%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU199+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU199+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:15:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(relation_rng_restriction_type, type, (
% 0.19/0.38 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_B_11_type, type, (
% 0.19/0.38 tptp_fun_B_11: $i)).
% 0.19/0.38 tff(tptp_fun_A_12_type, type, (
% 0.19/0.38 tptp_fun_A_12: $i)).
% 0.19/0.38 tff(ordered_pair_type, type, (
% 0.19/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_D_2_type, type, (
% 0.19/0.38 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_C_3_type, type, (
% 0.19/0.38 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(relation_type, type, (
% 0.19/0.38 relation: $i > $o)).
% 0.19/0.38 tff(tptp_fun_E_0_type, type, (
% 0.19/0.38 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_D_1_type, type, (
% 0.19/0.38 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 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')).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.38 tff(8,plain,(
% 0.19/0.38 ~((~relation(B!11)) | subset(relation_rng_restriction(A!12, B!11), B!11))),
% 0.19/0.38 inference(skolemize,[status(sab)],[7])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (relation(B!11)),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.38 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')).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.38 tff(18,plain,(
% 0.19/0.38 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (relation(relation_rng_restriction(A!12, B!11))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (^[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)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.39 tff(37,plain,(
% 0.19/0.39 ![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), 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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B)))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B)))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~![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_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 39, 23])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | ((~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | (~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | ((~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | (~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 9, 43])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))) | (subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (~subset(relation_rng_restriction(A!12, B!11), B!11)),
% 0.19/0.40 inference(or_elim,[status(thm)],[8])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))) | subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 53])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))) <=> in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | (~((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))) <=> in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 59, 57])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (^[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))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![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)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![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))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![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))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![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))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (^[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)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![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))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![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))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![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))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.41 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')).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![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))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![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))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.41 tff(77,plain,(
% 0.19/0.41 ![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))))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![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))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![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))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![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)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 63])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (((~![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(B!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> 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(B!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 ((~![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(B!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![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(B!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 80, 9])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11))))))))) <=> ((~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C)))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[90, 84, 23])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![D: $i, E: $i] : (~(((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11))))) | (~(((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))) <=> in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 91, 61])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------