TSTP Solution File: ITP005_5 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP005_5 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 04:14:43 EDT 2022
% Result : Theorem 54.01s 35.37s
% Output : Proof 54.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP005_5 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 02:22:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 54.01/35.37 % SZS status Theorem
% 54.01/35.37 % SZS output start Proof
% 54.01/35.37 tff(tptp_fun_V0R_779_type, type, (
% 54.01/35.37 tptp_fun_V0R_779: $i)).
% 54.01/35.37 tff(ap_type, type, (
% 54.01/35.37 ap: ( $i * $i ) > $i)).
% 54.01/35.37 tff(c_2Eset__relation_2Erel__to__reln_type, type, (
% 54.01/35.37 c_2Eset__relation_2Erel__to__reln: ( del * del ) > $i)).
% 54.01/35.37 tff(tptp_fun_A_27b_780_type, type, (
% 54.01/35.37 tptp_fun_A_27b_780: del)).
% 54.01/35.37 tff(tptp_fun_A_27a_781_type, type, (
% 54.01/35.37 tptp_fun_A_27a_781: del)).
% 54.01/35.37 tff(c_2Eset__relation_2Ereln__to__rel_type, type, (
% 54.01/35.37 c_2Eset__relation_2Ereln__to__rel: ( del * del ) > $i)).
% 54.01/35.37 tff(c_2Epair_2EUNCURRY_type, type, (
% 54.01/35.37 c_2Epair_2EUNCURRY: ( del * del * del ) > $i)).
% 54.01/35.37 tff(bool_type, type, (
% 54.01/35.37 bool: del)).
% 54.01/35.37 tff(c_2Epair_2ECURRY_type, type, (
% 54.01/35.37 c_2Epair_2ECURRY: ( del * del * del ) > $i)).
% 54.01/35.37 tff(mem_type, type, (
% 54.01/35.37 mem: ( $i * del ) > $o)).
% 54.01/35.37 tff(arr_type, type, (
% 54.01/35.37 arr: ( del * del ) > del)).
% 54.01/35.37 tff(1,plain,
% 54.01/35.37 ((~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))) <=> (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R)))),
% 54.01/35.37 inference(rewrite,[status(thm)],[])).
% 54.01/35.37 tff(2,plain,
% 54.01/35.37 ((~![A_27a: del, A_27b: del, V0R: $i] : (mem(V0R, arr(A_27a, arr(A_27b, bool))) => (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))) <=> (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R)))),
% 54.01/35.37 inference(rewrite,[status(thm)],[])).
% 54.01/35.37 tff(3,axiom,(~![A_27a: del, A_27b: del, V0R: $i] : (mem(V0R, arr(A_27a, arr(A_27b, bool))) => (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Eset__relation_2Erel__to__reln__inv')).
% 54.01/35.37 tff(4,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 54.01/35.37 tff(5,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 54.01/35.37 tff(6,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 54.01/35.37 tff(7,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 54.01/35.37 tff(8,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[7, 1])).
% 54.01/35.37 tff(9,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 54.01/35.37 tff(10,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[9, 1])).
% 54.01/35.37 tff(11,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[10, 1])).
% 54.01/35.37 tff(12,plain,
% 54.01/35.37 (~![A_27a: del, A_27b: del, V0R: $i] : ((~mem(V0R, arr(A_27a, arr(A_27b, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b), ap(c_2Eset__relation_2Erel__to__reln(A_27a, A_27b), V0R)) = V0R))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[11, 1])).
% 54.01/35.37 tff(13,plain,(
% 54.01/35.37 ~((~mem(V0R!779, arr(A_27a!781, arr(A_27b!780, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a!781, A_27b!780), ap(c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780), V0R!779)) = V0R!779))),
% 54.01/35.37 inference(skolemize,[status(sab)],[12])).
% 54.01/35.37 tff(14,plain,
% 54.01/35.37 (mem(V0R!779, arr(A_27a!781, arr(A_27b!780, bool)))),
% 54.01/35.37 inference(or_elim,[status(thm)],[13])).
% 54.01/35.37 tff(15,plain,
% 54.01/35.37 (^[A_27a: del, A_27b: del, A_27c: del, V0f: $i] : refl(((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)) <=> ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)))),
% 54.01/35.37 inference(bind,[status(th)],[])).
% 54.01/35.37 tff(16,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)) <=> ![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(quant_intro,[status(thm)],[15])).
% 54.01/35.37 tff(17,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)) <=> ![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(rewrite,[status(thm)],[])).
% 54.01/35.37 tff(18,plain,
% 54.01/35.37 (^[A_27a: del, A_27b: del, A_27c: del, V0f: $i] : rewrite((mem(V0f, arr(A_27a, arr(A_27b, A_27c))) => (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)) <=> ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)))),
% 54.01/35.37 inference(bind,[status(th)],[])).
% 54.01/35.37 tff(19,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : (mem(V0f, arr(A_27a, arr(A_27b, A_27c))) => (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f)) <=> ![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(quant_intro,[status(thm)],[18])).
% 54.01/35.37 tff(20,axiom,(![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : (mem(V0f, arr(A_27a, arr(A_27b, A_27c))) => (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))), file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP014_5.ax','conj_thm_2Epair_2ECURRY__UNCURRY__THM')).
% 54.01/35.37 tff(21,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 54.01/35.37 tff(22,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 54.01/35.37 tff(23,plain,(
% 54.01/35.37 ![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(skolemize,[status(sab)],[22])).
% 54.01/35.37 tff(24,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 54.01/35.37 tff(25,plain,
% 54.01/35.37 (((~![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))) | ((~mem(V0R!779, arr(A_27a!781, arr(A_27b!780, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool), ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779)) = V0R!779))) <=> ((~![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))) | (~mem(V0R!779, arr(A_27a!781, arr(A_27b!780, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool), ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779)) = V0R!779))),
% 54.01/35.37 inference(rewrite,[status(thm)],[])).
% 54.01/35.37 tff(26,plain,
% 54.01/35.37 ((~![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))) | ((~mem(V0R!779, arr(A_27a!781, arr(A_27b!780, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool), ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779)) = V0R!779))),
% 54.01/35.37 inference(quant_inst,[status(thm)],[])).
% 54.01/35.37 tff(27,plain,
% 54.01/35.37 ((~![A_27a: del, A_27b: del, A_27c: del, V0f: $i] : ((~mem(V0f, arr(A_27a, arr(A_27b, A_27c)))) | (ap(c_2Epair_2ECURRY(A_27a, A_27b, A_27c), ap(c_2Epair_2EUNCURRY(A_27a, A_27b, A_27c), V0f)) = V0f))) | (~mem(V0R!779, arr(A_27a!781, arr(A_27b!780, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool), ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779)) = V0R!779)),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 54.01/35.37 tff(28,plain,
% 54.01/35.37 (ap(c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool), ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779)) = V0R!779),
% 54.01/35.37 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 54.01/35.37 tff(29,plain,
% 54.01/35.37 (^[A_27a: del, A_27b: del] : refl((c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool)) <=> (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool)))),
% 54.01/35.37 inference(bind,[status(th)],[])).
% 54.01/35.37 tff(30,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool)) <=> ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 54.01/35.37 inference(quant_intro,[status(thm)],[29])).
% 54.01/35.37 tff(31,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool)) <=> ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 54.01/35.37 inference(rewrite,[status(thm)],[])).
% 54.01/35.37 tff(32,axiom,(![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY')).
% 54.01/35.37 tff(33,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 54.01/35.37 tff(34,plain,(
% 54.01/35.37 ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 54.01/35.37 inference(skolemize,[status(sab)],[33])).
% 54.01/35.37 tff(35,plain,
% 54.01/35.37 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 54.01/35.37 inference(modus_ponens,[status(thm)],[34, 30])).
% 54.01/35.37 tff(36,plain,
% 54.01/35.37 ((~![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))) | (c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780) = c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool))),
% 54.31/35.71 inference(quant_inst,[status(thm)],[])).
% 54.31/35.71 tff(37,plain,
% 54.31/35.71 (c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780) = c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool)),
% 54.31/35.71 inference(unit_resolution,[status(thm)],[36, 35])).
% 54.31/35.71 tff(38,plain,
% 54.31/35.71 (ap(c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780), V0R!779) = ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779)),
% 54.31/35.71 inference(monotonicity,[status(thm)],[37])).
% 54.31/35.71 tff(39,plain,
% 54.31/35.71 (^[A_27a: del, A_27b: del] : refl((c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool)) <=> (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool)))),
% 54.31/35.71 inference(bind,[status(th)],[])).
% 54.31/35.71 tff(40,plain,
% 54.31/35.71 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool)) <=> ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 54.31/35.71 inference(quant_intro,[status(thm)],[39])).
% 54.31/35.71 tff(41,plain,
% 54.31/35.71 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool)) <=> ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 54.31/35.71 inference(rewrite,[status(thm)],[])).
% 54.31/35.71 tff(42,axiom,(![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY')).
% 54.31/35.71 tff(43,plain,
% 54.31/35.71 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 54.31/35.71 inference(modus_ponens,[status(thm)],[42, 41])).
% 54.31/35.71 tff(44,plain,(
% 54.31/35.71 ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 54.31/35.71 inference(skolemize,[status(sab)],[43])).
% 54.31/35.71 tff(45,plain,
% 54.31/35.71 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 54.31/35.71 inference(modus_ponens,[status(thm)],[44, 40])).
% 54.31/35.71 tff(46,plain,
% 54.31/35.71 ((~![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))) | (c_2Eset__relation_2Ereln__to__rel(A_27a!781, A_27b!780) = c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool))),
% 54.31/35.71 inference(quant_inst,[status(thm)],[])).
% 54.31/35.71 tff(47,plain,
% 54.31/35.71 (c_2Eset__relation_2Ereln__to__rel(A_27a!781, A_27b!780) = c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool)),
% 54.31/35.71 inference(unit_resolution,[status(thm)],[46, 45])).
% 54.31/35.71 tff(48,plain,
% 54.31/35.71 (ap(c_2Eset__relation_2Ereln__to__rel(A_27a!781, A_27b!780), ap(c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780), V0R!779)) = ap(c_2Epair_2ECURRY(A_27a!781, A_27b!780, bool), ap(c_2Epair_2EUNCURRY(A_27a!781, A_27b!780, bool), V0R!779))),
% 54.31/35.71 inference(monotonicity,[status(thm)],[47, 38])).
% 54.31/35.71 tff(49,plain,
% 54.31/35.71 (ap(c_2Eset__relation_2Ereln__to__rel(A_27a!781, A_27b!780), ap(c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780), V0R!779)) = V0R!779),
% 54.31/35.71 inference(transitivity,[status(thm)],[48, 28])).
% 54.31/35.71 tff(50,plain,
% 54.31/35.71 (~(ap(c_2Eset__relation_2Ereln__to__rel(A_27a!781, A_27b!780), ap(c_2Eset__relation_2Erel__to__reln(A_27a!781, A_27b!780), V0R!779)) = V0R!779)),
% 54.31/35.71 inference(or_elim,[status(thm)],[13])).
% 54.31/35.71 tff(51,plain,
% 54.31/35.71 ($false),
% 54.31/35.71 inference(unit_resolution,[status(thm)],[50, 49])).
% 54.31/35.71 % SZS output end Proof
%------------------------------------------------------------------------------