TSTP Solution File: SEU246+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU246+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Tue Sep 20 07:28:28 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU246+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 11:05:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(in_type, type, (
% 0.21/0.49 in: ( $i * $i ) > $o)).
% 0.21/0.49 tff(relation_rng_restriction_type, type, (
% 0.21/0.49 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_B_12_type, type, (
% 0.21/0.49 tptp_fun_B_12: $i)).
% 0.21/0.49 tff(tptp_fun_A_13_type, type, (
% 0.21/0.49 tptp_fun_A_13: $i)).
% 0.21/0.49 tff(ordered_pair_type, type, (
% 0.21/0.49 ordered_pair: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_D_4_type, type, (
% 0.21/0.49 tptp_fun_D_4: ( $i * $i ) > $i)).
% 0.21/0.49 tff(relation_restriction_type, type, (
% 0.21/0.49 relation_restriction: ( $i * $i ) > $i)).
% 0.21/0.49 tff(relation_dom_restriction_type, type, (
% 0.21/0.49 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_C_5_type, type, (
% 0.21/0.49 tptp_fun_C_5: ( $i * $i ) > $i)).
% 0.21/0.49 tff(cartesian_product2_type, type, (
% 0.21/0.49 cartesian_product2: ( $i * $i ) > $i)).
% 0.21/0.49 tff(relation_type, type, (
% 0.21/0.49 relation: $i > $o)).
% 0.21/0.49 tff(tptp_fun_E_2_type, type, (
% 0.21/0.49 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_D_3_type, type, (
% 0.21/0.49 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_E_0_type, type, (
% 0.21/0.49 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_D_1_type, type, (
% 0.21/0.49 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.21/0.49 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)) <=> (~((~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)))))), introduced(assumption)).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (^[A: $i, B: $i, C: $i, D: $i] : refl((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))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.49 tff(4,plain,
% 0.21/0.49 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((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))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 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')).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.49 tff(9,plain,(
% 0.21/0.49 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[8])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13))), cartesian_product2(A!13, A!13)) <=> (~((~in(tptp_fun_C_5(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)) | (~in(tptp_fun_D_4(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13), relation_restriction(B!12, A!13)), A!13)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(13,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.21/0.50 tff(14,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)) <=> (~((~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))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(15,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))), B!12)), introduced(assumption)).
% 0.21/0.50 tff(16,plain,
% 0.21/0.50 (((~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))), 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)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(17,plain,
% 0.21/0.50 ((~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))), 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)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.50 tff(18,plain,
% 0.21/0.50 ((~![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))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(19,plain,
% 0.21/0.50 ((~![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))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(20,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')).
% 0.21/0.50 tff(21,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.50 tff(22,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.21/0.50 tff(23,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.50 tff(24,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.21/0.50 tff(25,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.21/0.50 tff(26,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.50 tff(27,plain,
% 0.21/0.50 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.21/0.50 tff(28,plain,(
% 0.21/0.50 ~((~relation(B!12)) | (relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[27])).
% 0.21/0.50 tff(29,plain,
% 0.21/0.50 (relation(B!12)),
% 0.21/0.50 inference(or_elim,[status(thm)],[28])).
% 0.21/0.50 tff(30,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : refl(((~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))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(31,plain,
% 0.21/0.50 (![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)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.50 tff(32,plain,
% 0.21/0.50 (^[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))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(33,plain,
% 0.21/0.50 (![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)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.50 tff(34,plain,
% 0.21/0.50 (![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)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(35,plain,
% 0.21/0.50 (^[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))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(36,plain,
% 0.21/0.50 (![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)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.50 tff(37,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')).
% 0.21/0.50 tff(38,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.50 tff(39,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.50 tff(40,plain,(
% 0.21/0.50 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[39])).
% 0.21/0.50 tff(41,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, 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))), 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)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, 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))), 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)))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, 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))), 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)))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, 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))), 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))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (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_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)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[45, 42, 29])).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 ((~(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_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))) | (~((~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)))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 ((~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_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)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 (~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_restriction(B!12, A!13))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[48, 17])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.50 tff(55,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.50 tff(58,plain,(
% 0.21/0.50 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[57])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!12)) | relation(relation_restriction(B!12, A!13)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!12)) | relation(relation_restriction(B!12, A!13))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (relation(relation_restriction(B!12, A!13))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[62, 59, 29])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (^[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)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 (![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))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 (^[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)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (![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))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 (![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))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[67, 65])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (^[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)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (![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))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (^[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)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (![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))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (![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)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (^[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)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(75,plain,
% 0.21/0.51 (![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)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.51 tff(76,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')).
% 0.21/0.51 tff(77,plain,
% 0.21/0.51 (![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)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.51 tff(78,plain,
% 0.21/0.51 (![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)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.21/0.51 tff(79,plain,(
% 0.21/0.51 ![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)))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[78])).
% 0.21/0.51 tff(80,plain,
% 0.21/0.51 (![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))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.21/0.51 tff(81,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.21/0.51 tff(82,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[81, 68])).
% 0.21/0.51 tff(83,plain,
% 0.21/0.51 (((~![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)))) | (~((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))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(84,plain,
% 0.21/0.51 ((~![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))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(85,plain,
% 0.21/0.51 ((~![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)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.51 tff(86,plain,
% 0.21/0.51 (![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)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[85, 82, 63])).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.51 tff(89,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.51 tff(92,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.21/0.51 tff(95,plain,(
% 0.21/0.51 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[94])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!12)) | relation(relation_rng_restriction(A!13, B!12)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(99,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!12)) | relation(relation_rng_restriction(A!13, B!12))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (relation(relation_rng_restriction(A!13, B!12))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[99, 96, 29])).
% 0.21/0.51 tff(101,plain,
% 0.21/0.51 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(102,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(104,plain,
% 0.21/0.51 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(105,plain,
% 0.21/0.51 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.51 tff(106,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.51 tff(109,plain,(
% 0.21/0.51 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[108])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 ((~![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)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 ((~![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (((~![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_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))))) | (~((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))))))))) <=> ((~![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_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))))) | (~((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))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 ((~![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_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))))) | (~((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))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 ((~![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_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))))) | (~((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)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 (~((~((~(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))))) | (~((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))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[117, 114, 86])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (((~((~(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))))) | (~((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)) | ((~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))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 ((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)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (~(relation_restriction(B!12, A!13) = relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))),
% 0.21/0.51 inference(or_elim,[status(thm)],[28])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 ((~((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)) | ((~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)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(123,plain,
% 0.21/0.52 ((~((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))))) | ((~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)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.52 tff(124,plain,
% 0.21/0.52 ((~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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.21/0.52 tff(125,plain,
% 0.21/0.52 ((~((~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))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(126,plain,
% 0.21/0.52 (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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.52 tff(127,plain,
% 0.21/0.52 (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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[126, 49])).
% 0.21/0.52 tff(128,plain,
% 0.21/0.52 (((~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)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(129,plain,
% 0.21/0.52 ((~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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[128, 15])).
% 0.21/0.52 tff(130,plain,
% 0.21/0.52 (^[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)) | (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)))))) | (~((~(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))))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(131,plain,
% 0.21/0.52 (![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)) | (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)))))) | (~((~(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)))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.52 tff(132,plain,
% 0.21/0.52 (^[A: $i, B: $i] : refl(((~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(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)))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(133,plain,
% 0.21/0.52 (![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(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))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.52 tff(134,plain,
% 0.21/0.52 (^[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(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)))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(135,plain,
% 0.21/0.52 (![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(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))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.52 tff(136,plain,
% 0.21/0.52 (![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(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))))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.52 tff(137,plain,
% 0.21/0.52 (^[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(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)))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 (![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(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))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 (^[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(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))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (![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(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)))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (![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))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (^[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))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (![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))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.52 tff(144,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')).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (![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))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (![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))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.21/0.52 tff(147,plain,(
% 0.21/0.52 ![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))))))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[146])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 (![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)))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (![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))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[148, 138])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 (![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))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[149, 136])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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)))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[150, 131])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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!12)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.52 tff(155,plain,
% 0.21/0.52 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[154, 151, 29])).
% 0.21/0.52 tff(156,plain,
% 0.21/0.52 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(157,plain,
% 0.21/0.53 (((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(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)) <=> ((~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)))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))))))) <=> ((~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(158,plain,
% 0.21/0.53 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(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)) <=> ((~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)))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[157])).
% 0.21/0.53 tff(159,plain,
% 0.21/0.53 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(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)) <=> ((~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)))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[158, 156])).
% 0.21/0.53 tff(160,plain,
% 0.21/0.53 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | ((~relation(relation_rng_restriction(A!13, B!12))) | (~((~((relation_rng_restriction(A!13, B!12) = relation_rng_restriction(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)) <=> ((~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)))))) | (~((~(relation_rng_restriction(A!13, B!12) = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(161,plain,
% 0.21/0.53 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(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) <=> ((~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)))))) | (~((~(C = relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12))))))))))) | (~relation(relation_rng_restriction(A!13, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.53 tff(162,plain,
% 0.21/0.53 (![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), B!12)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[161, 100, 155])).
% 0.21/0.53 tff(163,plain,
% 0.21/0.53 ((~![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), 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)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(164,plain,
% 0.21/0.53 (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))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.21/0.53 tff(165,plain,
% 0.21/0.53 ((~(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))) | (~((~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))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(166,plain,
% 0.21/0.53 ((~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))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.21/0.53 tff(167,plain,
% 0.21/0.53 (~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))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[166, 129])).
% 0.21/0.53 tff(168,plain,
% 0.21/0.53 (((~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))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(169,plain,
% 0.21/0.53 ((~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)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.21/0.53 tff(170,plain,
% 0.21/0.53 (^[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)) | (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)))))) | (~((~(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))))))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(171,plain,
% 0.21/0.53 (![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)) | (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)))))) | (~((~(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)))))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.53 tff(172,plain,
% 0.21/0.53 (^[A: $i] : refl(((~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(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)))))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(173,plain,
% 0.21/0.53 (![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(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))))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[172])).
% 0.21/0.53 tff(174,plain,
% 0.21/0.53 (^[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(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)))))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(175,plain,
% 0.21/0.53 (![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(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))))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[174])).
% 0.21/0.53 tff(176,plain,
% 0.21/0.53 (![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(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))))))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[175, 173])).
% 0.21/0.53 tff(177,plain,
% 0.21/0.53 (^[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(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)))))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(178,plain,
% 0.21/0.53 (![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(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))))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[177])).
% 0.21/0.53 tff(179,plain,
% 0.21/0.53 (^[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(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))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(180,plain,
% 0.21/0.53 (![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(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)))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.53 tff(181,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(182,plain,
% 0.21/0.53 (^[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))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(183,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[182])).
% 0.21/0.53 tff(184,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')).
% 0.21/0.53 tff(185,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.53 tff(186,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.21/0.54 tff(187,plain,(
% 0.21/0.54 ![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))))))))),
% 0.21/0.54 inference(skolemize,[status(sab)],[186])).
% 0.21/0.54 tff(188,plain,
% 0.21/0.54 (![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)))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.21/0.54 tff(189,plain,
% 0.21/0.54 (![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))))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.21/0.54 tff(190,plain,
% 0.21/0.54 (![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))))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[189, 176])).
% 0.21/0.54 tff(191,plain,
% 0.21/0.54 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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)))))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[190, 171])).
% 0.21/0.54 tff(192,plain,
% 0.21/0.54 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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(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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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(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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(193,plain,
% 0.21/0.54 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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(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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(194,plain,
% 0.21/0.54 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((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)))))) | (~((~(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(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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.54 tff(195,plain,
% 0.21/0.54 (![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(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))), C) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[194, 191, 100])).
% 0.21/0.54 tff(196,plain,
% 0.21/0.54 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(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))), C) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), 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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(197,plain,
% 0.21/0.54 (((~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)) | (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)) <=> ((~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))))))) | (~((~(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(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))))))) <=> ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(198,plain,
% 0.21/0.54 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(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))), C) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | ((~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)) | (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)) <=> ((~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))))))) | (~((~(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(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), 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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[197])).
% 0.21/0.54 tff(199,plain,
% 0.21/0.54 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(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))), C) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | ((~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)) | (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)) <=> ((~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))))))) | (~((~(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(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), 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(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) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))),
% 0.21/0.54 inference(transitivity,[status(thm)],[198, 196])).
% 0.21/0.54 tff(200,plain,
% 0.21/0.54 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(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))), C) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | ((~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)) | (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)) <=> ((~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))))))) | (~((~(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(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(201,plain,
% 0.21/0.54 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(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))), C) <=> ((~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))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, B!12), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.54 tff(202,plain,
% 0.21/0.54 (![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, B!12))))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[201, 114, 195])).
% 0.21/0.54 tff(203,plain,
% 0.21/0.54 ((~![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, B!12), A!13)) <=> (~((~in(D, A!13)) | (~in(ordered_pair(D, E), 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))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(204,plain,
% 0.21/0.54 (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)))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.21/0.54 tff(205,plain,
% 0.21/0.54 ((~(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))) | (~((~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)))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(206,plain,
% 0.21/0.55 ((~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)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.21/0.55 tff(207,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[206, 169, 127])).
% 0.21/0.55 tff(208,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))), B!12)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(209,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)).
% 0.21/0.55 tff(210,plain,
% 0.21/0.55 ((~(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)) | ((~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))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(211,plain,
% 0.21/0.55 (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))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[210, 46])).
% 0.21/0.55 tff(212,plain,
% 0.21/0.55 ((~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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[211, 209])).
% 0.21/0.55 tff(213,plain,
% 0.21/0.55 ((~((~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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(214,plain,
% 0.21/0.55 (~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))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[213, 212, 208])).
% 0.21/0.55 tff(215,plain,
% 0.21/0.55 ((~(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)) | ((~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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(216,plain,
% 0.21/0.55 ((~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))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[215, 214, 14])).
% 0.21/0.55 tff(217,plain,
% 0.21/0.55 (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))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[126, 209])).
% 0.21/0.55 tff(218,plain,
% 0.21/0.55 (~((~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))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[206, 217])).
% 0.21/0.55 tff(219,plain,
% 0.21/0.55 (((~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)),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(220,plain,
% 0.21/0.55 (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)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.21/0.55 tff(221,plain,
% 0.21/0.55 ((~((~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))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(222,plain,
% 0.21/0.55 (~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)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[221, 220, 216])).
% 0.21/0.55 tff(223,plain,
% 0.21/0.55 (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))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[168, 218])).
% 0.21/0.55 tff(224,plain,
% 0.21/0.55 (~((~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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[166, 223])).
% 0.21/0.55 tff(225,plain,
% 0.21/0.55 (((~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)),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(226,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[225, 224, 222])).
% 0.21/0.55 tff(227,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,[]))).
% 0.21/0.55 tff(228,plain,
% 0.21/0.55 ((~((~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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(229,plain,
% 0.21/0.55 ((~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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[228, 124])).
% 0.21/0.55 tff(230,plain,
% 0.21/0.55 (~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))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[229, 227])).
% 0.21/0.55 tff(231,plain,
% 0.21/0.55 ((~(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)) | ((~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))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(232,plain,
% 0.21/0.55 (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))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[231, 204])).
% 0.21/0.55 tff(233,plain,
% 0.21/0.55 ((~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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[232, 230])).
% 0.21/0.55 tff(234,plain,
% 0.21/0.55 (~((~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))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[48, 227])).
% 0.21/0.55 tff(235,plain,
% 0.21/0.55 (((~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))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(236,plain,
% 0.21/0.56 (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))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.21/0.56 tff(237,plain,
% 0.21/0.56 ((~(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))) | (~((~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))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(238,plain,
% 0.21/0.56 (~((~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)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[237, 236, 14])).
% 0.21/0.56 tff(239,plain,
% 0.21/0.56 (((~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)),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(240,plain,
% 0.21/0.56 (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)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.21/0.56 tff(241,plain,
% 0.21/0.56 ((~((~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)))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(242,plain,
% 0.21/0.56 (~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))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[241, 240, 233])).
% 0.21/0.56 tff(243,plain,
% 0.21/0.56 (((~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)),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(244,plain,
% 0.21/0.56 (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)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[243, 238])).
% 0.21/0.56 tff(245,plain,
% 0.21/0.56 ((~((~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))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(246,plain,
% 0.21/0.56 (~((~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)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[245, 244, 208])).
% 0.21/0.56 tff(247,plain,
% 0.21/0.56 ((~(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)) | ((~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)))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(248,plain,
% 0.21/0.56 (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)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[247, 164])).
% 0.21/0.56 tff(249,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[248, 246, 242])).
% 0.21/0.56 % SZS output end Proof
%------------------------------------------------------------------------------