%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO498+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:06:25 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO498+1 : TPTP v9.0.0. Released v7.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:56:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(tptp_fun_Xq_0_type, type, (
% 0.21/0.43 tptp_fun_Xq_0: $i)).
% 0.21/0.43 tff(tptp_fun_Xp_1_type, type, (
% 0.21/0.43 tptp_fun_Xp_1: $i)).
% 0.21/0.43 tff(s_type, type, (
% 0.21/0.43 s: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Xa_2_type, type, (
% 0.21/0.43 tptp_fun_Xa_2: $i)).
% 0.21/0.43 tff(s_m_type, type, (
% 0.21/0.43 s_m: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 ((~((Xp!1 = Xq!0) | (~(s(Xa!2, Xq!0) = s(Xa!2, Xp!1))))) <=> (~((Xp!1 = Xq!0) | (~(s(Xa!2, Xq!0) = s(Xa!2, Xp!1)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 ((~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp))))) <=> (~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 ((~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : (((~(s(Xa, Xp) = Xr)) | (~(s(Xa, Xq) = Xr))) | (Xp = Xq))) <=> (~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,axiom,(~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : (((~(s(Xa, Xp) = Xr)) | (~(s(Xa, Xq) = Xr))) | (Xp = Xq))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_8')).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (~![Xa: $i, Xp: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = s(Xa, Xp))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.43 tff(9,plain,(
% 0.21/0.43 ~((Xp!1 = Xq!0) | (~(s(Xa!2, Xq!0) = s(Xa!2, Xp!1))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[8])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (~((Xp!1 = Xq!0) | (~(s(Xa!2, Xq!0) = s(Xa!2, Xp!1))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (s(Xa!2, Xq!0) = s(Xa!2, Xp!1)),
% 0.21/0.43 inference(or_elim,[status(thm)],[10])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (s(Xa!2, Xp!1) = s(Xa!2, Xq!0)),
% 0.21/0.43 inference(symmetry,[status(thm)],[11])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (s_m(Xq!0, Xa!2, s(Xa!2, Xp!1)) <=> s_m(Xq!0, Xa!2, s(Xa!2, Xq!0))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (s_m(Xq!0, Xa!2, s(Xa!2, Xq!0)) <=> s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))),
% 0.21/0.43 inference(symmetry,[status(thm)],[13])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (^[Xp: $i, Xa: $i] : refl(s_m(Xp, Xa, s(Xa, Xp)) <=> s_m(Xp, Xa, s(Xa, Xp)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,axiom,(![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_4a')).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.43 tff(20,plain,(
% 0.21/0.43 ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.43 inference(skolemize,[status(sab)],[19])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xq!0, Xa!2, s(Xa!2, Xq!0))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (s_m(Xq!0, Xa!2, s(Xa!2, Xq!0))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 14])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (^[Xa: $i, Xm: $i, Xb: $i] : refl(((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(28,axiom,(![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_2')).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.44 tff(30,plain,(
% 0.21/0.44 ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.44 inference(skolemize,[status(sab)],[29])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xq!0))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xq!0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xq!0))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 ((~s_m(Xq!0, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[35, 24])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (^[Xp: $i, Xa: $i, Xq: $i] : refl(((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(40,axiom,(![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_6')).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.44 tff(42,plain,(
% 0.21/0.44 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[41])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)) | (Xq!0 = s(Xa!2, s(Xa!2, Xp!1))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)) | (Xq!0 = s(Xa!2, s(Xa!2, Xp!1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)) | (Xq!0 = s(Xa!2, s(Xa!2, Xp!1))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!2, Xp!1), Xa!2, Xq!0)) | (Xq!0 = s(Xa!2, s(Xa!2, Xp!1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (Xq!0 = s(Xa!2, s(Xa!2, Xp!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[46, 43, 36])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (s(Xa!2, s(Xa!2, Xp!1)) = Xq!0),
% 0.21/0.44 inference(symmetry,[status(thm)],[47])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xp!1, Xa!2, s(Xa!2, Xp!1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (s_m(Xp!1, Xa!2, s(Xa!2, Xp!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[49, 21])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xp!1, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xp!1))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xp!1, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xp!1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xp!1, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xp!1))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xp!1, Xa!2, s(Xa!2, Xp!1))) | s_m(s(Xa!2, Xp!1), Xa!2, Xp!1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (s_m(s(Xa!2, Xp!1), Xa!2, Xp!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[53, 31, 50])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!2, Xp!1), Xa!2, Xp!1)) | (Xp!1 = s(Xa!2, s(Xa!2, Xp!1))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!2, Xp!1), Xa!2, Xp!1)) | (Xp!1 = s(Xa!2, s(Xa!2, Xp!1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!2, Xp!1), Xa!2, Xp!1)) | (Xp!1 = s(Xa!2, s(Xa!2, Xp!1))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!2, Xp!1), Xa!2, Xp!1)) | (Xp!1 = s(Xa!2, s(Xa!2, Xp!1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (Xp!1 = s(Xa!2, s(Xa!2, Xp!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[57, 43, 54])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (Xp!1 = Xq!0),
% 0.21/0.45 inference(transitivity,[status(thm)],[58, 48])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (~(Xp!1 = Xq!0)),
% 0.21/0.45 inference(or_elim,[status(thm)],[10])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------