%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP005_5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 Jun 21 05:11:16 AM UTC 2025
% Result : Theorem 33.87s 34.08s
% Output : Proof 34.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP005_5 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:05:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 33.87/34.08 % SZS status Theorem
% 33.87/34.08 % SZS output start Proof
% 33.87/34.08 tff(tptp_fun_V0R_773_type, type, (
% 33.87/34.08 tptp_fun_V0R_773: $i)).
% 33.87/34.08 tff(ap_type, type, (
% 33.87/34.08 ap: ( $i * $i ) > $i)).
% 33.87/34.08 tff(c_2Eset__relation_2Erel__to__reln_type, type, (
% 33.87/34.08 c_2Eset__relation_2Erel__to__reln: ( del * del ) > $i)).
% 33.87/34.08 tff(tptp_fun_A_27b_774_type, type, (
% 33.87/34.08 tptp_fun_A_27b_774: del)).
% 33.87/34.08 tff(tptp_fun_A_27a_775_type, type, (
% 33.87/34.08 tptp_fun_A_27a_775: del)).
% 33.87/34.08 tff(c_2Eset__relation_2Ereln__to__rel_type, type, (
% 33.87/34.08 c_2Eset__relation_2Ereln__to__rel: ( del * del ) > $i)).
% 33.87/34.08 tff(c_2Epair_2EUNCURRY_type, type, (
% 33.87/34.08 c_2Epair_2EUNCURRY: ( del * del * del ) > $i)).
% 33.87/34.08 tff(bool_type, type, (
% 33.87/34.08 bool: del)).
% 33.87/34.08 tff(c_2Epair_2ECURRY_type, type, (
% 33.87/34.08 c_2Epair_2ECURRY: ( del * del * del ) > $i)).
% 33.87/34.08 tff(mem_type, type, (
% 33.87/34.08 mem: ( $i * del ) > $o)).
% 33.87/34.08 tff(arr_type, type, (
% 33.87/34.08 arr: ( del * del ) > del)).
% 33.87/34.08 tff(1,plain,
% 33.87/34.08 ((~![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)))),
% 33.87/34.08 inference(rewrite,[status(thm)],[])).
% 33.87/34.08 tff(2,plain,
% 33.87/34.08 ((~![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)))),
% 33.87/34.08 inference(rewrite,[status(thm)],[])).
% 33.87/34.08 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/sandbox/benchmark/theBenchmark.p','conj_thm_2Eset__relation_2Erel__to__reln__inv')).
% 33.87/34.08 tff(4,plain,
% 33.87/34.08 (~![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[3, 2])).
% 33.87/34.08 tff(5,plain,
% 33.87/34.08 (~![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[4, 1])).
% 33.87/34.08 tff(6,plain,
% 33.87/34.08 (~![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[5, 1])).
% 33.87/34.08 tff(7,plain,
% 33.87/34.08 (~![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[6, 1])).
% 33.87/34.08 tff(8,plain,(
% 33.87/34.08 ~((~mem(V0R!773, arr(A_27a!775, arr(A_27b!774, bool)))) | (ap(c_2Eset__relation_2Ereln__to__rel(A_27a!775, A_27b!774), ap(c_2Eset__relation_2Erel__to__reln(A_27a!775, A_27b!774), V0R!773)) = V0R!773))),
% 33.87/34.08 inference(skolemize,[status(sab)],[7])).
% 33.87/34.08 tff(9,plain,
% 33.87/34.08 (mem(V0R!773, arr(A_27a!775, arr(A_27b!774, bool)))),
% 33.87/34.08 inference(or_elim,[status(thm)],[8])).
% 33.87/34.08 tff(10,plain,
% 33.87/34.08 (^[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)))),
% 33.87/34.08 inference(bind,[status(th)],[])).
% 33.87/34.08 tff(11,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(quant_intro,[status(thm)],[10])).
% 33.87/34.08 tff(12,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(rewrite,[status(thm)],[])).
% 33.87/34.08 tff(13,plain,
% 33.87/34.08 (^[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)))),
% 33.87/34.08 inference(bind,[status(th)],[])).
% 33.87/34.08 tff(14,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(quant_intro,[status(thm)],[13])).
% 33.87/34.08 tff(15,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/sandbox/benchmark/Axioms/ITP001/ITP014_5.ax','conj_thm_2Epair_2ECURRY__UNCURRY__THM')).
% 33.87/34.08 tff(16,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[15, 14])).
% 33.87/34.08 tff(17,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[16, 12])).
% 33.87/34.08 tff(18,plain,(
% 33.87/34.08 ![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))),
% 33.87/34.08 inference(skolemize,[status(sab)],[17])).
% 33.87/34.08 tff(19,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[18, 11])).
% 33.87/34.08 tff(20,plain,
% 33.87/34.08 (((~![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!773, arr(A_27a!775, arr(A_27b!774, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool), ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773)) = V0R!773))) <=> ((~![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!773, arr(A_27a!775, arr(A_27b!774, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool), ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773)) = V0R!773))),
% 33.87/34.08 inference(rewrite,[status(thm)],[])).
% 33.87/34.08 tff(21,plain,
% 33.87/34.08 ((~![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!773, arr(A_27a!775, arr(A_27b!774, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool), ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773)) = V0R!773))),
% 33.87/34.08 inference(quant_inst,[status(thm)],[])).
% 33.87/34.08 tff(22,plain,
% 33.87/34.08 ((~![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!773, arr(A_27a!775, arr(A_27b!774, bool)))) | (ap(c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool), ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773)) = V0R!773)),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[21, 20])).
% 33.87/34.08 tff(23,plain,
% 33.87/34.08 (ap(c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool), ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773)) = V0R!773),
% 33.87/34.08 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 33.87/34.08 tff(24,plain,
% 33.87/34.08 (^[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)))),
% 33.87/34.08 inference(bind,[status(th)],[])).
% 33.87/34.08 tff(25,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(quant_intro,[status(thm)],[24])).
% 33.87/34.08 tff(26,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(rewrite,[status(thm)],[])).
% 33.87/34.08 tff(27,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/sandbox/benchmark/theBenchmark.p','conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY')).
% 33.87/34.08 tff(28,plain,
% 33.87/34.08 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[27, 26])).
% 33.87/34.08 tff(29,plain,(
% 33.87/34.08 ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 33.87/34.08 inference(skolemize,[status(sab)],[28])).
% 33.87/34.08 tff(30,plain,
% 33.87/34.08 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Erel__to__reln(A_27a, A_27b) = c_2Epair_2EUNCURRY(A_27a, A_27b, bool))),
% 33.87/34.08 inference(modus_ponens,[status(thm)],[29, 25])).
% 33.87/34.08 tff(31,plain,
% 33.87/34.08 ((~![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!775, A_27b!774) = c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool))),
% 33.87/34.08 inference(quant_inst,[status(thm)],[])).
% 33.87/34.08 tff(32,plain,
% 33.87/34.08 (c_2Eset__relation_2Erel__to__reln(A_27a!775, A_27b!774) = c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool)),
% 33.87/34.08 inference(unit_resolution,[status(thm)],[31, 30])).
% 33.87/34.08 tff(33,plain,
% 33.87/34.08 (ap(c_2Eset__relation_2Erel__to__reln(A_27a!775, A_27b!774), V0R!773) = ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773)),
% 33.87/34.08 inference(monotonicity,[status(thm)],[32])).
% 33.87/34.08 tff(34,plain,
% 33.87/34.08 (^[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)))),
% 33.87/34.08 inference(bind,[status(th)],[])).
% 33.87/34.08 tff(35,plain,
% 33.87/34.08 (![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))),
% 33.87/34.08 inference(quant_intro,[status(thm)],[34])).
% 33.87/34.08 tff(36,plain,
% 33.87/34.08 (![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))),
% 34.34/34.49 inference(rewrite,[status(thm)],[])).
% 34.34/34.49 tff(37,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/sandbox/benchmark/theBenchmark.p','conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY')).
% 34.34/34.49 tff(38,plain,
% 34.34/34.49 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 34.34/34.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 34.34/34.49 tff(39,plain,(
% 34.34/34.49 ![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 34.34/34.49 inference(skolemize,[status(sab)],[38])).
% 34.34/34.49 tff(40,plain,
% 34.34/34.49 (![A_27a: del, A_27b: del] : (c_2Eset__relation_2Ereln__to__rel(A_27a, A_27b) = c_2Epair_2ECURRY(A_27a, A_27b, bool))),
% 34.34/34.49 inference(modus_ponens,[status(thm)],[39, 35])).
% 34.34/34.49 tff(41,plain,
% 34.34/34.49 ((~![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!775, A_27b!774) = c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool))),
% 34.34/34.49 inference(quant_inst,[status(thm)],[])).
% 34.34/34.49 tff(42,plain,
% 34.34/34.49 (c_2Eset__relation_2Ereln__to__rel(A_27a!775, A_27b!774) = c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool)),
% 34.34/34.49 inference(unit_resolution,[status(thm)],[41, 40])).
% 34.34/34.49 tff(43,plain,
% 34.34/34.49 (ap(c_2Eset__relation_2Ereln__to__rel(A_27a!775, A_27b!774), ap(c_2Eset__relation_2Erel__to__reln(A_27a!775, A_27b!774), V0R!773)) = ap(c_2Epair_2ECURRY(A_27a!775, A_27b!774, bool), ap(c_2Epair_2EUNCURRY(A_27a!775, A_27b!774, bool), V0R!773))),
% 34.34/34.49 inference(monotonicity,[status(thm)],[42, 33])).
% 34.34/34.49 tff(44,plain,
% 34.34/34.49 (ap(c_2Eset__relation_2Ereln__to__rel(A_27a!775, A_27b!774), ap(c_2Eset__relation_2Erel__to__reln(A_27a!775, A_27b!774), V0R!773)) = V0R!773),
% 34.34/34.49 inference(transitivity,[status(thm)],[43, 23])).
% 34.34/34.49 tff(45,plain,
% 34.34/34.49 (~(ap(c_2Eset__relation_2Ereln__to__rel(A_27a!775, A_27b!774), ap(c_2Eset__relation_2Erel__to__reln(A_27a!775, A_27b!774), V0R!773)) = V0R!773)),
% 34.34/34.49 inference(or_elim,[status(thm)],[8])).
% 34.34/34.49 tff(46,plain,
% 34.34/34.49 ($false),
% 34.34/34.49 inference(unit_resolution,[status(thm)],[45, 44])).
% 34.34/34.49 % SZS output end Proof
% 34.34/34.51 % E exiting
%------------------------------------------------------------------------------