%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU197+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:27:12 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU197+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:16:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(in_type, type, (
% 0.20/0.46 in: ( $i * $i ) > $o)).
% 0.20/0.46 tff(relation_rng_restriction_type, type, (
% 0.20/0.46 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_C_10_type, type, (
% 0.20/0.46 tptp_fun_C_10: $i)).
% 0.20/0.46 tff(tptp_fun_B_11_type, type, (
% 0.20/0.46 tptp_fun_B_11: $i)).
% 0.20/0.46 tff(ordered_pair_type, type, (
% 0.20/0.46 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_A_12_type, type, (
% 0.20/0.46 tptp_fun_A_12: $i)).
% 0.20/0.46 tff(tptp_fun_D_2_type, type, (
% 0.20/0.46 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.20/0.46 tff(relation_rng_type, type, (
% 0.20/0.46 relation_rng: $i > $i)).
% 0.20/0.46 tff(relation_type, type, (
% 0.20/0.46 relation: $i > $o)).
% 0.20/0.46 tff(tptp_fun_E_0_type, type, (
% 0.20/0.46 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_D_1_type, type, (
% 0.20/0.46 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_C_3_type, type, (
% 0.20/0.46 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_D_4_type, type, (
% 0.20/0.46 tptp_fun_D_4: ( $i * $i ) > $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t115_relat_1')).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.46 tff(8,plain,(
% 0.20/0.46 ~((~relation(C!10)) | (in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[7])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (relation(C!10)),
% 0.20/0.46 inference(or_elim,[status(thm)],[8])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.46 tff(15,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.46 tff(18,plain,(
% 0.20/0.46 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[17])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!10)) | relation(relation_rng_restriction(B!11, C!10)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!10)) | relation(relation_rng_restriction(B!11, C!10)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!10)) | relation(relation_rng_restriction(B!11, C!10)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!10)) | relation(relation_rng_restriction(B!11, C!10))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (relation(relation_rng_restriction(B!11, C!10))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) <=> ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), rewrite((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.47 tff(36,axiom,(![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_1')).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.47 tff(39,plain,(
% 0.20/0.47 ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[38])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[41, 25])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(C!10)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(C!10)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(C!10)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(C!10)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[45, 42, 9])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (((~relation(relation_rng_restriction(B!11, C!10))) | (~((~((relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), relation_rng_restriction(B!11, C!10))))) | (~((~(relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10))))))))) <=> ((~relation(relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | (~((~((relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), relation_rng_restriction(B!11, C!10))))) | (~((~(relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | (~((~((relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), relation_rng_restriction(B!11, C!10))))) | (~((~(relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | (~((~((relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(B!11, C!10), C!10, B!11), tptp_fun_E_0(relation_rng_restriction(B!11, C!10), C!10, B!11)), relation_rng_restriction(B!11, C!10))))) | (~((~(relation_rng_restriction(B!11, C!10) = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10)))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(B!11, C!10)) | (((~in(tptp_fun_E_0(C, C!10, B!11), B!11)) | (~in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C!10))) <=> in(ordered_pair(tptp_fun_D_1(C, C!10, B!11), tptp_fun_E_0(C, C!10, B!11)), C)))) | (~((~(C = relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(B!11, C!10))) | ![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[52, 46, 23])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 ((~![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10))))) | (~(((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (~(((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.48 tff(56,assumption,(~in(A!12, relation_rng(C!10))), introduced(assumption)).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) | in(A!12, relation_rng(C!10))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 ((~(~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))) <=> (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 ((~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))))) <=> (~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 ((in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))))) <=> (~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 ((in(A!12, B!11) & in(A!12, relation_rng(C!10))) <=> (~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 ((in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10)))) <=> (in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ((in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10)))) <=> (~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10)))) <=> (~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[64, 60])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 ((~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10))))) <=> (~(~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 ((~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10))))) <=> (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[66, 59])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) <=> (in(A!12, B!11) & in(A!12, relation_rng(C!10))))),
% 0.20/0.49 inference(or_elim,[status(thm)],[8])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 ((~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10))))) | in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | (~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 ((~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10))))) | in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[71, 58])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A)) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A)) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (^[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)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.49 tff(83,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/sandbox2/benchmark/theBenchmark.p','d5_relat_1')).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.49 tff(86,plain,(
% 0.20/0.49 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A)) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[85])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | (~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((B = relation_rng(relation_rng_restriction(B!11, C!10))) | (~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))))))))))) <=> ((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((B = relation_rng(relation_rng_restriction(B!11, C!10))) | (~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((B = relation_rng(relation_rng_restriction(B!11, C!10))) | (~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | (~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((B = relation_rng(relation_rng_restriction(B!11, C!10))) | (~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | (~relation(relation_rng_restriction(B!11, C!10))) | ![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 (![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[94, 88, 23])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 ((~(~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (((~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~$true) <=> $false),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | $true) <=> $true),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 ((relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10))) <=> $true),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) <=> ((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 ((~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))) <=> (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 (((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))))) <=> ((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 ((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) <=> (~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) <=> ((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | $true)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[105, 101])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) <=> $true),
% 0.20/0.51 inference(transitivity,[status(thm)],[106, 100])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10))))) <=> (~$true)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 ((~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10))))) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[108, 99])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 ((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))))) <=> ((~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))) | $false)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[110, 109])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[111, 98])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 ((~((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10))))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 ((~((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[113, 97])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 (((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | (~((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | (~((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[115, 96])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 ((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | (~((~((~(relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10))) | in(ordered_pair(tptp_fun_D_4(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10)), relation_rng(relation_rng_restriction(B!11, C!10)))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(relation_rng_restriction(B!11, C!10)), relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (relation_rng(relation_rng_restriction(B!11, C!10)) = relation_rng(relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 ((~![B: $i] : (~((~((~(B = relation_rng(relation_rng_restriction(B!11, C!10)))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10))))))))) | (~((~((~(in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B) | in(ordered_pair(tptp_fun_D_4(B, relation_rng_restriction(B!11, C!10)), tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10)))) | (~((~in(tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10)), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, relation_rng_restriction(B!11, C!10))), relation_rng_restriction(B!11, C!10))))))) | (B = relation_rng(relation_rng_restriction(B!11, C!10)))))))) | ![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 (![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[118, 95])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 ((~![C: $i] : (~((~((~in(C, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(C, relation_rng_restriction(B!11, C!10)), C), relation_rng_restriction(B!11, C!10)))) | (~(in(C, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, C), relation_rng_restriction(B!11, C!10)))))))) | (~((~((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))) | (~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (~((~((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))) | (~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (((~((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))) | (~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))))) | ((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 ((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.52 tff(124,plain,
% 0.20/0.52 ((~((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))) | (~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 ((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 (in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[125, 72])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 ((((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))) | (~((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10)))) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 ((((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))) | (~((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 (~((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[128, 55])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 (in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.52 tff(132,plain,
% 0.20/0.52 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | (~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 (((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((B = relation_rng(C!10)) | (~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10))))))))))) <=> ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((B = relation_rng(C!10)) | (~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((B = relation_rng(C!10)) | (~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | (~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10)))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | ((~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((B = relation_rng(C!10)) | (~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | in(ordered_pair(tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)), A))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, A)), A)))))))))))) | (~relation(C!10)) | ![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[137, 88, 9])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 (((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 ((~(~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (((~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | $true) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 ((relation_rng(C!10) = relation_rng(C!10)) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 (((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) <=> ((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 ((~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))) <=> (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))))) <=> ((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 ((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) <=> (~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))) <=> ((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | $true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[147, 143])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))) <=> $true),
% 0.20/0.52 inference(transitivity,[status(thm)],[148, 142])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 ((~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10)))) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 ((~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10)))) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[150, 99])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 ((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 (((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))))) <=> ((~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))) | $false)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[152, 151])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 (((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[153, 141])).
% 0.20/0.52 tff(155,plain,
% 0.20/0.52 ((~((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.53 tff(156,plain,
% 0.20/0.53 ((~((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10)))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[155, 140])).
% 0.20/0.53 tff(157,plain,
% 0.20/0.53 (((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | (~((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[156])).
% 0.20/0.53 tff(158,plain,
% 0.20/0.53 (((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | (~((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[157, 139])).
% 0.20/0.53 tff(159,plain,
% 0.20/0.53 ((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | (~((~((~(relation_rng(C!10) = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10)) | in(ordered_pair(tptp_fun_D_4(relation_rng(C!10), C!10), tptp_fun_C_3(relation_rng(C!10), C!10)), C!10))) | (~((~in(tptp_fun_C_3(relation_rng(C!10), C!10), relation_rng(C!10))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(relation_rng(C!10), C!10)), C!10)))))) | (relation_rng(C!10) = relation_rng(C!10))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(160,plain,
% 0.20/0.53 ((~![B: $i] : (~((~((~(B = relation_rng(C!10))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!10)))))))) | (~((~((~(in(tptp_fun_C_3(B, C!10), B) | in(ordered_pair(tptp_fun_D_4(B, C!10), tptp_fun_C_3(B, C!10)), C!10))) | (~((~in(tptp_fun_C_3(B, C!10), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_3(B, C!10)), C!10)))))) | (B = relation_rng(C!10))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.53 tff(161,plain,
% 0.20/0.53 (![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[160, 138])).
% 0.20/0.53 tff(162,plain,
% 0.20/0.53 ((~![C: $i] : (~((~((~in(C, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(C, C!10), C), C!10))) | (~(in(C, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, C), C!10))))))) | (~((~((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | (~(in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(163,plain,
% 0.20/0.53 (~((~((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | (~(in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.20/0.53 tff(164,plain,
% 0.20/0.53 (((~((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | (~(in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10))))) | (in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(165,plain,
% 0.20/0.53 (in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.53 tff(166,plain,
% 0.20/0.53 ((~(in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10)))) | in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(167,plain,
% 0.20/0.53 ((~(in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10)))) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[166, 56])).
% 0.20/0.53 tff(168,plain,
% 0.20/0.53 (![D: $i] : (~in(ordered_pair(D, A!12), C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[167, 165])).
% 0.20/0.53 tff(169,plain,
% 0.20/0.53 ((~![D: $i] : (~in(ordered_pair(D, A!12), C!10))) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(170,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[169, 168, 131])).
% 0.20/0.53 tff(171,plain,(in(A!12, relation_rng(C!10))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(172,plain,
% 0.20/0.53 ((~![D: $i, E: $i] : (~(((~in(E, B!11)) | (~in(ordered_pair(D, E), C!10))) <=> in(ordered_pair(D, E), relation_rng_restriction(B!11, C!10))))) | (~(((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), relation_rng_restriction(B!11, C!10))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(173,plain,
% 0.20/0.53 (~(((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[172, 53])).
% 0.20/0.53 tff(174,assumption,(~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))), introduced(assumption)).
% 0.20/0.53 tff(175,plain,
% 0.20/0.53 (~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[71, 174])).
% 0.20/0.53 tff(176,plain,
% 0.20/0.53 (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) | in(A!12, B!11)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(177,plain,
% 0.20/0.53 (in(A!12, B!11)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.53 tff(178,plain,
% 0.20/0.53 (((~((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | (~(in(A!12, relation_rng(C!10)) | ![D: $i] : (~in(ordered_pair(D, A!12), C!10))))) | ((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(179,plain,
% 0.20/0.53 ((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[178, 163])).
% 0.20/0.53 tff(180,plain,
% 0.20/0.53 ((~((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | (~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(181,plain,
% 0.20/0.53 ((~((~in(A!12, relation_rng(C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[180, 171])).
% 0.20/0.53 tff(182,plain,
% 0.20/0.53 (in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[181, 179])).
% 0.20/0.53 tff(183,plain,
% 0.20/0.53 ((~((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)))) | (~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(184,plain,
% 0.20/0.53 ((~((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)))) | (~in(A!12, B!11))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.20/0.53 tff(185,plain,
% 0.20/0.53 (~((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[184, 177])).
% 0.20/0.53 tff(186,plain,
% 0.20/0.53 ((((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), relation_rng_restriction(B!11, C!10))) | ((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), C!10))) | in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(187,plain,
% 0.20/0.53 (in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[186, 185, 173])).
% 0.20/0.53 tff(188,plain,
% 0.20/0.53 (((~((~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10)))) | (~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))))) | (in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(189,plain,
% 0.20/0.53 (in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[188, 121])).
% 0.20/0.53 tff(190,plain,
% 0.20/0.53 ((~(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10))))) | in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(191,plain,
% 0.20/0.53 (in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))) | ![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.53 tff(192,plain,
% 0.20/0.53 (![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[191, 174])).
% 0.20/0.53 tff(193,plain,
% 0.20/0.53 ((~![D: $i] : (~in(ordered_pair(D, A!12), relation_rng_restriction(B!11, C!10)))) | (~in(ordered_pair(tptp_fun_D_2(A!12, C!10), A!12), relation_rng_restriction(B!11, C!10)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(194,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[193, 192, 187])).
% 0.20/0.53 tff(195,plain,(in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(196,plain,
% 0.20/0.53 (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) | (~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))) | (~(((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) <=> in(A!12, relation_rng(relation_rng_restriction(B!11, C!10)))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(197,plain,
% 0.20/0.53 (((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))) | (~in(A!12, relation_rng(relation_rng_restriction(B!11, C!10))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[196, 69])).
% 0.20/0.53 tff(198,plain,
% 0.20/0.53 ((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[197, 195])).
% 0.20/0.53 tff(199,plain,
% 0.20/0.53 ((~((~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10))))) | (~in(A!12, B!11)) | (~in(A!12, relation_rng(C!10)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(200,plain,
% 0.20/0.53 (~in(A!12, B!11)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[199, 198, 171])).
% 0.20/0.53 tff(201,plain,
% 0.20/0.53 (((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) | in(A!12, B!11)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(202,plain,
% 0.20/0.53 ((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.20/0.53 tff(203,plain,
% 0.20/0.53 (in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[125, 195])).
% 0.20/0.53 tff(204,plain,
% 0.20/0.53 (((~in(A!12, B!11)) | (~in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), C!10))) <=> in(ordered_pair(tptp_fun_D_2(A!12, relation_rng_restriction(B!11, C!10)), A!12), relation_rng_restriction(B!11, C!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[127, 203, 202])).
% 0.20/0.53 tff(205,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[54, 53, 204])).
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------