%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU177+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:27:09 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU177+1 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:12:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(in_type, type, (
% 0.19/0.44 in: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_C_4_type, type, (
% 0.19/0.44 tptp_fun_C_4: $i)).
% 0.19/0.44 tff(ordered_pair_type, type, (
% 0.19/0.44 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_A_6_type, type, (
% 0.19/0.44 tptp_fun_A_6: $i)).
% 0.19/0.44 tff(relation_dom_type, type, (
% 0.19/0.44 relation_dom: $i > $i)).
% 0.19/0.44 tff(tptp_fun_D_7_type, type, (
% 0.19/0.44 tptp_fun_D_7: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_C_8_type, type, (
% 0.19/0.44 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_D_9_type, type, (
% 0.19/0.44 tptp_fun_D_9: ( $i * $i ) > $i)).
% 0.19/0.44 tff(relation_type, type, (
% 0.19/0.44 relation: $i > $o)).
% 0.19/0.44 tff(tptp_fun_B_5_type, type, (
% 0.19/0.44 tptp_fun_B_5: $i)).
% 0.19/0.44 tff(relation_rng_type, type, (
% 0.19/0.44 relation_rng: $i > $i)).
% 0.19/0.44 tff(tptp_fun_D_10_type, type, (
% 0.19/0.44 tptp_fun_D_10: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_C_11_type, type, (
% 0.19/0.44 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_D_12_type, type, (
% 0.19/0.44 tptp_fun_D_12: ( $i * $i ) > $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(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_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(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_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(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_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A)) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A)) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(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_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.44 tff(11,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')).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.44 tff(14,plain,(
% 0.19/0.44 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A)) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 ((~((in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4))) | (~in(ordered_pair(A!6, B!5), C!4)) | (~relation(C!4)))) <=> (~((in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4))) | (~in(ordered_pair(A!6, B!5), C!4)) | (~relation(C!4))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C)))) <=> (~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(20,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_relat_1')).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (~![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~in(ordered_pair(A, B), C)) | (~relation(C)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.45 tff(25,plain,(
% 0.19/0.45 ~((in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4))) | (~in(ordered_pair(A!6, B!5), C!4)) | (~relation(C!4)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[24])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (~((in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4))) | (~in(ordered_pair(A!6, B!5), C!4)) | (~relation(C!4)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (relation(C!4)),
% 0.19/0.45 inference(or_elim,[status(thm)],[26])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | (~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((B = relation_dom(C!4)) | (~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4))))))))))) <=> ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((B = relation_dom(C!4)) | (~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((B = relation_dom(C!4)) | (~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | (~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((B = relation_dom(C!4)) | (~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | in(ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)), A))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, A), D), A)))))))))))) | (~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[33, 27, 16])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 ((~(~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (((~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 ((~$true) <=> $false),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | $true) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 ((relation_dom(C!4) = relation_dom(C!4)) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4))) <=> ((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 ((~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))) <=> (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4))))) <=> ((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 ((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) <=> (~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))) <=> ((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | $true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[44, 40])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))) <=> $true),
% 0.19/0.45 inference(transitivity,[status(thm)],[45, 39])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 ((~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4)))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4)))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[47, 38])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 ((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))))) <=> ((~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[49, 48])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[50, 37])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((~((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4)))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[52, 36])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | (~((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | (~((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[54, 35])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 ((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | (~((~((~(relation_dom(C!4) = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4)) | in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), tptp_fun_D_9(relation_dom(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_8(relation_dom(C!4), C!4), relation_dom(C!4))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(relation_dom(C!4), C!4), D), C!4)))))) | (relation_dom(C!4) = relation_dom(C!4))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 ((~![B: $i] : (~((~((~(B = relation_dom(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!4)))))))) | (~((~((~(in(tptp_fun_C_8(B, C!4), B) | in(ordered_pair(tptp_fun_C_8(B, C!4), tptp_fun_D_9(B, C!4)), C!4))) | (~((~in(tptp_fun_C_8(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_8(B, C!4), D), C!4)))))) | (B = relation_dom(C!4))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[57, 34])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 ((~![C: $i] : (~((~((~in(C, relation_dom(C!4))) | in(ordered_pair(C, tptp_fun_D_7(C, C!4)), C!4))) | (~(in(C, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(C, D), C!4))))))) | (~((~((~in(A!6, relation_dom(C!4))) | in(ordered_pair(A!6, tptp_fun_D_7(A!6, C!4)), C!4))) | (~(in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (~((~((~in(A!6, relation_dom(C!4))) | in(ordered_pair(A!6, tptp_fun_D_7(A!6, C!4)), C!4))) | (~(in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (((~((~in(A!6, relation_dom(C!4))) | in(ordered_pair(A!6, tptp_fun_D_7(A!6, C!4)), C!4))) | (~(in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4))))) | (in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.46 tff(63,assumption,((~((~in(B!5, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(B!5, C!4), B!5), C!4))) | (~(in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4))))), introduced(assumption)).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A)) & ((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A)) & ((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.46 tff(74,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_relat_1')).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.46 tff(77,plain,(
% 0.19/0.46 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A)) & ((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[76])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))) | (~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))) | ((~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4)))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_11(B, A), B) | in(ordered_pair(tptp_fun_D_12(B, A), tptp_fun_C_11(B, A)), A))) | (~((~in(tptp_fun_C_11(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, A)), A)))))))))))) | (~relation(C!4)) | ![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[82, 27, 79])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 ((~(~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (((~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (($true | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))) <=> $true),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) <=> ((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 ((~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))) <=> (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))) <=> ((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 ((~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))) <=> (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 ((relation_rng(C!4) = relation_rng(C!4)) <=> $true),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))) <=> ($true | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[92, 91])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))) <=> $true),
% 0.19/0.46 inference(transitivity,[status(thm)],[93, 87])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))))) <=> (~$true)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 ((~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))))) <=> $false),
% 0.19/0.46 inference(transitivity,[status(thm)],[95, 38])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 ((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))))) <=> ((~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))) | $false)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[97, 96])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[98, 86])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 ((~((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 ((~((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4)))))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[100, 85])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | (~((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | (~((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[102, 84])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | (~((~((~(relation_rng(C!4) = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((relation_rng(C!4) = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4)) | in(ordered_pair(tptp_fun_D_12(relation_rng(C!4), C!4), tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))) | (~((~in(tptp_fun_C_11(relation_rng(C!4), C!4), relation_rng(C!4))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(relation_rng(C!4), C!4)), C!4))))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ((~![B: $i] : (~((~((~(B = relation_rng(C!4))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!4)))))))) | (~((B = relation_rng(C!4)) | (~((~(in(tptp_fun_C_11(B, C!4), B) | in(ordered_pair(tptp_fun_D_12(B, C!4), tptp_fun_C_11(B, C!4)), C!4))) | (~((~in(tptp_fun_C_11(B, C!4), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_11(B, C!4)), C!4))))))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 83])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 ((~![C: $i] : (~((~((~in(C, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(C, C!4), C), C!4))) | (~(in(C, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, C), C!4))))))) | (~((~((~in(B!5, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(B!5, C!4), B!5), C!4))) | (~(in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[107, 106, 63])).
% 0.19/0.47 tff(109,plain,(~((~((~in(B!5, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(B!5, C!4), B!5), C!4))) | (~(in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (((~((~in(B!5, relation_rng(C!4))) | in(ordered_pair(tptp_fun_D_10(B!5, C!4), B!5), C!4))) | (~(in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4))))) | (in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.47 tff(112,assumption,(![D: $i] : (~in(ordered_pair(D, B!5), C!4))), introduced(assumption)).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (in(ordered_pair(A!6, B!5), C!4)),
% 0.19/0.47 inference(or_elim,[status(thm)],[26])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 ((~![D: $i] : (~in(ordered_pair(D, B!5), C!4))) | (~in(ordered_pair(A!6, B!5), C!4))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[114, 113, 112])).
% 0.19/0.47 tff(116,plain,(~![D: $i] : (~in(ordered_pair(D, B!5), C!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 ((~(in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4)))) | in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 ((~(in(B!5, relation_rng(C!4)) | ![D: $i] : (~in(ordered_pair(D, B!5), C!4)))) | in(B!5, relation_rng(C!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (in(B!5, relation_rng(C!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[118, 111])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 ((~(~((~in(A!6, relation_dom(C!4))) | (~in(B!5, relation_rng(C!4)))))) <=> ((~in(A!6, relation_dom(C!4))) | (~in(B!5, relation_rng(C!4))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 ((in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4))) <=> (~((~in(A!6, relation_dom(C!4))) | (~in(B!5, relation_rng(C!4)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 ((~(in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4)))) <=> (~(~((~in(A!6, relation_dom(C!4))) | (~in(B!5, relation_rng(C!4))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 ((~(in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4)))) <=> ((~in(A!6, relation_dom(C!4))) | (~in(B!5, relation_rng(C!4))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (~(in(A!6, relation_dom(C!4)) & in(B!5, relation_rng(C!4)))),
% 0.19/0.47 inference(or_elim,[status(thm)],[26])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 ((~in(A!6, relation_dom(C!4))) | (~in(B!5, relation_rng(C!4)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (~in(A!6, relation_dom(C!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[125, 119])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 ((~(in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4)))) | in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 ((~(in(A!6, relation_dom(C!4)) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4)))) | ![D: $i] : (~in(ordered_pair(A!6, D), C!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (![D: $i] : (~in(ordered_pair(A!6, D), C!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[128, 62])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 ((~![D: $i] : (~in(ordered_pair(A!6, D), C!4))) | (~in(ordered_pair(A!6, B!5), C!4))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[130, 113, 129])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------