TSTP Solution File: SEU199+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU199+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 07:28:07 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU199+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 10:13:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(in_type, type, (
% 0.21/0.47 in: ( $i * $i ) > $o)).
% 0.21/0.47 tff(tptp_fun_B_11_type, type, (
% 0.21/0.47 tptp_fun_B_11: $i)).
% 0.21/0.47 tff(ordered_pair_type, type, (
% 0.21/0.47 ordered_pair: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_D_2_type, type, (
% 0.21/0.47 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.21/0.47 tff(relation_rng_restriction_type, type, (
% 0.21/0.47 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_A_12_type, type, (
% 0.21/0.47 tptp_fun_A_12: $i)).
% 0.21/0.47 tff(tptp_fun_C_3_type, type, (
% 0.21/0.47 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.21/0.47 tff(subset_type, type, (
% 0.21/0.47 subset: ( $i * $i ) > $o)).
% 0.21/0.47 tff(relation_type, type, (
% 0.21/0.47 relation: $i > $o)).
% 0.21/0.47 tff(tptp_fun_E_0_type, type, (
% 0.21/0.47 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_D_1_type, type, (
% 0.21/0.47 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t117_relat_1')).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.47 tff(11,plain,(
% 0.21/0.47 ~((~relation(B!11)) | subset(relation_rng_restriction(A!12, B!11), B!11))),
% 0.21/0.47 inference(skolemize,[status(sab)],[10])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (relation(B!11)),
% 0.21/0.47 inference(or_elim,[status(thm)],[11])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.47 tff(18,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.47 tff(21,plain,(
% 0.21/0.47 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[20])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!11)) | relation(relation_rng_restriction(A!12, B!11))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (relation(relation_rng_restriction(A!12, B!11))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[30, 28])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))) <=> (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))), ((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), rewrite((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))), ((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))))), (![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.48 tff(37,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_relat_1')).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.48 tff(40,plain,(
% 0.21/0.48 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[39])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B)))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B)))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), B)))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.48 tff(46,plain,
% 0.21/0.48 (![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[45, 42, 26])).
% 0.21/0.48 tff(47,plain,
% 0.21/0.48 (((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | ((~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | (~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(48,plain,
% 0.21/0.48 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | ((~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(49,plain,
% 0.21/0.48 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_rng_restriction(A!12, B!11), B) | (~((~in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B, relation_rng_restriction(A!12, B!11))), B))))))))) | (~relation(B!11)) | (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (~((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[49, 12, 46])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (((~((~subset(relation_rng_restriction(A!12, B!11), B!11)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(C, D), B!11)))) | (~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))) | (subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 (subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (~subset(relation_rng_restriction(A!12, B!11), B!11)),
% 0.21/0.49 inference(or_elim,[status(thm)],[11])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 ((~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))) | subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 ((~(subset(relation_rng_restriction(A!12, B!11), B!11) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))) | (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (~((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 (((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 ((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 (((~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)) | in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[61, 56])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 ((~(in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11)) <=> (~((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11))) | (~((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (~(in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11)) <=> (~((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[63, 62, 60])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B)))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (^[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_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) <=> ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), rewrite((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 (![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.50 tff(79,axiom,(![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_1')).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.50 tff(82,plain,(
% 0.21/0.50 ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[81])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | ((~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)) <=> (in(tptp_fun_E_0(C, B, A), A) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B))))))) | (~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[84, 71])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A)) | (~in(ordered_pair(D, E), B)))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[85, 66])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(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!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(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!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(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!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> ((~in(tptp_fun_E_0(C, B, A), A)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), B)))))) | (~((~(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!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[89, 86, 12])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11)) <=> ((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11)))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))))))) <=> ((~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11)) <=> ((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11)))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11)) <=> ((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11)))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | ((~relation(relation_rng_restriction(A!12, B!11))) | (~((~((relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), relation_rng_restriction(A!12, B!11)) <=> ((~in(tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_rng_restriction(A!12, B!11), B!11, A!12), tptp_fun_E_0(relation_rng_restriction(A!12, B!11), B!11, A!12)), B!11)))))) | (~((~(relation_rng_restriction(A!12, B!11) = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!12, B!11)) | (in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), C) <=> ((~in(tptp_fun_E_0(C, B!11, A!12), A!12)) | (~in(ordered_pair(tptp_fun_D_1(C, B!11, A!12), tptp_fun_E_0(C, B!11, A!12)), B!11)))))) | (~((~(C = relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11))))))))))) | (~relation(relation_rng_restriction(A!12, B!11))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[96, 90, 26])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 ((~![D: $i, E: $i] : (in(ordered_pair(D, E), relation_rng_restriction(A!12, B!11)) <=> (~((~in(E, A!12)) | (~in(ordered_pair(D, E), B!11)))))) | (in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), relation_rng_restriction(A!12, B!11)) <=> (~((~in(tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11)), A!12)) | (~in(ordered_pair(tptp_fun_C_3(B!11, relation_rng_restriction(A!12, B!11)), tptp_fun_D_2(B!11, relation_rng_restriction(A!12, B!11))), B!11)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(99,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[98, 97, 64])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------