%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU212+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:15 AM UTC 2025
% Result : Theorem 0.23s 0.46s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEU212+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 06:18:39 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.46 % SZS status Theorem
% 0.23/0.46 % SZS output start Proof
% 0.23/0.46 tff(in_type, type, (
% 0.23/0.46 in: ( $i * $i ) > $o)).
% 0.23/0.46 tff(tptp_fun_C_10_type, type, (
% 0.23/0.46 tptp_fun_C_10: $i)).
% 0.23/0.46 tff(ordered_pair_type, type, (
% 0.23/0.46 ordered_pair: ( $i * $i ) > $i)).
% 0.23/0.46 tff(tptp_fun_B_11_type, type, (
% 0.23/0.46 tptp_fun_B_11: $i)).
% 0.23/0.46 tff(tptp_fun_A_12_type, type, (
% 0.23/0.46 tptp_fun_A_12: $i)).
% 0.23/0.46 tff(apply_type, type, (
% 0.23/0.46 apply: ( $i * $i ) > $i)).
% 0.23/0.46 tff(relation_dom_type, type, (
% 0.23/0.46 relation_dom: $i > $i)).
% 0.23/0.46 tff(tptp_fun_D_0_type, type, (
% 0.23/0.46 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.23/0.46 tff(tptp_fun_C_1_type, type, (
% 0.23/0.46 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.23/0.46 tff(tptp_fun_D_2_type, type, (
% 0.23/0.46 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.23/0.46 tff(relation_type, type, (
% 0.23/0.46 relation: $i > $o)).
% 0.23/0.46 tff(function_type, type, (
% 0.23/0.46 function: $i > $o)).
% 0.23/0.46 tff(empty_set_type, type, (
% 0.23/0.46 empty_set: $i)).
% 0.23/0.46 tff(1,assumption,((~((~in(A!12, relation_dom(C!10))) | in(ordered_pair(A!12, tptp_fun_D_0(A!12, C!10)), C!10))) | (~(in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10))))), introduced(assumption)).
% 0.23/0.46 tff(2,plain,
% 0.23/0.46 ((~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))) <=> (~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(3,plain,
% 0.23/0.46 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))) <=> (~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(4,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_funct_1')).
% 0.23/0.46 tff(5,plain,
% 0.23/0.46 (~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.46 tff(6,plain,
% 0.23/0.46 (~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.23/0.46 tff(7,plain,
% 0.23/0.46 (~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.46 tff(8,plain,
% 0.23/0.46 (~![A: $i, B: $i, C: $i] : ((~(relation(C) & function(C))) | (in(ordered_pair(A, B), C) <=> (in(A, relation_dom(C)) & (B = apply(C, A)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.23/0.46 tff(9,plain,(
% 0.23/0.46 ~((~(relation(C!10) & function(C!10))) | (in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12)))))),
% 0.23/0.46 inference(skolemize,[status(sab)],[8])).
% 0.23/0.46 tff(10,plain,
% 0.23/0.46 (relation(C!10) & function(C!10)),
% 0.23/0.46 inference(or_elim,[status(thm)],[9])).
% 0.23/0.46 tff(11,plain,
% 0.23/0.46 (relation(C!10)),
% 0.23/0.46 inference(and_elim,[status(thm)],[10])).
% 0.23/0.46 tff(12,plain,
% 0.23/0.46 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(13,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[12])).
% 0.23/0.46 tff(14,plain,
% 0.23/0.46 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(15,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.46 tff(16,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[15, 13])).
% 0.23/0.46 tff(17,plain,
% 0.23/0.46 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(18,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[17])).
% 0.23/0.46 tff(19,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(20,plain,
% 0.23/0.46 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(21,plain,
% 0.23/0.46 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[20])).
% 0.23/0.46 tff(22,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relat_1')).
% 0.23/0.46 tff(23,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.46 tff(24,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.23/0.46 tff(25,plain,(
% 0.23/0.46 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))),
% 0.23/0.46 inference(skolemize,[status(sab)],[24])).
% 0.23/0.46 tff(26,plain,
% 0.23/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.23/0.47 tff(27,plain,
% 0.23/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.23/0.47 tff(28,plain,
% 0.23/0.47 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10)))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(29,plain,
% 0.23/0.47 (((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((B = relation_dom(C!10)) | (~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10))))))))))) <=> ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10)))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(30,plain,
% 0.23/0.47 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((B = relation_dom(C!10)) | (~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[29])).
% 0.23/0.47 tff(31,plain,
% 0.23/0.47 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((B = relation_dom(C!10)) | (~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10)))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[30, 28])).
% 0.23/0.47 tff(32,plain,
% 0.23/0.47 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((B = relation_dom(C!10)) | (~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(33,plain,
% 0.23/0.47 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_2(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, A), D), A)))))))))))) | (~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.23/0.47 tff(34,plain,
% 0.23/0.47 (![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[33, 27, 11])).
% 0.23/0.47 tff(35,plain,
% 0.23/0.47 (((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(36,plain,
% 0.23/0.47 ((~(~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(37,plain,
% 0.23/0.47 (((~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(38,plain,
% 0.23/0.47 ((~$true) <=> $false),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(39,plain,
% 0.23/0.47 (((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | $true) <=> $true),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(40,plain,
% 0.23/0.48 ((relation_dom(C!10) = relation_dom(C!10)) <=> $true),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(41,plain,
% 0.23/0.48 (((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10))) <=> ((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(42,plain,
% 0.23/0.48 ((~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))) <=> (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[41])).
% 0.23/0.48 tff(43,plain,
% 0.23/0.48 (((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10))))) <=> ((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[42])).
% 0.23/0.48 tff(44,plain,
% 0.23/0.48 ((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) <=> (~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[43])).
% 0.23/0.48 tff(45,plain,
% 0.23/0.48 (((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))) <=> ((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | $true)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[44, 40])).
% 0.23/0.48 tff(46,plain,
% 0.23/0.48 (((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))) <=> $true),
% 0.23/0.48 inference(transitivity,[status(thm)],[45, 39])).
% 0.23/0.48 tff(47,plain,
% 0.23/0.48 ((~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10)))) <=> (~$true)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[46])).
% 0.23/0.48 tff(48,plain,
% 0.23/0.48 ((~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10)))) <=> $false),
% 0.23/0.48 inference(transitivity,[status(thm)],[47, 38])).
% 0.23/0.48 tff(49,plain,
% 0.23/0.48 ((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(50,plain,
% 0.23/0.48 (((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))))) <=> ((~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))) | $false)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[49, 48])).
% 0.23/0.48 tff(51,plain,
% 0.23/0.48 (((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[50, 37])).
% 0.23/0.48 tff(52,plain,
% 0.23/0.48 ((~((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[51])).
% 0.23/0.48 tff(53,plain,
% 0.23/0.48 ((~((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10)))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[52, 36])).
% 0.23/0.48 tff(54,plain,
% 0.23/0.48 (((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | (~((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[53])).
% 0.23/0.48 tff(55,plain,
% 0.23/0.48 (((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | (~((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[54, 35])).
% 0.23/0.48 tff(56,plain,
% 0.23/0.48 ((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | (~((~((~(relation_dom(C!10) = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10)) | in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), tptp_fun_D_2(relation_dom(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_1(relation_dom(C!10), C!10), relation_dom(C!10))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(relation_dom(C!10), C!10), D), C!10)))))) | (relation_dom(C!10) = relation_dom(C!10))))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(57,plain,
% 0.23/0.48 ((~![B: $i] : (~((~((~(B = relation_dom(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!10)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!10), B) | in(ordered_pair(tptp_fun_C_1(B, C!10), tptp_fun_D_2(B, C!10)), C!10))) | (~((~in(tptp_fun_C_1(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_1(B, C!10), D), C!10)))))) | (B = relation_dom(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.23/0.48 tff(58,plain,
% 0.23/0.48 (![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[57, 34])).
% 0.23/0.48 tff(59,plain,
% 0.23/0.48 ((~![C: $i] : (~((~((~in(C, relation_dom(C!10))) | in(ordered_pair(C, tptp_fun_D_0(C, C!10)), C!10))) | (~(in(C, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(C, D), C!10))))))) | (~((~((~in(A!12, relation_dom(C!10))) | in(ordered_pair(A!12, tptp_fun_D_0(A!12, C!10)), C!10))) | (~(in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10))))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(60,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[59, 58, 1])).
% 0.23/0.48 tff(61,plain,(~((~((~in(A!12, relation_dom(C!10))) | in(ordered_pair(A!12, tptp_fun_D_0(A!12, C!10)), C!10))) | (~(in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10)))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(62,plain,
% 0.23/0.48 (((~((~in(A!12, relation_dom(C!10))) | in(ordered_pair(A!12, tptp_fun_D_0(A!12, C!10)), C!10))) | (~(in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10))))) | (in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10)))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(63,plain,
% 0.23/0.48 (in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.23/0.48 tff(64,assumption,(![D: $i] : (~in(ordered_pair(A!12, D), C!10))), introduced(assumption)).
% 0.23/0.48 tff(65,assumption,(~in(ordered_pair(A!12, B!11), C!10)), introduced(assumption)).
% 0.23/0.48 tff(66,plain,
% 0.23/0.48 ((~(~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))) <=> (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(67,plain,
% 0.23/0.48 ((~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10))) <=> (~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(68,plain,
% 0.23/0.48 ((in(ordered_pair(A!12, B!11), C!10) <=> (~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))))) <=> (~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(69,plain,
% 0.23/0.48 ((in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12))) <=> (~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(70,plain,
% 0.23/0.48 ((in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12)))) <=> (in(ordered_pair(A!12, B!11), C!10) <=> (~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[69])).
% 0.23/0.48 tff(71,plain,
% 0.23/0.48 ((in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12)))) <=> (~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[70, 68])).
% 0.23/0.48 tff(72,plain,
% 0.23/0.48 ((in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12)))) <=> (~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[71, 67])).
% 0.23/0.48 tff(73,plain,
% 0.23/0.48 ((~(in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12))))) <=> (~(~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[72])).
% 0.23/0.48 tff(74,plain,
% 0.23/0.48 ((~(in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12))))) <=> (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.48 inference(transitivity,[status(thm)],[73, 66])).
% 0.23/0.48 tff(75,plain,
% 0.23/0.48 (~(in(ordered_pair(A!12, B!11), C!10) <=> (in(A!12, relation_dom(C!10)) & (B!11 = apply(C!10, A!12))))),
% 0.23/0.48 inference(or_elim,[status(thm)],[9])).
% 0.23/0.48 tff(76,plain,
% 0.23/0.48 (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.23/0.49 tff(77,plain,
% 0.23/0.49 ((~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12))))) | in(ordered_pair(A!12, B!11), C!10) | (~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(78,plain,
% 0.23/0.49 ((~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12))))) | in(ordered_pair(A!12, B!11), C!10)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.23/0.49 tff(79,plain,
% 0.23/0.49 (~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[78, 65])).
% 0.23/0.49 tff(80,plain,
% 0.23/0.49 (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) | (B!11 = apply(C!10, A!12))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(81,plain,
% 0.23/0.49 (B!11 = apply(C!10, A!12)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.23/0.49 tff(82,plain,
% 0.23/0.49 (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) | in(A!12, relation_dom(C!10))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(83,plain,
% 0.23/0.49 (in(A!12, relation_dom(C!10))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.23/0.49 tff(84,plain,
% 0.23/0.49 (function(C!10)),
% 0.23/0.49 inference(and_elim,[status(thm)],[10])).
% 0.23/0.49 tff(85,plain,
% 0.23/0.49 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(86,plain,
% 0.23/0.49 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[85])).
% 0.23/0.49 tff(87,plain,
% 0.23/0.49 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(88,plain,
% 0.23/0.49 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[87])).
% 0.23/0.49 tff(89,plain,
% 0.23/0.49 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[88, 86])).
% 0.23/0.49 tff(90,plain,
% 0.23/0.49 (^[A: $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))))), quant_intro(proof_bind(^[B: $i, C: $i] : rewrite((((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))) <=> (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))), (![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))) <=> ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))), (((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))), (((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(91,plain,
% 0.23/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[90])).
% 0.23/0.49 tff(92,plain,
% 0.23/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(93,plain,
% 0.23/0.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : rewrite(((in(B, relation_dom(A)) => ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & ((~in(B, relation_dom(A))) => ((C = apply(A, B)) <=> (C = empty_set)))) <=> (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))), (![B: $i, C: $i] : ((in(B, relation_dom(A)) => ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & ((~in(B, relation_dom(A))) => ((C = apply(A, B)) <=> (C = empty_set)))) <=> ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))), (((relation(A) & function(A)) => ![B: $i, C: $i] : ((in(B, relation_dom(A)) => ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & ((~in(B, relation_dom(A))) => ((C = apply(A, B)) <=> (C = empty_set))))) <=> ((relation(A) & function(A)) => ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))))), rewrite(((relation(A) & function(A)) => ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set))))) <=> ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))), (((relation(A) & function(A)) => ![B: $i, C: $i] : ((in(B, relation_dom(A)) => ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & ((~in(B, relation_dom(A))) => ((C = apply(A, B)) <=> (C = empty_set))))) <=> ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(94,plain,
% 0.23/0.49 (![A: $i] : ((relation(A) & function(A)) => ![B: $i, C: $i] : ((in(B, relation_dom(A)) => ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & ((~in(B, relation_dom(A))) => ((C = apply(A, B)) <=> (C = empty_set))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[93])).
% 0.23/0.49 tff(95,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i, C: $i] : ((in(B, relation_dom(A)) => ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & ((~in(B, relation_dom(A))) => ((C = apply(A, B)) <=> (C = empty_set)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_funct_1')).
% 0.23/0.49 tff(96,plain,
% 0.23/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.23/0.49 tff(97,plain,
% 0.23/0.49 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.23/0.49 tff(98,plain,(
% 0.23/0.49 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i, C: $i] : (((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A))) & (in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))),
% 0.23/0.49 inference(skolemize,[status(sab)],[97])).
% 0.23/0.49 tff(99,plain,
% 0.23/0.49 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.23/0.49 tff(100,plain,
% 0.23/0.49 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.23/0.49 tff(101,plain,
% 0.23/0.49 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | (![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))) | (~function(C!10)) | (~relation(C!10)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))) | (~function(C!10)) | (~relation(C!10)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(102,plain,
% 0.23/0.49 (((~relation(C!10)) | (~function(C!10)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set))))))) <=> (![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))) | (~function(C!10)) | (~relation(C!10)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(103,plain,
% 0.23/0.49 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | ((~relation(C!10)) | (~function(C!10)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | (![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))) | (~function(C!10)) | (~relation(C!10))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[102])).
% 0.23/0.49 tff(104,plain,
% 0.23/0.49 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | ((~relation(C!10)) | (~function(C!10)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))) | (~function(C!10)) | (~relation(C!10)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[103, 101])).
% 0.23/0.49 tff(105,plain,
% 0.23/0.49 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | ((~relation(C!10)) | (~function(C!10)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(106,plain,
% 0.23/0.49 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(A))) | ((C = apply(A, B)) <=> in(ordered_pair(B, C), A)))) | (~(in(B, relation_dom(A)) | ((C = apply(A, B)) <=> (C = empty_set)))))))) | ![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set)))))) | (~function(C!10)) | (~relation(C!10))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.23/0.49 tff(107,plain,
% 0.23/0.49 (![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set))))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[106, 100, 11, 84])).
% 0.23/0.49 tff(108,plain,
% 0.23/0.49 ((~![B: $i, C: $i] : (~((~((~in(B, relation_dom(C!10))) | ((C = apply(C!10, B)) <=> in(ordered_pair(B, C), C!10)))) | (~(in(B, relation_dom(C!10)) | ((C = apply(C!10, B)) <=> (C = empty_set))))))) | (~((~((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)))) | (~(in(A!12, relation_dom(C!10)) | ((B!11 = apply(C!10, A!12)) <=> (B!11 = empty_set))))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(109,plain,
% 0.23/0.49 (~((~((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)))) | (~(in(A!12, relation_dom(C!10)) | ((B!11 = apply(C!10, A!12)) <=> (B!11 = empty_set)))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.23/0.49 tff(110,plain,
% 0.23/0.49 (((~((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)))) | (~(in(A!12, relation_dom(C!10)) | ((B!11 = apply(C!10, A!12)) <=> (B!11 = empty_set))))) | ((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(111,plain,
% 0.23/0.49 ((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.23/0.49 tff(112,plain,
% 0.23/0.49 ((~((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)))) | (~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(113,plain,
% 0.23/0.49 ((~in(A!12, relation_dom(C!10))) | ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.23/0.49 tff(114,plain,
% 0.23/0.49 ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[113, 83])).
% 0.23/0.49 tff(115,plain,
% 0.23/0.49 ((~((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10))) | (~(B!11 = apply(C!10, A!12))) | in(ordered_pair(A!12, B!11), C!10)),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(116,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[115, 114, 81, 65])).
% 0.23/0.49 tff(117,plain,(in(ordered_pair(A!12, B!11), C!10)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(118,plain,
% 0.23/0.49 ((~![D: $i] : (~in(ordered_pair(A!12, D), C!10))) | (~in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(119,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[118, 117, 64])).
% 0.23/0.49 tff(120,plain,(~![D: $i] : (~in(ordered_pair(A!12, D), C!10))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(121,plain,
% 0.23/0.49 ((~(in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10)))) | in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(122,plain,
% 0.23/0.49 ((~(in(A!12, relation_dom(C!10)) | ![D: $i] : (~in(ordered_pair(A!12, D), C!10)))) | in(A!12, relation_dom(C!10))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.23/0.49 tff(123,plain,
% 0.23/0.49 (in(A!12, relation_dom(C!10))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[122, 63])).
% 0.23/0.49 tff(124,plain,
% 0.23/0.49 ((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[113, 123])).
% 0.23/0.49 tff(125,plain,
% 0.23/0.49 (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) | (~in(ordered_pair(A!12, B!11), C!10)) | (~(((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) <=> in(ordered_pair(A!12, B!11), C!10)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(126,plain,
% 0.23/0.49 (((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))) | (~in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[125, 76])).
% 0.23/0.49 tff(127,plain,
% 0.23/0.49 ((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[126, 117])).
% 0.23/0.49 tff(128,plain,
% 0.23/0.49 ((~((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12))))) | (~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(129,plain,
% 0.23/0.49 ((~in(A!12, relation_dom(C!10))) | (~(B!11 = apply(C!10, A!12)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.23/0.49 tff(130,plain,
% 0.23/0.49 (~(B!11 = apply(C!10, A!12))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[129, 123])).
% 0.23/0.49 tff(131,plain,
% 0.23/0.49 ((~((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10))) | (B!11 = apply(C!10, A!12)) | (~in(ordered_pair(A!12, B!11), C!10))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(132,plain,
% 0.23/0.49 ((~((B!11 = apply(C!10, A!12)) <=> in(ordered_pair(A!12, B!11), C!10))) | (B!11 = apply(C!10, A!12))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[131, 117])).
% 0.23/0.49 tff(133,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[132, 130, 124])).
% 0.23/0.49 % SZS output end Proof
% 0.23/0.50 % E exiting
%------------------------------------------------------------------------------