%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX046+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:37:49 AM UTC 2025
% Result : Theorem 1.22s 1.39s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWX046+1 : TPTP v9.1.0. Released v9.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:22:01 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.22/1.39 % SZS status Theorem
% 1.22/1.39 % SZS output start Proof
% 1.22/1.39 tff(tptp_fun______succeeds__type, type, (
% 1.22/1.39 tptp_fun______succeeds_: ( $i * $i ) > $o)).
% 1.22/1.39 tff(tptp_fun______type, type, (
% 1.22/1.39 tptp_fun_____: ( $i * $i ) > $i)).
% 1.22/1.39 tff(tptp_fun______type, type, (
% 1.22/1.39 tptp_fun_____: ( $i * $i ) > $i)).
% 1.22/1.39 tff(tptp_fun_Xz_32_type, type, (
% 1.22/1.39 tptp_fun_Xz_32: ( $i * $i ) > $i)).
% 1.22/1.39 tff(tptp_fun_Xy_41_type, type, (
% 1.22/1.39 tptp_fun_Xy_41: $i)).
% 1.22/1.39 tff(tptp_fun_Xz_40_type, type, (
% 1.22/1.39 tptp_fun_Xz_40: $i)).
% 1.22/1.39 tff(tptp_fun_Xx_42_type, type, (
% 1.22/1.39 tptp_fun_Xx_42: $i)).
% 1.22/1.39 tff(plus_succeeds_type, type, (
% 1.22/1.39 plus_succeeds: ( $i * $i * $i ) > $o)).
% 1.22/1.39 tff(nat_succeeds_type, type, (
% 1.22/1.39 nat_succeeds: $i > $o)).
% 1.22/1.39 tff(1,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))) <=> (~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(2,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : (((nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz)) & nat_succeeds(Xz)) => tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))) <=> (~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(3,axiom,(~![Xx: $i, Xy: $i, Xz: $i] : (((nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz)) & nat_succeeds(Xz)) => tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(times:leq:second)'')).
% 1.22/1.39 tff(4,plain,
% 1.22/1.39 (~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 1.22/1.39 tff(5,plain,
% 1.22/1.39 (~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 1.22/1.39 tff(6,plain,
% 1.22/1.39 (~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.22/1.39 tff(7,plain,
% 1.22/1.39 (~![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & tptp_fun______succeeds_(Xy, Xz) & nat_succeeds(Xz))) | tptp_fun______succeeds_(tptp_fun_____(Xx, Xy), tptp_fun_____(Xx, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 1.22/1.39 tff(8,plain,(
% 1.22/1.39 ~((~(nat_succeeds(Xx!42) & tptp_fun______succeeds_(Xy!41, Xz!40) & nat_succeeds(Xz!40))) | tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, Xz!40)))),
% 1.22/1.39 inference(skolemize,[status(sab)],[7])).
% 1.22/1.39 tff(9,plain,
% 1.22/1.39 (nat_succeeds(Xx!42) & tptp_fun______succeeds_(Xy!41, Xz!40) & nat_succeeds(Xz!40)),
% 1.22/1.39 inference(or_elim,[status(thm)],[8])).
% 1.22/1.39 tff(10,plain,
% 1.22/1.39 (tptp_fun______succeeds_(Xy!41, Xz!40)),
% 1.22/1.39 inference(and_elim,[status(thm)],[9])).
% 1.22/1.39 tff(11,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : refl((nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy))) <=> (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(12,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy))) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[11])).
% 1.22/1.39 tff(13,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy))) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(14,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : rewrite((tptp_fun______succeeds_(Xx, Xy) => nat_succeeds(Xx)) <=> (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(15,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (tptp_fun______succeeds_(Xx, Xy) => nat_succeeds(Xx)) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[14])).
% 1.22/1.39 tff(16,axiom,(![Xx: $i, Xy: $i] : (tptp_fun______succeeds_(Xx, Xy) => nat_succeeds(Xx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(leq:types)'')).
% 1.22/1.39 tff(17,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.22/1.39 tff(18,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.22/1.39 tff(19,plain,(
% 1.22/1.39 ![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(skolemize,[status(sab)],[18])).
% 1.22/1.39 tff(20,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.22/1.39 tff(21,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))) | (nat_succeeds(Xy!41) | (~tptp_fun______succeeds_(Xy!41, Xz!40)))) <=> ((~![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))) | nat_succeeds(Xy!41) | (~tptp_fun______succeeds_(Xy!41, Xz!40)))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(22,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))) | (nat_succeeds(Xy!41) | (~tptp_fun______succeeds_(Xy!41, Xz!40)))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(23,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i] : (nat_succeeds(Xx) | (~tptp_fun______succeeds_(Xx, Xy)))) | nat_succeeds(Xy!41) | (~tptp_fun______succeeds_(Xy!41, Xz!40))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.22/1.39 tff(24,plain,
% 1.22/1.39 (nat_succeeds(Xy!41)),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 1.22/1.39 tff(25,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : refl(((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))) <=> ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(26,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[25])).
% 1.22/1.39 tff(27,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(28,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : rewrite((nat_succeeds(Xx) => ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))) <=> ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(29,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xx) => ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[28])).
% 1.22/1.39 tff(30,axiom,(![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xx) => ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''(@+)/2'')).
% 1.22/1.39 tff(31,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.22/1.39 tff(32,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.22/1.39 tff(33,plain,(
% 1.22/1.39 ![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(skolemize,[status(sab)],[32])).
% 1.22/1.39 tff(34,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.22/1.39 tff(35,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))) | ((~nat_succeeds(Xy!41)) | ((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)))) <=> ((~![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))) | (~nat_succeeds(Xy!41)) | ((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(36,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))) | ((~nat_succeeds(Xy!41)) | ((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(37,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : ((~nat_succeeds(Xx)) | ((tptp_fun_____(Xx, Xy) = Xz) <=> plus_succeeds(Xx, Xy, Xz)))) | (~nat_succeeds(Xy!41)) | ((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.22/1.39 tff(38,plain,
% 1.22/1.39 ((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[37, 34, 24])).
% 1.22/1.39 tff(39,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : refl(((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy)) <=> ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy)))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(40,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy)) <=> ![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[39])).
% 1.22/1.39 tff(41,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy)) <=> ![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(42,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : rewrite((tptp_fun______succeeds_(Xx, Xy) => ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy)) <=> ((~tptp_fun______succeeds_(Xx, Xy)) | ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy)))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(43,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (tptp_fun______succeeds_(Xx, Xy) => ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy)) <=> ![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[42])).
% 1.22/1.39 tff(44,axiom,(![Xx: $i, Xy: $i] : (tptp_fun______succeeds_(Xx, Xy) => ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(leq:plus)'')).
% 1.22/1.39 tff(45,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.22/1.39 tff(46,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | ?[Xz: $i] : plus_succeeds(Xx, Xz, Xy))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.22/1.39 tff(47,plain,(
% 1.22/1.39 ![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))),
% 1.22/1.39 inference(skolemize,[status(sab)],[46])).
% 1.22/1.39 tff(48,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 1.22/1.39 tff(49,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))) | ((~tptp_fun______succeeds_(Xy!41, Xz!40)) | plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))) <=> ((~![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))) | (~tptp_fun______succeeds_(Xy!41, Xz!40)) | plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(50,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))) | ((~tptp_fun______succeeds_(Xy!41, Xz!40)) | plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(51,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i] : ((~tptp_fun______succeeds_(Xx, Xy)) | plus_succeeds(Xx, tptp_fun_Xz_32(Xy, Xx), Xy))) | (~tptp_fun______succeeds_(Xy!41, Xz!40)) | plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.22/1.39 tff(52,plain,
% 1.22/1.39 (plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[51, 48, 10])).
% 1.22/1.39 tff(53,plain,
% 1.22/1.39 ((~((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))) | (tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) | (~plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(54,plain,
% 1.22/1.39 ((~((tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40) <=> plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))) | (tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40)),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 1.22/1.39 tff(55,plain,
% 1.22/1.39 (tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)) = Xz!40),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[54, 38])).
% 1.22/1.39 tff(56,plain,
% 1.22/1.39 (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(Xx!42, Xz!40)),
% 1.22/1.39 inference(monotonicity,[status(thm)],[55])).
% 1.22/1.39 tff(57,plain,
% 1.22/1.39 (nat_succeeds(Xz!40)),
% 1.22/1.39 inference(and_elim,[status(thm)],[9])).
% 1.22/1.39 tff(58,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : refl((nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))) <=> (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(59,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))) <=> ![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[58])).
% 1.22/1.39 tff(60,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : trans(monotonicity(trans(monotonicity(rewrite((plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)) <=> (~((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))))), ((~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))) <=> (~(~((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))))))), rewrite((~(~((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))))) <=> ((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))), ((~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))) <=> ((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz))))), ((nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)))) <=> (nat_succeeds(Xy) | ((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))))), rewrite((nat_succeeds(Xy) | ((~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))) <=> (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))), ((nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)))) <=> (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(61,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)))) <=> ![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[60])).
% 1.22/1.39 tff(62,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)))) <=> ![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(63,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : rewrite(((plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)) => nat_succeeds(Xy)) <=> (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(64,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)) => nat_succeeds(Xy)) <=> ![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[63])).
% 1.22/1.39 tff(65,axiom,(![Xx: $i, Xy: $i, Xz: $i] : ((plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz)) => nat_succeeds(Xy))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(plus:types:3)'')).
% 1.22/1.39 tff(66,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.22/1.39 tff(67,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.22/1.39 tff(68,plain,(
% 1.22/1.39 ![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~(plus_succeeds(Xx, Xy, Xz) & nat_succeeds(Xz))))),
% 1.22/1.39 inference(skolemize,[status(sab)],[67])).
% 1.22/1.39 tff(69,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.22/1.39 tff(70,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[69, 59])).
% 1.22/1.39 tff(71,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))) | (nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41)) | (~nat_succeeds(Xz!40)) | (~plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)))) <=> ((~![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))) | nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41)) | (~nat_succeeds(Xz!40)) | (~plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(72,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))) | (nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41)) | (~nat_succeeds(Xz!40)) | (~plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40)))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(73,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : (nat_succeeds(Xy) | (~nat_succeeds(Xz)) | (~plus_succeeds(Xx, Xy, Xz)))) | nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41)) | (~nat_succeeds(Xz!40)) | (~plus_succeeds(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41), Xz!40))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.22/1.39 tff(74,plain,
% 1.22/1.39 (nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[73, 70, 57, 52])).
% 1.22/1.39 tff(75,plain,
% 1.22/1.39 (nat_succeeds(Xx!42)),
% 1.22/1.39 inference(and_elim,[status(thm)],[9])).
% 1.22/1.39 tff(76,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : refl(((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))) <=> ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(77,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[76])).
% 1.22/1.39 tff(78,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : trans(monotonicity(trans(monotonicity(rewrite((nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz)) <=> (~((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))))), ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) <=> (~(~((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))))))), rewrite((~(~((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))))) <=> ((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))), ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) <=> ((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))))), (((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> (((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))))), rewrite((((~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))), (((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(79,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[78])).
% 1.22/1.39 tff(80,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(81,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i, Xz: $i] : trans(monotonicity(rewrite(((nat_succeeds(Xx) & nat_succeeds(Xy)) & nat_succeeds(Xz)) <=> (nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))), ((((nat_succeeds(Xx) & nat_succeeds(Xy)) & nat_succeeds(Xz)) => (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ((nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz)) => (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))))), rewrite(((nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz)) => (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))), ((((nat_succeeds(Xx) & nat_succeeds(Xy)) & nat_succeeds(Xz)) => (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(82,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : (((nat_succeeds(Xx) & nat_succeeds(Xy)) & nat_succeeds(Xz)) => (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy)))) <=> ![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[81])).
% 1.22/1.39 tff(83,axiom,(![Xx: $i, Xy: $i, Xz: $i] : (((nat_succeeds(Xx) & nat_succeeds(Xy)) & nat_succeeds(Xz)) => (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''corollary-(plus:times:distributive)'')).
% 1.22/1.39 tff(84,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.22/1.39 tff(85,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[84, 80])).
% 1.22/1.39 tff(86,plain,(
% 1.22/1.39 ![Xx: $i, Xy: $i, Xz: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy) & nat_succeeds(Xz))) | (tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))))),
% 1.22/1.39 inference(skolemize,[status(sab)],[85])).
% 1.22/1.39 tff(87,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[86, 79])).
% 1.22/1.39 tff(88,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[87, 77])).
% 1.22/1.39 tff(89,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | ((~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))) | (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))) <=> ((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))) | (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(90,plain,
% 1.22/1.39 (((tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41)))) <=> ((~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))) | (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(91,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | ((tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))))) <=> ((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | ((~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))) | (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[90])).
% 1.22/1.39 tff(92,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | ((tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))))) <=> ((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))) | (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[91, 89])).
% 1.22/1.39 tff(93,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | ((tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(94,plain,
% 1.22/1.39 ((~![Xx: $i, Xy: $i, Xz: $i] : ((tptp_fun_____(Xz, tptp_fun_____(Xx, Xy)) = tptp_fun_____(tptp_fun_____(Xz, Xx), tptp_fun_____(Xz, Xy))) | (~nat_succeeds(Xx)) | (~nat_succeeds(Xz)) | (~nat_succeeds(Xy)))) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(tptp_fun_Xz_32(Xz!40, Xy!41))) | (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.22/1.39 tff(95,plain,
% 1.22/1.39 (tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[94, 88, 75, 24, 74])).
% 1.22/1.39 tff(96,plain,
% 1.22/1.39 (tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(Xx!42, tptp_fun_____(Xy!41, tptp_fun_Xz_32(Xz!40, Xy!41)))),
% 1.22/1.39 inference(symmetry,[status(thm)],[95])).
% 1.22/1.39 tff(97,plain,
% 1.22/1.39 (tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))) = tptp_fun_____(Xx!42, Xz!40)),
% 1.22/1.39 inference(transitivity,[status(thm)],[96, 56])).
% 1.22/1.39 tff(98,plain,
% 1.22/1.39 (tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))) <=> tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, Xz!40))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[97])).
% 1.22/1.39 tff(99,plain,
% 1.22/1.39 (tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, Xz!40)) <=> tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[98])).
% 1.22/1.39 tff(100,plain,
% 1.22/1.39 ((~tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, Xz!40))) <=> (~tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[99])).
% 1.22/1.39 tff(101,plain,
% 1.22/1.39 (~tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, Xz!40))),
% 1.22/1.39 inference(or_elim,[status(thm)],[8])).
% 1.22/1.39 tff(102,plain,
% 1.22/1.39 (~tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.22/1.39 tff(103,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : refl((nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) <=> (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(104,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[103])).
% 1.22/1.39 tff(105,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : trans(monotonicity(trans(monotonicity(rewrite((nat_succeeds(Xx) & nat_succeeds(Xy)) <=> (~((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))), ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) <=> (~(~((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))))), rewrite((~(~((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))) <=> ((~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))), ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) <=> ((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))), ((nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy)))) <=> (nat_succeeds(tptp_fun_____(Xx, Xy)) | ((~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))))), rewrite((nat_succeeds(tptp_fun_____(Xx, Xy)) | ((~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) <=> (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))), ((nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy)))) <=> (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(106,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy)))) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[105])).
% 1.22/1.39 tff(107,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy)))) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(108,plain,
% 1.22/1.39 (^[Xx: $i, Xy: $i] : rewrite(((nat_succeeds(Xx) & nat_succeeds(Xy)) => nat_succeeds(tptp_fun_____(Xx, Xy))) <=> (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy)))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(109,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : ((nat_succeeds(Xx) & nat_succeeds(Xy)) => nat_succeeds(tptp_fun_____(Xx, Xy))) <=> ![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[108])).
% 1.22/1.39 tff(110,axiom,(![Xx: $i, Xy: $i] : ((nat_succeeds(Xx) & nat_succeeds(Xy)) => nat_succeeds(tptp_fun_____(Xx, Xy)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''corollary-(times:types)'')).
% 1.22/1.39 tff(111,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.22/1.39 tff(112,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.22/1.39 tff(113,plain,(
% 1.22/1.39 ![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~(nat_succeeds(Xx) & nat_succeeds(Xy))))),
% 1.22/1.39 inference(skolemize,[status(sab)],[112])).
% 1.22/1.39 tff(114,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[113, 106])).
% 1.22/1.39 tff(115,plain,
% 1.22/1.39 (![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[114, 104])).
% 1.22/1.39 tff(116,plain,
% 1.22/1.39 (((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)))) <=> ((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(117,plain,
% 1.22/1.40 ((nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42))) <=> (nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(118,plain,
% 1.22/1.40 (((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)))) <=> ((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[117])).
% 1.22/1.40 tff(119,plain,
% 1.22/1.40 (((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)))) <=> ((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41)))),
% 1.22/1.40 inference(transitivity,[status(thm)],[118, 116])).
% 1.22/1.40 tff(120,plain,
% 1.22/1.40 ((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xy!41)) | (~nat_succeeds(Xx!42)))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(121,plain,
% 1.22/1.40 ((~![Xx: $i, Xy: $i] : (nat_succeeds(tptp_fun_____(Xx, Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | nat_succeeds(tptp_fun_____(Xx!42, Xy!41)) | (~nat_succeeds(Xx!42)) | (~nat_succeeds(Xy!41))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.22/1.40 tff(122,plain,
% 1.22/1.40 (nat_succeeds(tptp_fun_____(Xx!42, Xy!41))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[121, 115, 75, 24])).
% 1.22/1.40 tff(123,plain,
% 1.22/1.40 (^[Xx: $i, Xy: $i] : refl(((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))) <=> ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(124,plain,
% 1.22/1.40 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))) <=> ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[123])).
% 1.22/1.40 tff(125,plain,
% 1.22/1.40 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))) <=> ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(126,plain,
% 1.22/1.40 (^[Xx: $i, Xy: $i] : rewrite((nat_succeeds(Xx) => tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))) <=> ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(127,plain,
% 1.22/1.40 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) => tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy))) <=> ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[126])).
% 1.22/1.40 tff(128,axiom,(![Xx: $i, Xy: $i] : (nat_succeeds(Xx) => tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''corollary-(leq:plus:first)'')).
% 1.22/1.40 tff(129,plain,
% 1.22/1.40 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.22/1.40 tff(130,plain,
% 1.22/1.40 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[129, 125])).
% 1.22/1.41 tff(131,plain,(
% 1.22/1.41 ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.41 inference(skolemize,[status(sab)],[130])).
% 1.22/1.41 tff(132,plain,
% 1.22/1.41 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[131, 124])).
% 1.22/1.41 tff(133,plain,
% 1.22/1.41 (((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))) | ((~nat_succeeds(tptp_fun_____(Xx!42, Xy!41))) | tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))) <=> ((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))) | (~nat_succeeds(tptp_fun_____(Xx!42, Xy!41))) | tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(134,plain,
% 1.22/1.41 ((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))) | ((~nat_succeeds(tptp_fun_____(Xx!42, Xy!41))) | tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41)))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(135,plain,
% 1.22/1.41 ((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | tptp_fun______succeeds_(Xx, tptp_fun_____(Xx, Xy)))) | (~nat_succeeds(tptp_fun_____(Xx!42, Xy!41))) | tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.22/1.41 tff(136,plain,
% 1.22/1.41 (tptp_fun______succeeds_(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(tptp_fun_____(Xx!42, Xy!41), tptp_fun_____(Xx!42, tptp_fun_Xz_32(Xz!40, Xy!41))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[135, 132, 122])).
% 1.22/1.41 tff(137,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[136, 102])).
% 1.22/1.41 % SZS output end Proof
% 1.22/1.41 % E exiting
%------------------------------------------------------------------------------