%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO499+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO499+1 : TPTP v9.0.0. Released v7.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:56:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(s_t_type, type, (
% 0.20/0.46 s_t: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(s_type, type, (
% 0.20/0.46 s: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_Xp_3_type, type, (
% 0.20/0.46 tptp_fun_Xp_3: $i)).
% 0.20/0.46 tff(tptp_fun_Xa_0_type, type, (
% 0.20/0.46 tptp_fun_Xa_0: $i)).
% 0.20/0.46 tff(tptp_fun_Xq_2_type, type, (
% 0.20/0.46 tptp_fun_Xq_2: $i)).
% 0.20/0.46 tff(tptp_fun_Xr_1_type, type, (
% 0.20/0.46 tptp_fun_Xr_1: $i)).
% 0.20/0.46 tff(s_m_type, type, (
% 0.20/0.46 s_m: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[Xp: $i, Xa: $i] : refl(s_m(Xp, Xa, s(Xa, Xp)) <=> s_m(Xp, Xa, s(Xa, Xp)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,axiom,(![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_4a')).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.46 tff(6,plain,(
% 0.20/0.46 ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.20/0.46 inference(skolemize,[status(sab)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (^[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)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(13,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')).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.46 tff(15,plain,(
% 0.20/0.46 ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.20/0.46 inference(skolemize,[status(sab)],[14])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))) | s_m(s(Xa!0, Xp!3), Xa!0, Xp!3))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))) | s_m(s(Xa!0, Xp!3), Xa!0, Xp!3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))) | s_m(s(Xa!0, Xp!3), Xa!0, Xp!3))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))) | s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(24,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')).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.46 tff(26,plain,(
% 0.20/0.46 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[25])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)) | (Xp!3 = s(Xa!0, s(Xa!0, Xp!3))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)) | (Xp!3 = s(Xa!0, s(Xa!0, Xp!3))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)) | (Xp!3 = s(Xa!0, s(Xa!0, Xp!3))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)) | (Xp!3 = s(Xa!0, s(Xa!0, Xp!3)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (Xp!3 = s(Xa!0, s(Xa!0, Xp!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (s(Xa!0, s(Xa!0, Xp!3)) = Xp!3),
% 0.20/0.46 inference(symmetry,[status(thm)],[31])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[33, 7])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))) | s_m(s(Xa!0, Xq!2), Xa!0, Xq!2))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))) | s_m(s(Xa!0, Xq!2), Xa!0, Xq!2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))) | s_m(s(Xa!0, Xq!2), Xa!0, Xq!2))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))) | s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[37, 16, 34])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)) | (Xq!2 = s(Xa!0, s(Xa!0, Xq!2))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)) | (Xq!2 = s(Xa!0, s(Xa!0, Xq!2))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)) | (Xq!2 = s(Xa!0, s(Xa!0, Xq!2))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)) | (Xq!2 = s(Xa!0, s(Xa!0, Xq!2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (Xq!2 = s(Xa!0, s(Xa!0, Xq!2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[41, 27, 38])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (s(Xa!0, s(Xa!0, Xq!2)) = Xq!2),
% 0.20/0.46 inference(symmetry,[status(thm)],[42])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[44, 7])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))) | s_m(s(Xa!0, Xr!1), Xa!0, Xr!1))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))) | s_m(s(Xa!0, Xr!1), Xa!0, Xr!1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))) | s_m(s(Xa!0, Xr!1), Xa!0, Xr!1))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))) | s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[48, 16, 45])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)) | (Xr!1 = s(Xa!0, s(Xa!0, Xr!1))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)) | (Xr!1 = s(Xa!0, s(Xa!0, Xr!1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)) | (Xr!1 = s(Xa!0, s(Xa!0, Xr!1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)) | (Xr!1 = s(Xa!0, s(Xa!0, Xr!1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (Xr!1 = s(Xa!0, s(Xa!0, Xr!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[52, 27, 49])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (s(Xa!0, s(Xa!0, Xr!1)) = Xr!1),
% 0.20/0.46 inference(symmetry,[status(thm)],[53])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3))) <=> s_t(Xr!1, Xq!2, Xp!3)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[54, 43, 32])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (s_t(Xr!1, Xq!2, Xp!3) <=> s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[55])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 ((~s_t(Xr!1, Xq!2, Xp!3)) <=> (~s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ((~(s_t(Xp!3, Xq!2, Xr!1) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))))) <=> (~(s_t(Xp!3, Xq!2, Xr!1) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 ((~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))) <=> (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(60,axiom,(~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_15b')).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[61, 59])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.46 tff(65,plain,(
% 0.20/0.46 ~(s_t(Xp!3, Xq!2, Xr!1) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[64])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (~(s_t(Xp!3, Xq!2, Xr!1) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (~s_t(Xp!3, Xq!2, Xr!1)),
% 0.20/0.46 inference(or_elim,[status(thm)],[66])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (^[Xa: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(71,axiom,(![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_2')).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.47 tff(73,plain,(
% 0.20/0.47 ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.47 inference(skolemize,[status(sab)],[72])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xr!1, Xq!2, Xp!3)) | s_t(Xp!3, Xq!2, Xr!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xr!1, Xq!2, Xp!3)) | s_t(Xp!3, Xq!2, Xr!1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xr!1, Xq!2, Xp!3)) | s_t(Xp!3, Xq!2, Xr!1))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xr!1, Xq!2, Xp!3)) | s_t(Xp!3, Xq!2, Xr!1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (~s_t(Xr!1, Xq!2, Xp!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[77, 74, 67])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (~s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[78, 57])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))),
% 0.20/0.47 inference(or_elim,[status(thm)],[66])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[83, 74, 80])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (^[Xp: $i, Xq: $i, Xr: $i, Xa: $i] : refl(((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))) <=> ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))) <=> ![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))) <=> ![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(88,axiom,(![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_15a')).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.48 tff(90,plain,(
% 0.20/0.48 ![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[89])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (((~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))) | ((~s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3))) | s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3))))) <=> ((~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))) | (~s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3))) | s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 ((~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))) | ((~s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3))) | s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 ((~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))) | (~s_t(s(Xa!0, Xr!1), s(Xa!0, Xq!2), s(Xa!0, Xp!3))) | s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (s_t(s(Xa!0, s(Xa!0, Xr!1)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xp!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[94, 91, 84])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[95, 79])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------