%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU199+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:13 AM UTC 2025
% Result : Theorem 15.54s 15.70s
% Output : Proof 15.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU199+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:19:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 15.54/15.70 % SZS status Theorem
% 15.54/15.70 % SZS output start Proof
% 15.54/15.70 tff(in_type, type, (
% 15.54/15.70 in: ( $i * $i ) > $o)).
% 15.54/15.70 tff(relation_rng_restriction_type, type, (
% 15.54/15.70 relation_rng_restriction: ( $i * $i ) > $i)).
% 15.54/15.70 tff(tptp_fun_B_52_type, type, (
% 15.54/15.70 tptp_fun_B_52: $i)).
% 15.54/15.70 tff(tptp_fun_A_53_type, type, (
% 15.54/15.70 tptp_fun_A_53: $i)).
% 15.54/15.70 tff(ordered_pair_type, type, (
% 15.54/15.70 ordered_pair: ( $i * $i ) > $i)).
% 15.54/15.70 tff(tptp_fun_D_24_type, type, (
% 15.54/15.70 tptp_fun_D_24: ( $i * $i ) > $i)).
% 15.54/15.70 tff(tptp_fun_C_25_type, type, (
% 15.54/15.70 tptp_fun_C_25: ( $i * $i ) > $i)).
% 15.54/15.70 tff(subset_type, type, (
% 15.54/15.70 subset: ( $i * $i ) > $o)).
% 15.54/15.70 tff(relation_type, type, (
% 15.54/15.70 relation: $i > $o)).
% 15.54/15.70 tff(tptp_fun_E_4_type, type, (
% 15.54/15.70 tptp_fun_E_4: ( $i * $i * $i ) > $i)).
% 15.54/15.70 tff(tptp_fun_D_5_type, type, (
% 15.54/15.70 tptp_fun_D_5: ( $i * $i * $i ) > $i)).
% 15.54/15.70 tff(1,plain,
% 15.54/15.70 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(2,plain,
% 15.54/15.70 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t117_relat_1')).
% 15.54/15.70 tff(4,plain,
% 15.54/15.70 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[3, 2])).
% 15.54/15.70 tff(5,plain,
% 15.54/15.70 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[4, 1])).
% 15.54/15.70 tff(6,plain,
% 15.54/15.70 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[5, 1])).
% 15.54/15.70 tff(7,plain,
% 15.54/15.70 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[6, 1])).
% 15.54/15.70 tff(8,plain,(
% 15.54/15.70 ~((~relation(B!52)) | subset(relation_rng_restriction(A!53, B!52), B!52))),
% 15.54/15.70 inference(skolemize,[status(sab)],[7])).
% 15.54/15.70 tff(9,plain,
% 15.54/15.70 (relation(B!52)),
% 15.54/15.70 inference(or_elim,[status(thm)],[8])).
% 15.54/15.70 tff(10,plain,
% 15.54/15.70 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 15.54/15.70 inference(bind,[status(th)],[])).
% 15.54/15.70 tff(11,plain,
% 15.54/15.70 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(quant_intro,[status(thm)],[10])).
% 15.54/15.70 tff(12,plain,
% 15.54/15.70 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(13,plain,
% 15.54/15.70 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 15.54/15.70 inference(bind,[status(th)],[])).
% 15.54/15.70 tff(14,plain,
% 15.54/15.70 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(quant_intro,[status(thm)],[13])).
% 15.54/15.70 tff(15,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 15.54/15.70 tff(16,plain,
% 15.54/15.70 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[15, 14])).
% 15.54/15.70 tff(17,plain,
% 15.54/15.70 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[16, 12])).
% 15.54/15.70 tff(18,plain,(
% 15.54/15.70 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(skolemize,[status(sab)],[17])).
% 15.54/15.70 tff(19,plain,
% 15.54/15.70 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[18, 11])).
% 15.54/15.70 tff(20,plain,
% 15.54/15.70 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52)))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(21,plain,
% 15.54/15.70 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52)))),
% 15.54/15.70 inference(quant_inst,[status(thm)],[])).
% 15.54/15.70 tff(22,plain,
% 15.54/15.70 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[21, 20])).
% 15.54/15.70 tff(23,plain,
% 15.54/15.70 (relation(relation_rng_restriction(A!53, B!52))),
% 15.54/15.70 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 15.54/15.70 tff(24,plain,
% 15.54/15.70 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))))),
% 15.54/15.70 inference(bind,[status(th)],[])).
% 15.54/15.70 tff(25,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))),
% 15.54/15.70 inference(quant_intro,[status(thm)],[24])).
% 15.54/15.70 tff(26,plain,
% 15.54/15.70 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))))),
% 15.54/15.70 inference(bind,[status(th)],[])).
% 15.54/15.70 tff(27,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))),
% 15.54/15.70 inference(quant_intro,[status(thm)],[26])).
% 15.54/15.70 tff(28,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))),
% 15.54/15.70 inference(transitivity,[status(thm)],[27, 25])).
% 15.54/15.70 tff(29,plain,
% 15.54/15.70 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))))))),
% 15.54/15.70 inference(bind,[status(th)],[])).
% 15.54/15.70 tff(30,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))),
% 15.54/15.70 inference(quant_intro,[status(thm)],[29])).
% 15.54/15.70 tff(31,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(32,plain,
% 15.54/15.70 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))) <=> (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))), ((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), rewrite((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))), ((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))))), (![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))))),
% 15.54/15.70 inference(bind,[status(th)],[])).
% 15.54/15.70 tff(33,plain,
% 15.54/15.70 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 15.54/15.70 inference(quant_intro,[status(thm)],[32])).
% 15.54/15.70 tff(34,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_relat_1')).
% 15.54/15.70 tff(35,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[34, 33])).
% 15.54/15.70 tff(36,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[35, 31])).
% 15.54/15.70 tff(37,plain,(
% 15.54/15.70 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))),
% 15.54/15.70 inference(skolemize,[status(sab)],[36])).
% 15.54/15.70 tff(38,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[37, 30])).
% 15.54/15.70 tff(39,plain,
% 15.54/15.70 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[38, 28])).
% 15.54/15.70 tff(40,plain,
% 15.54/15.70 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))) | (~relation(relation_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B)))))))))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(41,plain,
% 15.54/15.70 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B)))))))))),
% 15.54/15.70 inference(quant_inst,[status(thm)],[])).
% 15.54/15.70 tff(42,plain,
% 15.54/15.70 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), A)) | in(ordered_pair(tptp_fun_C_25(B, A), tptp_fun_D_24(B, A)), B)))))))))) | (~relation(relation_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B))))))))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[41, 40])).
% 15.54/15.70 tff(43,plain,
% 15.54/15.70 (![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B))))))))),
% 15.54/15.70 inference(unit_resolution,[status(thm)],[42, 39, 23])).
% 15.54/15.70 tff(44,plain,
% 15.54/15.70 (((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B))))))))) | ((~relation(B!52)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B!52)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B!52)))) | (~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B))))))))) | (~relation(B!52)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B!52)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B!52)))) | (~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))))))),
% 15.54/15.70 inference(rewrite,[status(thm)],[])).
% 15.54/15.70 tff(45,plain,
% 15.54/15.70 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B))))))))) | ((~relation(B!52)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B!52)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B!52)))) | (~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))))))),
% 15.54/15.70 inference(quant_inst,[status(thm)],[])).
% 15.54/15.70 tff(46,plain,
% 15.54/15.70 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!53, B!52), B) | (~((~in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B, relation_rng_restriction(A!53, B!52))), B))))))))) | (~relation(B!52)) | (~((~((~subset(relation_rng_restriction(A!53, B!52), B!52)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B!52)))) | (~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)))))))),
% 15.54/15.70 inference(modus_ponens,[status(thm)],[45, 44])).
% 15.54/15.70 tff(47,plain,
% 15.54/15.70 (~((~((~subset(relation_rng_restriction(A!53, B!52), B!52)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B!52)))) | (~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))))),
% 15.54/15.70 inference(unit_resolution,[status(thm)],[46, 9, 43])).
% 15.54/15.70 tff(48,plain,
% 15.54/15.70 (((~((~subset(relation_rng_restriction(A!53, B!52), B!52)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(C, D), B!52)))) | (~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)))))) | (subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))),
% 15.54/15.70 inference(tautology,[status(thm)],[])).
% 15.54/15.70 tff(49,plain,
% 15.54/15.70 (subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)))),
% 15.54/15.70 inference(unit_resolution,[status(thm)],[48, 47])).
% 15.54/15.70 tff(50,plain,
% 15.54/15.70 (~subset(relation_rng_restriction(A!53, B!52), B!52)),
% 15.54/15.70 inference(or_elim,[status(thm)],[8])).
% 15.54/15.70 tff(51,plain,
% 15.54/15.70 ((~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))) | subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)))),
% 15.54/15.70 inference(tautology,[status(thm)],[])).
% 15.54/15.70 tff(52,plain,
% 15.54/15.70 ((~(subset(relation_rng_restriction(A!53, B!52), B!52) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))))) | (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)))),
% 15.54/15.70 inference(unit_resolution,[status(thm)],[51, 50])).
% 15.54/15.70 tff(53,plain,
% 15.54/15.70 (~((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))),
% 15.54/15.70 inference(unit_resolution,[status(thm)],[52, 49])).
% 15.54/15.70 tff(54,plain,
% 15.54/15.70 (((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))),
% 15.54/15.71 inference(tautology,[status(thm)],[])).
% 15.54/15.71 tff(55,plain,
% 15.54/15.71 (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)),
% 15.54/15.71 inference(unit_resolution,[status(thm)],[54, 53])).
% 15.54/15.71 tff(56,plain,
% 15.54/15.71 (((~in(tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52)), A!53)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)),
% 15.54/15.71 inference(tautology,[status(thm)],[])).
% 15.54/15.71 tff(57,plain,
% 15.54/15.71 ((~in(tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52)), A!53)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))),
% 15.54/15.71 inference(unit_resolution,[status(thm)],[56, 55])).
% 15.54/15.71 tff(58,plain,
% 15.54/15.71 (((~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)) | in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))),
% 15.54/15.71 inference(tautology,[status(thm)],[])).
% 15.54/15.71 tff(59,plain,
% 15.54/15.71 (in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))),
% 15.54/15.71 inference(unit_resolution,[status(thm)],[58, 53])).
% 15.54/15.71 tff(60,plain,
% 15.54/15.71 ((((~in(tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52)), A!53)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))) <=> in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))) | (~((~in(tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52)), A!53)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52)))) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52)))),
% 15.54/15.71 inference(tautology,[status(thm)],[])).
% 15.54/15.71 tff(61,plain,
% 15.54/15.71 (((~in(tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52)), A!53)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))) <=> in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))),
% 15.54/15.71 inference(unit_resolution,[status(thm)],[60, 59, 57])).
% 15.54/15.71 tff(62,plain,
% 15.54/15.71 (^[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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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))))))))))),
% 15.54/15.71 inference(bind,[status(th)],[])).
% 15.54/15.71 tff(63,plain,
% 15.54/15.71 (![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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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)))))))))),
% 15.54/15.71 inference(quant_intro,[status(thm)],[62])).
% 15.54/15.71 tff(64,plain,
% 15.54/15.71 (^[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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))))))))),
% 15.54/15.71 inference(bind,[status(th)],[])).
% 15.54/15.71 tff(65,plain,
% 15.54/15.71 (![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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C))))))))),
% 15.54/15.71 inference(quant_intro,[status(thm)],[64])).
% 15.54/15.71 tff(66,plain,
% 15.54/15.71 (^[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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))))))))),
% 15.54/15.71 inference(bind,[status(th)],[])).
% 15.54/15.71 tff(67,plain,
% 15.54/15.71 (![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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C))))))))),
% 15.54/15.71 inference(quant_intro,[status(thm)],[66])).
% 15.54/15.71 tff(68,plain,
% 15.54/15.71 (![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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C))))))))),
% 15.54/15.71 inference(transitivity,[status(thm)],[67, 65])).
% 15.54/15.71 tff(69,plain,
% 15.54/15.71 (^[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_5(C, B, A), tptp_fun_E_4(C, B, A)), C) <=> (in(tptp_fun_E_4(C, B, A), A) & in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))))))))),
% 15.54/15.71 inference(bind,[status(th)],[])).
% 15.54/15.71 tff(70,plain,
% 15.54/15.71 (![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_5(C, B, A), tptp_fun_E_4(C, B, A)), C) <=> (in(tptp_fun_E_4(C, B, A), A) & in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C))))))))),
% 15.54/15.71 inference(quant_intro,[status(thm)],[69])).
% 15.54/15.71 tff(71,plain,
% 15.54/15.71 (![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))))))),
% 15.54/15.71 inference(rewrite,[status(thm)],[])).
% 15.54/15.71 tff(72,plain,
% 15.54/15.71 (^[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))))))))),
% 15.54/15.71 inference(bind,[status(th)],[])).
% 15.54/15.71 tff(73,plain,
% 15.54/15.71 (![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))))))),
% 15.54/15.71 inference(quant_intro,[status(thm)],[72])).
% 15.54/15.71 tff(74,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/sandbox/benchmark/theBenchmark.p','d12_relat_1')).
% 15.54/15.71 tff(75,plain,
% 15.54/15.71 (![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))))))),
% 15.54/15.71 inference(modus_ponens,[status(thm)],[74, 73])).
% 15.54/15.71 tff(76,plain,
% 15.54/15.71 (![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))))))),
% 15.54/15.71 inference(modus_ponens,[status(thm)],[75, 71])).
% 15.54/15.71 tff(77,plain,(
% 15.54/15.71 ![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_5(C, B, A), tptp_fun_E_4(C, B, A)), C) <=> (in(tptp_fun_E_4(C, B, A), A) & in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))))))))),
% 15.54/15.71 inference(skolemize,[status(sab)],[76])).
% 15.54/15.71 tff(78,plain,
% 15.54/15.71 (![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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C))))))))),
% 15.54/15.71 inference(modus_ponens,[status(thm)],[77, 70])).
% 15.54/15.71 tff(79,plain,
% 15.54/15.71 (![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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C))))))))),
% 15.54/15.71 inference(modus_ponens,[status(thm)],[78, 68])).
% 15.54/15.71 tff(80,plain,
% 15.54/15.71 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(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)))))))))),
% 15.54/15.71 inference(modus_ponens,[status(thm)],[79, 63])).
% 15.54/15.71 tff(81,plain,
% 15.54/15.71 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(B!52)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> 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_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(B!52)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C)))))))))),
% 15.54/15.71 inference(rewrite,[status(thm)],[])).
% 15.54/15.71 tff(82,plain,
% 15.54/15.71 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(B!52)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C)))))))))),
% 15.54/15.71 inference(quant_inst,[status(thm)],[])).
% 15.54/15.71 tff(83,plain,
% 15.54/15.71 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_4(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_5(C, B, A), tptp_fun_E_4(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(B!52)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))),
% 15.54/15.71 inference(modus_ponens,[status(thm)],[82, 81])).
% 15.54/15.71 tff(84,plain,
% 15.54/15.71 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))),
% 15.54/15.71 inference(unit_resolution,[status(thm)],[83, 80, 9])).
% 15.54/15.71 tff(85,plain,
% 15.54/15.71 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))),
% 15.54/15.71 inference(rewrite,[status(thm)],[])).
% 15.54/15.71 tff(86,plain,
% 15.54/15.71 (((~relation(relation_rng_restriction(A!53, B!52))) | (~((~((relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), relation_rng_restriction(A!53, B!52))))) | (~((~(relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52))))))))) <=> ((~relation(relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))),
% 15.54/15.71 inference(rewrite,[status(thm)],[])).
% 15.54/15.71 tff(87,plain,
% 15.54/15.71 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | (~((~((relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), relation_rng_restriction(A!53, B!52))))) | (~((~(relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52))))))),
% 15.54/15.71 inference(monotonicity,[status(thm)],[86])).
% 15.54/15.71 tff(88,plain,
% 15.54/15.71 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | (~((~((relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), relation_rng_restriction(A!53, B!52))))) | (~((~(relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))),
% 15.54/15.73 inference(transitivity,[status(thm)],[87, 85])).
% 15.54/15.73 tff(89,plain,
% 15.54/15.73 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!53, B!52))) | (~((~((relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(relation_rng_restriction(A!53, B!52), B!52, A!53), tptp_fun_E_4(relation_rng_restriction(A!53, B!52), B!52, A!53)), relation_rng_restriction(A!53, B!52))))) | (~((~(relation_rng_restriction(A!53, B!52) = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52)))))))))),
% 15.54/15.73 inference(quant_inst,[status(thm)],[])).
% 15.54/15.73 tff(90,plain,
% 15.54/15.73 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!53, B!52)) | (((~in(tptp_fun_E_4(C, B!52, A!53), A!53)) | (~in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), B!52))) <=> in(ordered_pair(tptp_fun_D_5(C, B!52, A!53), tptp_fun_E_4(C, B!52, A!53)), C)))) | (~((~(C = relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!53, B!52))) | ![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52))))),
% 15.54/15.73 inference(modus_ponens,[status(thm)],[89, 88])).
% 15.54/15.73 tff(91,plain,
% 15.54/15.73 (![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52))))),
% 15.54/15.73 inference(unit_resolution,[status(thm)],[90, 84, 23])).
% 15.54/15.73 tff(92,plain,
% 15.54/15.73 ((~![D: $i, E: $i] : (~(((~in(E, A!53)) | (~in(ordered_pair(D, E), B!52))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!53, B!52))))) | (~(((~in(tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52)), A!53)) | (~in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), B!52))) <=> in(ordered_pair(tptp_fun_C_25(B!52, relation_rng_restriction(A!53, B!52)), tptp_fun_D_24(B!52, relation_rng_restriction(A!53, B!52))), relation_rng_restriction(A!53, B!52))))),
% 15.54/15.73 inference(quant_inst,[status(thm)],[])).
% 15.54/15.73 tff(93,plain,
% 15.54/15.73 ($false),
% 15.54/15.73 inference(unit_resolution,[status(thm)],[92, 91, 61])).
% 15.54/15.73 % SZS output end Proof
% 15.54/15.76 % E exiting
%------------------------------------------------------------------------------