11])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), rewrite((relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))) <=> (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))), (((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))), (((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite(((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.48 tff(35,axiom,(![A: $i, B: $i] : ((relation(A) & function(A)) => (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc4_funct_1')).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.48 tff(38,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~(relation(A) & function(A))) | (relation(relation_dom_restriction(A, B)) & function(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[37])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | (~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (((~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78)))))) <=> ((~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 ((~((~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))))) <=> (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (((~relation(C!76)) | (~function(C!76)) | (~((~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78)))))) <=> ((~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~relation(C!76)) | (~function(C!76)) | (~((~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78)))))) <=> ((~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(C!76)) | (~function(C!76)) | (~((~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(C!76)) | (~function(C!76)) | (~((~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | (~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[46, 41])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | ((~relation(C!76)) | (~function(C!76)) | (~((~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(relation_dom_restriction(A, B))) | (~function(relation_dom_restriction(A, B))))))) | (~relation(C!76)) | (~function(C!76)) | (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (~((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[49, 40, 12, 27])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78)))) | function(relation_dom_restriction(C!76, A!78))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (function(relation_dom_restriction(C!76, A!78))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))),
% 0.20/0.48 inference(or_elim,[status(thm)],[10])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (~(apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))),
% 0.20/0.48 inference(or_elim,[status(thm)],[10])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))) | (~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[55, 54, 53])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))))) | ((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), rewrite(((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))), rewrite(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (![A: $i, B: $i] : ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.48 inference(pull_quant,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))) <=> ?[D: $i] : (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))), (((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | ?[D: $i] : (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), pull_quant(((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | ?[D: $i] : (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))), (((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), ((~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> (~?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), pull_quant((~?[D: $i] : ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), ((~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ((~(B = relation_dom_restriction(C, A))) | ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), pull_quant(((~(B = relation_dom_restriction(C, A))) | ![D: $i] : (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) <=> (~![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))))), pull_quant((~![D: $i] : ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) <=> ?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) <=> ?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))))), (((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))) <=> (?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))), pull_quant((?[D: $i] : (~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))) <=> ?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))), (((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))) <=> ?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))), ((~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> (~?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), pull_quant((~?[D: $i] : ((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))), ((~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), pull_quant(((~relation(C)) | (~function(C)) | ![D: $i] : (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))), (![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ![C: $i] : ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), pull_quant(![C: $i] : ![D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), (((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))), pull_quant(((~relation(B)) | (~function(B)) | ![C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), (((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i] : ![C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[66, 62])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), trans(monotonicity(rewrite(((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) <=> ((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), rewrite(((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))) <=> ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))), ((((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))) <=> (((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))), rewrite((((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))) <=> (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))), ((((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))) <=> (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))) <=> (((~relation(C)) | (~function(C))) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), rewrite((((~relation(C)) | (~function(C))) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))), (((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))) <=> ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))), (![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))) <=> ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))), (((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))) <=> ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), rewrite(((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))) <=> ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))), (((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))) <=> ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), (![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))) <=> ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.49 tff(78,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : (in(D, relation_dom(B)) => (apply(B, D) = apply(C, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t68_funct_1')).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ((B = relation_dom_restriction(C, A)) <=> ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.49 tff(81,plain,(
% 0.20/0.49 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | ((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[80])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (((~(B = relation_dom_restriction(C, A))) | ((relation_dom(B) = set_intersection2(relation_dom(C), A)) & ![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D))))) & ((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~![D: $i] : ((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((B = relation_dom_restriction(C, A)) | (~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[84, 60])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | ((~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | (~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))))))) <=> ((~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ((~((~((~(relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78)) | (~((~in(tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)), relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))) = apply(C!76, tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)))))))))) <=> (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~((~(relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78)) | (~((~in(tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)), relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))) = apply(C!76, tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))))))))))) <=> ((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~((~(relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78)) | (~((~in(tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)), relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))) = apply(C!76, tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))))))))))) <=> ((~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | ((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~((~(relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78)) | (~((~in(tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)), relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))) = apply(C!76, tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | ((~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | ((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~((~(relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78)) | (~((~in(tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)), relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))) = apply(C!76, tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | (~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[91, 86])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | ((~relation(C!76)) | (~function(C!76)) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(relation_dom_restriction(C!76, A!78))) | (~((~((~(relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)))))))) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (relation_dom_restriction(C!76, A!78) = relation_dom_restriction(C!76, A!78)) | (~((~in(tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)), relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78))) = apply(C!76, tptp_fun_D_75(C!76, relation_dom_restriction(C!76, A!78)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (~((~((~(B = relation_dom_restriction(C, A))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (~((~in(D, relation_dom(B))) | (apply(B, D) = apply(C, D)))))))) | (~((~(relation_dom(B) = set_intersection2(relation_dom(C), A))) | (B = relation_dom_restriction(C, A)) | (~((~in(tptp_fun_D_75(C, B), relation_dom(B))) | (apply(B, tptp_fun_D_75(C, B)) = apply(C, tptp_fun_D_75(C, B))))))))))) | (~relation(C!76)) | (~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78))) | (~function(C!76)) | (~((~(relation_dom(relation_dom_restriction(C!76, A!78)) = set_intersection2(relation_dom(C!76), A!78))) | (~((~in(B!77, relation_dom(relation_dom_restriction(C!76, A!78)))) | (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 ((~function(relation_dom_restriction(C!76, A!78))) | (~relation(relation_dom_restriction(C!76, A!78)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[94, 85, 12, 27, 58])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[95, 52, 26])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------