TSTP Solution File: SEU202+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU202+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 07:28:09 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU202+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 10:25:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(in_type, type, (
% 0.20/0.41 in: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_C_11_type, type, (
% 0.20/0.41 tptp_fun_C_11: $i)).
% 0.20/0.41 tff(ordered_pair_type, type, (
% 0.20/0.41 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_E_2_type, type, (
% 0.20/0.41 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_A_13_type, type, (
% 0.20/0.41 tptp_fun_A_13: $i)).
% 0.20/0.41 tff(relation_dom_restriction_type, type, (
% 0.20/0.41 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_B_12_type, type, (
% 0.20/0.41 tptp_fun_B_12: $i)).
% 0.20/0.41 tff(relation_rng_restriction_type, type, (
% 0.20/0.41 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_D_3_type, type, (
% 0.20/0.41 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(relation_type, type, (
% 0.20/0.41 relation: $i > $o)).
% 0.20/0.41 tff(tptp_fun_E_0_type, type, (
% 0.20/0.41 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_D_1_type, type, (
% 0.20/0.41 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(1,assumption,(~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t140_relat_1')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.41 tff(12,plain,(
% 0.20/0.41 ~((~relation(C!11)) | (relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (relation(C!11)),
% 0.20/0.41 inference(or_elim,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.41 tff(19,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.41 tff(22,plain,(
% 0.20/0.41 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[21])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (relation(relation_dom_restriction(C!11, B!12))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (^[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))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![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)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[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)))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![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))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (^[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)))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![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))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![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))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (^[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)))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![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))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite(((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) <=> ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))), ((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), rewrite((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))), ((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))))), (![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), ((relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> (relation(A) => ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))))), rewrite((relation(A) => ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), ((relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![A: $i] : (relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.41 tff(42,axiom,(![A: $i] : (relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d11_relat_1')).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.41 tff(45,plain,(
% 0.20/0.41 ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[44])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), A))))))) | (~((C = relation_dom_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), A))))))) | (~((C = relation_dom_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 34])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![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)))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 29])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~![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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11)))))))))))) <=> ((~![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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11)))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~![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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11)))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~![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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[52, 49, 13])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11)))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11)))))))))) <=> ((~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11)))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11)))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11)))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C) <=> ((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11)))))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), C!11))))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[59, 53, 27])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11)))))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)) | ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)) | ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[64, 1])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[66, 1])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.42 tff(73,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.42 tff(76,plain,(
% 0.20/0.42 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[75])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (relation(relation_rng_restriction(A!13, C!11))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 77, 13])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 23, 81])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (^[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))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![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)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (^[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)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![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))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (^[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)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![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))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![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))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (^[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)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![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))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (^[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))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) <=> ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), rewrite((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,axiom,(![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_1')).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.43 tff(103,plain,(
% 0.20/0.43 ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_E_2(C, B, A), A) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[102])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)) <=> (in(tptp_fun_E_2(C, B, A), A) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> ((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> ((~in(tptp_fun_E_2(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), B))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 92])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![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)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 87])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (((~![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(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, 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(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((~![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(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~![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(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[111, 27])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C) <=> ((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[115, 112, 85])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.44 (((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))))))) | ((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))),
% 0.20/0.44 inference(or_elim,[status(thm)],[12])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[124, 67])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (((~![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, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))))))))) <=> ((~![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, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 ((~![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, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 ((~![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, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[128, 49, 81])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))))))) <=> ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C) <=> ((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11))))))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[135, 85, 129])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~![D: $i, E: $i] : (in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 ((~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 125])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) | in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[144, 143, 65])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[146, 141])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (((~![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(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))))))))) <=> ((~![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(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 ((~![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(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 ((~![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(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[150, 107, 13])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | (~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11)) <=> ((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11)))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))))))) <=> ((~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11)) <=> ((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11)))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[153])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11)) <=> ((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11)))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | (~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[154, 152])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11)) <=> ((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11)))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C) <=> ((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11)))))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))))))))))) | (~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[157, 151, 81])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ((~![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)) <=> (~((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11)))))) | (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)) <=> (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)) <=> (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)) <=> (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))) | (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))) | (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[162, 147])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[164, 163, 145])).
% 0.20/0.46 tff(166,plain,(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))) | (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 ((~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))) | (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[167, 62])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[168, 166])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 (in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.20/0.47 tff(172,assumption,(~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))), introduced(assumption)).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[173, 122])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[174, 172])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) <=> (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[176, 138])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[177, 175])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[179, 169])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) | in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[181, 172])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 ((~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[183, 182, 180])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 ((~(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)) <=> (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)) | ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)) | ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[185, 160])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[186, 184])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 ((~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))) | (~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[188, 187, 178, 171])).
% 0.20/0.47 tff(190,plain,((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 ((~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))) | (~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[191, 190, 166])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[124, 190])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[140, 195])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[146, 196])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[162, 197, 194])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------