TSTP Solution File: GEO499+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO499+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 20:36:48 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO499+1 : TPTP v8.1.0. Released v7.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 10:50:00 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(s_t_type, type, (
% 0.21/0.49 s_t: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(s_type, type, (
% 0.21/0.49 s: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_Xr_1_type, type, (
% 0.21/0.49 tptp_fun_Xr_1: $i)).
% 0.21/0.49 tff(tptp_fun_Xa_0_type, type, (
% 0.21/0.49 tptp_fun_Xa_0: $i)).
% 0.21/0.49 tff(tptp_fun_Xq_2_type, type, (
% 0.21/0.49 tptp_fun_Xq_2: $i)).
% 0.21/0.49 tff(tptp_fun_Xp_3_type, type, (
% 0.21/0.49 tptp_fun_Xp_3: $i)).
% 0.21/0.49 tff(s_m_type, type, (
% 0.21/0.49 s_m: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 (^[Xp: $i, Xa: $i] : refl(s_m(Xp, Xa, s(Xa, Xp)) <=> s_m(Xp, Xa, s(Xa, Xp)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_4a')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,(
% 0.21/0.49 ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.49 inference(skolemize,[status(sab)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (s_m(Xr!1, Xa!0, s(Xa!0, Xr!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (^[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)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 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')).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.49 tff(15,plain,(
% 0.21/0.49 ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.49 inference(skolemize,[status(sab)],[14])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (s_m(s(Xa!0, Xr!1), Xa!0, Xr!1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 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')).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.49 tff(26,plain,(
% 0.21/0.49 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[25])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (((~![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 ((~![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))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (Xr!1 = s(Xa!0, s(Xa!0, Xr!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (s(Xa!0, s(Xa!0, Xr!1)) = Xr!1),
% 0.21/0.49 inference(symmetry,[status(thm)],[31])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (s_m(Xq!2, Xa!0, s(Xa!0, Xq!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[33, 7])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (s_m(s(Xa!0, Xq!2), Xa!0, Xq!2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[37, 16, 34])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (((~![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 ((~![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))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (Xq!2 = s(Xa!0, s(Xa!0, Xq!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[41, 27, 38])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 (s(Xa!0, s(Xa!0, Xq!2)) = Xq!2),
% 0.21/0.49 inference(symmetry,[status(thm)],[42])).
% 0.21/0.49 tff(44,plain,
% 0.21/0.49 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (s_m(Xp!3, Xa!0, s(Xa!0, Xp!3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[44, 7])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (s_m(s(Xa!0, Xp!3), Xa!0, Xp!3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[48, 16, 45])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (((~![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 ((~![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))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (Xp!3 = s(Xa!0, s(Xa!0, Xp!3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[52, 27, 49])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (s(Xa!0, s(Xa!0, Xp!3)) = Xp!3),
% 0.21/0.49 inference(symmetry,[status(thm)],[53])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 (s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1))) <=> s_t(Xp!3, Xq!2, Xr!1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[54, 43, 32])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (s_t(Xp!3, Xq!2, Xr!1) <=> s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[55])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 ((~s_t(Xp!3, Xq!2, Xr!1)) <=> (~s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 ((~(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)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 ((~![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)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 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')).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[61, 59])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[64, 59])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : (s_t(Xp, Xq, Xr) | (~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.50 tff(68,plain,(
% 0.21/0.50 ~(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))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[67])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (~(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))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (~s_t(Xp!3, Xq!2, Xr!1)),
% 0.21/0.50 inference(or_elim,[status(thm)],[69])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (~s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[70, 57])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))),
% 0.21/0.50 inference(or_elim,[status(thm)],[69])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(76,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')).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.50 tff(78,plain,(
% 0.21/0.50 ![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[77])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (((~![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, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1))))) <=> ((~![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, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 ((~![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, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 ((~![Xp: $i, Xq: $i, Xr: $i, Xa: $i] : ((~s_t(Xp, Xq, Xr)) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))) | (~s_t(s(Xa!0, Xp!3), s(Xa!0, Xq!2), s(Xa!0, Xr!1))) | s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (s_t(s(Xa!0, s(Xa!0, Xp!3)), s(Xa!0, s(Xa!0, Xq!2)), s(Xa!0, s(Xa!0, Xr!1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[82, 79, 72])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[83, 71])).
% 0.21/0.50 % SZS output end Proof
%------------------------------------------------------------------------------