%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU246+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:22 AM UTC 2025
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU246+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 06:28:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(in_type, type, (
% 0.20/0.45 in: ( $i * $i ) > $o)).
% 0.20/0.45 tff(relation_rng_restriction_type, type, (
% 0.20/0.45 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_B_12_type, type, (
% 0.20/0.45 tptp_fun_B_12: $i)).
% 0.20/0.45 tff(tptp_fun_A_13_type, type, (
% 0.20/0.45 tptp_fun_A_13: $i)).
% 0.20/0.45 tff(ordered_pair_type, type, (
% 0.20/0.45 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_D_4_type, type, (
% 0.20/0.45 tptp_fun_D_4: ( $i * $i ) > $i)).
% 0.20/0.45 tff(relation_restriction_type, type, (
% 0.20/0.45 relation_restriction: ( $i * $i ) > $i)).
% 0.20/0.45 tff(relation_dom_restriction_type, type, (
% 0.20/0.45 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_C_5_type, type, (
% 0.20/0.45 tptp_fun_C_5: ( $i * $i ) > $i)).
% 0.20/0.45 tff(cartesian_product2_type, type, (
% 0.20/0.45 cartesian_product2: ( $i * $i ) > $i)).
% 0.20/0.45 tff(relation_type, type, (
% 0.20/0.45 relation: $i > $o)).
% 0.20/0.45 tff(tptp_fun_E_0_type, type, (
% 0.20/0.45 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_D_1_type, type, (
% 0.20/0.45 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_E_2_type, type, (
% 0.20/0.45 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_D_3_type, type, (
% 0.20/0.45 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.20/0.45 tff(1,assumption,(~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))), introduced(assumption)).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(7,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.45 tff(9,plain,(
% 0.20/0.45 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[8])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (~(((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 ((((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))) | ((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 ((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 ((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(21,axiom,(~![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_wellord1')).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.20/0.46 tff(26,plain,(
% 0.20/0.46 ~((~relation(B!12)) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[25])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (relation(B!12)),
% 0.20/0.46 inference(or_elim,[status(thm)],[26])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.46 tff(35,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_wellord1')).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.46 tff(38,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[37])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!12)) | (~(((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!12)) | (~(((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!12)) | (~(((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!12)) | (~(((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (~(((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 ((((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))) | (~((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 ((~((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[46, 18])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.47 tff(53,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.47 tff(56,plain,(
% 0.20/0.47 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[55])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!12)) | relation(relation_restriction(B!12, A!13)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!12)) | relation(relation_restriction(B!12, A!13)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!12)) | relation(relation_restriction(B!12, A!13)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!12)) | relation(relation_restriction(B!12, A!13))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (relation(relation_restriction(B!12, A!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[60, 57, 27])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))) & ((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))) & ((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((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)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))) <=> ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))), ((relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) <=> (relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))), rewrite((relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))))), ((relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))))))), (![B: $i] : (relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) <=> ![B: $i] : ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | ((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)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ((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)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.47 tff(72,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_relat_1')).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((A = B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.47 tff(75,plain,(
% 0.20/0.47 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B))) & ((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[74])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | ((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | (~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((relation_restriction(B!12, A!13) = B) | (~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))))))))) <=> ((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | ((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((relation_restriction(B!12, A!13) = B) | (~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | ((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | ((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((relation_restriction(B!12, A!13) = B) | (~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | (~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | ((~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((relation_restriction(B!12, A!13) = B) | (~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B)))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(A = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A) <=> in(ordered_pair(C, D), B)))) | (~((A = B) | (~(in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), A) <=> in(ordered_pair(tptp_fun_C_5(B, A), tptp_fun_D_4(B, A)), B)))))))))) | (~relation(relation_restriction(B!12, A!13))) | ![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[83, 77, 61])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.48 tff(90,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.48 tff(93,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[92])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!12)) | relation(relation_rng_restriction(A!13, B!12)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!12)) | relation(relation_rng_restriction(A!13, B!12)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!12)) | relation(relation_rng_restriction(A!13, B!12)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!12)) | relation(relation_rng_restriction(A!13, B!12))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (relation(relation_rng_restriction(A!13, B!12))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[97, 94, 27])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.48 tff(104,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.48 tff(107,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[106])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(relation_rng_restriction(A!13, B!12))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(relation_rng_restriction(A!13, B!12))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(relation_rng_restriction(A!13, B!12))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(relation_rng_restriction(A!13, B!12))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[111, 108, 98])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (((~![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 ((~![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 ((~![B: $i] : ((~relation(B)) | (~((~((~(relation_restriction(B!12, A!13) = B)) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), B)))) | (~((~(in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(B, relation_restriction(B!12, A!13)), tptp_fun_D_4(B, relation_restriction(B!12, A!13))), B))) | (relation_restriction(B!12, A!13) = B))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (~((~((~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[115, 112, 84])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (((~((~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), relation_restriction(B!12, A!13)) <=> in(ordered_pair(C, D), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | ((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 ((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(or_elim,[status(thm)],[26])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 ((~((~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))) | (~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 (~(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 ((in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[124, 47])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (^[A: $i] : refl(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite(((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) <=> ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))), ((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), rewrite((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))), ((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))))), (![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), ((relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> (relation(A) => ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))))), rewrite((relation(A) => ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), ((relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (![A: $i] : (relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.49 tff(138,axiom,(![A: $i] : (relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d11_relat_1')).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.49 tff(141,plain,(
% 0.20/0.49 ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[140])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[143, 127])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 (((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))))))) <=> ((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), 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)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[150, 144, 98])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), A!13)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))))) <=> ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), A!13)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[153])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), A!13)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[154, 152])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), A!13)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), A!13, relation_rng_restriction(A!13, B!12))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, B!12)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, B!12))), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[157, 112, 151])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : (~(((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))) | (~(((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (~(((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 ((((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 ((~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[162, 125])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 (((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) | in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 ((~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)))) | (~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[166, 165, 16])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[168, 163])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (^[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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (^[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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 (![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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (^[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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 (![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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[174])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 (![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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (^[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_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_E_2(C, B, A), A) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 (![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_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_E_2(C, B, A), A) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) <=> ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), rewrite((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.50 tff(182,axiom,(![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_1')).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.20/0.50 tff(185,plain,(
% 0.20/0.50 ![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_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_E_2(C, B, A), A) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[184])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (![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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (![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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[187, 171])).
% 0.20/0.51 tff(189,plain,
% 0.20/0.51 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> 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_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(190,plain,
% 0.20/0.51 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(191,plain,
% 0.20/0.51 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[191, 188, 27])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 (((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), relation_rng_restriction(A!13, B!12))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))))) <=> ((~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), relation_rng_restriction(A!13, B!12))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), relation_rng_restriction(A!13, B!12))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[195, 193])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, B!12), B!12, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, B!12), B!12, A!13)), relation_rng_restriction(A!13, B!12))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, B!12)) | (((~in(tptp_fun_E_2(C, B!12, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), B!12))) <=> in(ordered_pair(tptp_fun_D_3(C, B!12, A!13), tptp_fun_E_2(C, B!12, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 (![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[198, 98, 192])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))) | (~(((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 (~(((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 ((((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))) | (~((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 ((~((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 (~((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[203, 169])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) | in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[205, 204, 167])).
% 0.20/0.51 tff(207,plain,(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 ((((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))) | (~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 ((~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[208, 13])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[209, 207])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 (((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) | in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 (in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.20/0.52 tff(213,assumption,(~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))), introduced(assumption)).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[124, 213])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 (~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[162, 214])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[168, 215])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 ((((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))) | ((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 (((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[217, 44])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 ((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[218, 213])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 ((~((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[220, 219, 207])).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 (((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 ((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[203, 223, 216])).
% 0.20/0.52 tff(225,plain,(in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(226,plain,
% 0.20/0.52 ((in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13)) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 ((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_restriction(B!12, A!13))) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[226, 122])).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[227, 225])).
% 0.20/0.52 tff(229,plain,
% 0.20/0.52 ((((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[229, 160])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 ((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[230, 228])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 ((~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))))) | (~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[232, 231, 212])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 (((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13))) | in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[234, 210])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 (~((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[46, 225])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 (((~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 ((~((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)))) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(240,plain,
% 0.20/0.52 (~((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[239, 238, 235])).
% 0.20/0.52 tff(241,plain,
% 0.20/0.52 ((((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) <=> in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))) | ((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(242,plain,
% 0.20/0.52 (((~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), B!12))) | in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), relation_rng_restriction(A!13, B!12))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[241, 201])).
% 0.20/0.52 tff(243,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[242, 240, 233])).
% 0.20/0.52 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------