TSTP Solution File: SEU225+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU225+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:18 EDT 2022
% Result : Theorem 2.04s 1.55s
% Output : Proof 2.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU225+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 10:43:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.04/1.55 % SZS status Theorem
% 2.04/1.55 % SZS output start Proof
% 2.04/1.55 tff(apply_type, type, (
% 2.04/1.55 apply: ( $i * $i ) > $i)).
% 2.04/1.55 tff(tptp_fun_B_77_type, type, (
% 2.04/1.55 tptp_fun_B_77: $i)).
% 2.04/1.55 tff(tptp_fun_C_76_type, type, (
% 2.04/1.55 tptp_fun_C_76: $i)).
% 2.04/1.55 tff(relation_dom_restriction_type, type, (
% 2.04/1.55 relation_dom_restriction: ( $i * $i ) > $i)).
% 2.04/1.55 tff(tptp_fun_A_78_type, type, (
% 2.04/1.55 tptp_fun_A_78: $i)).
% 2.04/1.55 tff(identity_relation_type, type, (
% 2.04/1.55 identity_relation: $i > $i)).
% 2.04/1.55 tff(in_type, type, (
% 2.04/1.55 in: ( $i * $i ) > $o)).
% 2.04/1.55 tff(function_type, type, (
% 2.04/1.55 function: $i > $o)).
% 2.04/1.55 tff(relation_type, type, (
% 2.04/1.55 relation: $i > $o)).
% 2.04/1.55 tff(relation_composition_type, type, (
% 2.04/1.55 relation_composition: ( $i * $i ) > $i)).
% 2.04/1.55 tff(relation_dom_type, type, (
% 2.04/1.55 relation_dom: $i > $i)).
% 2.04/1.55 tff(relation_rng_type, type, (
% 2.04/1.55 relation_rng: $i > $i)).
% 2.04/1.55 tff(1,plain,
% 2.04/1.55 ((~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78)))) <=> (~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(2,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))) <=> (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(3,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, A) => (apply(relation_dom_restriction(C, A), B) = apply(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(4,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, A) => (apply(relation_dom_restriction(C, A), B) = apply(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t72_funct_1')).
% 2.04/1.55 tff(5,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.04/1.55 tff(6,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[5, 2])).
% 2.04/1.55 tff(7,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.04/1.55 tff(8,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[7, 2])).
% 2.04/1.55 tff(9,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[8, 2])).
% 2.04/1.55 tff(10,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.04/1.55 tff(11,plain,
% 2.04/1.55 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[10, 2])).
% 2.04/1.55 tff(12,plain,(
% 2.04/1.55 ~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78)))),
% 2.04/1.55 inference(skolemize,[status(sab)],[11])).
% 2.04/1.55 tff(13,plain,
% 2.04/1.55 (~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[12, 1])).
% 2.04/1.55 tff(14,plain,
% 2.04/1.55 (in(B!77, A!78)),
% 2.04/1.55 inference(or_elim,[status(thm)],[13])).
% 2.04/1.55 tff(15,plain,
% 2.04/1.55 (^[A: $i, B: $i] : refl(((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(16,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[15])).
% 2.04/1.55 tff(17,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(18,plain,
% 2.04/1.55 (^[A: $i, B: $i] : rewrite((in(B, A) => (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(19,plain,
% 2.04/1.55 (![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[18])).
% 2.04/1.55 tff(20,axiom,(![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t35_funct_1')).
% 2.04/1.55 tff(21,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.04/1.55 tff(22,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.04/1.55 tff(23,plain,(
% 2.04/1.55 ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(skolemize,[status(sab)],[22])).
% 2.04/1.55 tff(24,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[23, 16])).
% 2.04/1.55 tff(25,plain,
% 2.04/1.55 (((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(26,plain,
% 2.04/1.55 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(27,plain,
% 2.04/1.55 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77)),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[26, 25])).
% 2.04/1.55 tff(28,plain,
% 2.04/1.55 (apply(identity_relation(A!78), B!77) = B!77),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 2.04/1.55 tff(29,plain,
% 2.04/1.55 (B!77 = apply(identity_relation(A!78), B!77)),
% 2.04/1.55 inference(symmetry,[status(thm)],[28])).
% 2.04/1.55 tff(30,plain,
% 2.04/1.55 (apply(C!76, B!77) = apply(C!76, apply(identity_relation(A!78), B!77))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[29])).
% 2.04/1.55 tff(31,plain,
% 2.04/1.55 (apply(C!76, apply(identity_relation(A!78), B!77)) = apply(C!76, B!77)),
% 2.04/1.55 inference(symmetry,[status(thm)],[30])).
% 2.04/1.55 tff(32,plain,
% 2.04/1.55 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(33,plain,
% 2.04/1.55 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[32])).
% 2.04/1.55 tff(34,plain,
% 2.04/1.55 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(35,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 2.04/1.55 tff(36,plain,
% 2.04/1.55 (![A: $i] : relation(identity_relation(A))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.04/1.55 tff(37,plain,(
% 2.04/1.55 ![A: $i] : relation(identity_relation(A))),
% 2.04/1.55 inference(skolemize,[status(sab)],[36])).
% 2.04/1.55 tff(38,plain,
% 2.04/1.55 (![A: $i] : relation(identity_relation(A))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[37, 33])).
% 2.04/1.55 tff(39,plain,
% 2.04/1.55 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!78))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(40,plain,
% 2.04/1.55 (relation(identity_relation(A!78))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[39, 38])).
% 2.04/1.55 tff(41,plain,
% 2.04/1.55 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(42,plain,
% 2.04/1.55 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[41])).
% 2.04/1.55 tff(43,plain,
% 2.04/1.55 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(44,plain,
% 2.04/1.55 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[43])).
% 2.04/1.55 tff(45,plain,
% 2.04/1.55 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(46,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_funct_1')).
% 2.04/1.55 tff(47,plain,
% 2.04/1.55 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[46, 45])).
% 2.04/1.55 tff(48,plain,(
% 2.04/1.55 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 2.04/1.55 inference(skolemize,[status(sab)],[47])).
% 2.04/1.55 tff(49,plain,
% 2.04/1.55 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[48, 44])).
% 2.04/1.55 tff(50,plain,
% 2.04/1.55 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[49, 42])).
% 2.04/1.55 tff(51,plain,
% 2.04/1.55 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78)))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(52,plain,
% 2.04/1.55 (~((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[51, 50])).
% 2.04/1.55 tff(53,plain,
% 2.04/1.55 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78)))) | function(identity_relation(A!78))),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(54,plain,
% 2.04/1.55 (function(identity_relation(A!78))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[53, 52])).
% 2.04/1.55 tff(55,plain,
% 2.04/1.55 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(56,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[55])).
% 2.04/1.55 tff(57,plain,
% 2.04/1.55 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(58,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[57])).
% 2.04/1.55 tff(59,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 2.04/1.55 inference(transitivity,[status(thm)],[58, 56])).
% 2.04/1.55 tff(60,plain,
% 2.04/1.55 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(61,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[60])).
% 2.04/1.55 tff(62,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(63,plain,
% 2.04/1.55 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(64,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[63])).
% 2.04/1.55 tff(65,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_funct_1')).
% 2.04/1.55 tff(66,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.04/1.55 tff(67,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.04/1.55 tff(68,plain,(
% 2.04/1.55 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 2.04/1.55 inference(skolemize,[status(sab)],[67])).
% 2.04/1.55 tff(69,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.04/1.55 tff(70,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[69, 59])).
% 2.04/1.55 tff(71,plain,
% 2.04/1.55 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | (~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(72,plain,
% 2.04/1.55 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) <=> ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(73,plain,
% 2.04/1.55 (^[C: $i] : rewrite(((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(74,plain,
% 2.04/1.55 (![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[73])).
% 2.04/1.55 tff(75,plain,
% 2.04/1.55 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C)))) <=> ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[74])).
% 2.04/1.55 tff(76,plain,
% 2.04/1.55 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C)))) <=> ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 2.04/1.55 inference(transitivity,[status(thm)],[75, 72])).
% 2.04/1.55 tff(77,plain,
% 2.04/1.55 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[76])).
% 2.04/1.55 tff(78,plain,
% 2.04/1.55 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | (~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 2.04/1.55 inference(transitivity,[status(thm)],[77, 71])).
% 2.04/1.55 tff(79,plain,
% 2.04/1.55 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(80,plain,
% 2.04/1.55 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | (~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.04/1.55 tff(81,plain,
% 2.04/1.55 ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[80, 70])).
% 2.04/1.55 tff(82,plain,
% 2.04/1.55 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[81, 54, 40])).
% 2.04/1.55 tff(83,plain,
% 2.04/1.55 (^[A: $i] : refl((~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))) <=> (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(84,plain,
% 2.04/1.55 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))) <=> ![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[83])).
% 2.04/1.55 tff(85,plain,
% 2.04/1.55 (^[A: $i] : rewrite(((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(86,plain,
% 2.04/1.55 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> ![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[85])).
% 2.04/1.55 tff(87,plain,
% 2.04/1.55 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(88,axiom,(![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t71_relat_1')).
% 2.04/1.55 tff(89,plain,
% 2.04/1.55 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[88, 87])).
% 2.04/1.55 tff(90,plain,(
% 2.04/1.55 ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 2.04/1.55 inference(skolemize,[status(sab)],[89])).
% 2.04/1.55 tff(91,plain,
% 2.04/1.55 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[90, 86])).
% 2.04/1.55 tff(92,plain,
% 2.04/1.55 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[91, 84])).
% 2.04/1.55 tff(93,plain,
% 2.04/1.55 ((~![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))) | (~((~(relation_dom(identity_relation(A!78)) = A!78)) | (~(relation_rng(identity_relation(A!78)) = A!78))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(94,plain,
% 2.04/1.55 (~((~(relation_dom(identity_relation(A!78)) = A!78)) | (~(relation_rng(identity_relation(A!78)) = A!78)))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[93, 92])).
% 2.04/1.55 tff(95,plain,
% 2.04/1.55 (((~(relation_dom(identity_relation(A!78)) = A!78)) | (~(relation_rng(identity_relation(A!78)) = A!78))) | (relation_dom(identity_relation(A!78)) = A!78)),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(96,plain,
% 2.04/1.55 (relation_dom(identity_relation(A!78)) = A!78),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[95, 94])).
% 2.04/1.55 tff(97,plain,
% 2.04/1.55 (in(B!77, relation_dom(identity_relation(A!78))) <=> in(B!77, A!78)),
% 2.04/1.55 inference(monotonicity,[status(thm)],[96])).
% 2.04/1.55 tff(98,plain,
% 2.04/1.55 (in(B!77, A!78) <=> in(B!77, relation_dom(identity_relation(A!78)))),
% 2.04/1.55 inference(symmetry,[status(thm)],[97])).
% 2.04/1.55 tff(99,plain,
% 2.04/1.55 (in(B!77, relation_dom(identity_relation(A!78)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[14, 98])).
% 2.04/1.55 tff(100,plain,
% 2.04/1.55 (relation(C!76) & function(C!76)),
% 2.04/1.55 inference(or_elim,[status(thm)],[13])).
% 2.04/1.55 tff(101,plain,
% 2.04/1.55 (function(C!76)),
% 2.04/1.55 inference(and_elim,[status(thm)],[100])).
% 2.04/1.55 tff(102,plain,
% 2.04/1.55 (relation(C!76)),
% 2.04/1.55 inference(and_elim,[status(thm)],[100])).
% 2.04/1.55 tff(103,plain,
% 2.04/1.55 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | ((~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | (~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(104,plain,
% 2.04/1.55 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | ((~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(105,plain,
% 2.04/1.55 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | (~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.04/1.55 tff(106,plain,
% 2.04/1.55 (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[105, 102, 101, 99, 82])).
% 2.04/1.55 tff(107,plain,
% 2.04/1.55 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(108,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[107])).
% 2.04/1.55 tff(109,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(110,plain,
% 2.04/1.55 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(111,plain,
% 2.04/1.55 (![A: $i, B: $i] : (relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[110])).
% 2.04/1.55 tff(112,axiom,(![A: $i, B: $i] : (relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t94_relat_1')).
% 2.08/1.56 tff(113,plain,
% 2.08/1.56 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.08/1.56 tff(114,plain,
% 2.08/1.56 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[113, 109])).
% 2.08/1.56 tff(115,plain,(
% 2.08/1.56 ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.08/1.56 inference(skolemize,[status(sab)],[114])).
% 2.08/1.56 tff(116,plain,
% 2.08/1.56 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[115, 108])).
% 2.08/1.56 tff(117,plain,
% 2.08/1.56 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | ((~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | (~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(118,plain,
% 2.08/1.56 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | ((~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(119,plain,
% 2.08/1.56 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | (~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[118, 117])).
% 2.08/1.56 tff(120,plain,
% 2.08/1.56 (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[119, 102, 116])).
% 2.08/1.56 tff(121,plain,
% 2.08/1.56 (relation_composition(identity_relation(A!78), C!76) = relation_dom_restriction(C!76, A!78)),
% 2.08/1.56 inference(symmetry,[status(thm)],[120])).
% 2.08/1.56 tff(122,plain,
% 2.08/1.56 (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(relation_dom_restriction(C!76, A!78), B!77)),
% 2.08/1.56 inference(monotonicity,[status(thm)],[121])).
% 2.08/1.56 tff(123,plain,
% 2.08/1.56 (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(relation_composition(identity_relation(A!78), C!76), B!77)),
% 2.08/1.56 inference(symmetry,[status(thm)],[122])).
% 2.08/1.56 tff(124,plain,
% 2.08/1.56 (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)),
% 2.08/1.56 inference(transitivity,[status(thm)],[123, 106, 31])).
% 2.08/1.56 tff(125,plain,
% 2.08/1.56 (~(apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))),
% 2.08/1.56 inference(or_elim,[status(thm)],[13])).
% 2.08/1.56 tff(126,plain,
% 2.08/1.56 ($false),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[125, 124])).
% 2.08/1.56 % SZS output end Proof
%------------------------------------------------------------------------------