TSTP Solution File: GEO498+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.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 : Wed Aug 31 10:40:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(s_m_type, type, (
% 0.19/0.44 s_m: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_Xp_2_type, type, (
% 0.19/0.44 tptp_fun_Xp_2: $i)).
% 0.19/0.44 tff(tptp_fun_Xa_3_type, type, (
% 0.19/0.44 tptp_fun_Xa_3: $i)).
% 0.19/0.44 tff(tptp_fun_Xr_1_type, type, (
% 0.19/0.44 tptp_fun_Xr_1: $i)).
% 0.19/0.44 tff(s_type, type, (
% 0.19/0.44 s: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_Xq_0_type, type, (
% 0.19/0.44 tptp_fun_Xq_0: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((~((Xp!2 = Xq!0) | (~(s(Xa!3, Xq!0) = Xr!1)) | (~(s(Xa!3, Xp!2) = Xr!1)))) <=> (~((Xp!2 = Xq!0) | (~(s(Xa!3, Xq!0) = Xr!1)) | (~(s(Xa!3, Xp!2) = Xr!1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))) <=> (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : (((~(s(Xa, Xp) = Xr)) | (~(s(Xa, Xq) = Xr))) | (Xp = Xq))) <=> (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 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')).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (~![Xa: $i, Xp: $i, Xr: $i, Xq: $i] : ((Xp = Xq) | (~(s(Xa, Xq) = Xr)) | (~(s(Xa, Xp) = Xr)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.44 tff(12,plain,(
% 0.19/0.44 ~((Xp!2 = Xq!0) | (~(s(Xa!3, Xq!0) = Xr!1)) | (~(s(Xa!3, Xp!2) = Xr!1)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[11])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (~((Xp!2 = Xq!0) | (~(s(Xa!3, Xq!0) = Xr!1)) | (~(s(Xa!3, Xp!2) = Xr!1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (s(Xa!3, Xp!2) = Xr!1),
% 0.19/0.44 inference(or_elim,[status(thm)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (Xr!1 = s(Xa!3, Xp!2)),
% 0.19/0.44 inference(symmetry,[status(thm)],[14])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (s_m(Xp!2, Xa!3, Xr!1) <=> s_m(Xp!2, Xa!3, s(Xa!3, Xp!2))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (s_m(Xp!2, Xa!3, s(Xa!3, Xp!2)) <=> s_m(Xp!2, Xa!3, Xr!1)),
% 0.19/0.44 inference(symmetry,[status(thm)],[16])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (^[Xp: $i, Xa: $i] : refl(s_m(Xp, Xa, s(Xa, Xp)) <=> s_m(Xp, Xa, s(Xa, Xp)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(21,axiom,(![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_4a')).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.44 tff(23,plain,(
% 0.19/0.44 ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.44 inference(skolemize,[status(sab)],[22])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xp!2, Xa!3, s(Xa!3, Xp!2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (s_m(Xp!2, Xa!3, s(Xa!3, Xp!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (s_m(Xp!2, Xa!3, Xr!1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (^[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)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(31,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')).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.44 tff(33,plain,(
% 0.19/0.44 ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.44 inference(skolemize,[status(sab)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xp!2, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xp!2))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xp!2, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xp!2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xp!2, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xp!2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xp!2, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xp!2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 ((~s_m(Xp!2, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xp!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (s_m(Xr!1, Xa!3, Xp!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[38, 27])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (s(Xa!3, Xq!0) = Xr!1),
% 0.19/0.44 inference(or_elim,[status(thm)],[13])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (Xr!1 = s(Xa!3, Xq!0)),
% 0.19/0.44 inference(symmetry,[status(thm)],[40])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (s_m(Xq!0, Xa!3, Xr!1) <=> s_m(Xq!0, Xa!3, s(Xa!3, Xq!0))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (s_m(Xq!0, Xa!3, s(Xa!3, Xq!0)) <=> s_m(Xq!0, Xa!3, Xr!1)),
% 0.19/0.44 inference(symmetry,[status(thm)],[42])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xq!0, Xa!3, s(Xa!3, Xq!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (s_m(Xq!0, Xa!3, s(Xa!3, Xq!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[44, 24])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (s_m(Xq!0, Xa!3, Xr!1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xq!0, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xq!0))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xq!0, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xq!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xq!0, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xq!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xq!0, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xq!0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 ((~s_m(Xq!0, Xa!3, Xr!1)) | s_m(Xr!1, Xa!3, Xq!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[49, 34])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (s_m(Xr!1, Xa!3, Xq!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[50, 46])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.45 (~(Xp!2 = Xq!0)),
% 0.19/0.45 inference(or_elim,[status(thm)],[13])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (^[Xp: $i, Xa: $i, Xr: $i, Xq: $i] : refl(((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr))) <=> ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr))) <=> ![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr))) <=> ![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (^[Xp: $i, Xa: $i, Xr: $i, Xq: $i] : trans(monotonicity(rewrite(((~s_m(Xp, Xa, Xr)) | (~s_m(Xp, Xa, Xq))) <=> ((~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))), ((((~s_m(Xp, Xa, Xr)) | (~s_m(Xp, Xa, Xq))) | (Xr = Xq)) <=> (((~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr))) | (Xr = Xq)))), rewrite((((~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr))) | (Xr = Xq)) <=> ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))), ((((~s_m(Xp, Xa, Xr)) | (~s_m(Xp, Xa, Xq))) | (Xr = Xq)) <=> ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : (((~s_m(Xp, Xa, Xr)) | (~s_m(Xp, Xa, Xq))) | (Xr = Xq)) <=> ![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.45 tff(58,axiom,(![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : (((~s_m(Xp, Xa, Xr)) | (~s_m(Xp, Xa, Xq))) | (Xr = Xq))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_4b')).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.45 tff(61,plain,(
% 0.19/0.45 ![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[60])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (((~![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))) | ((Xp!2 = Xq!0) | (~s_m(Xr!1, Xa!3, Xq!0)) | (~s_m(Xr!1, Xa!3, Xp!2)))) <=> ((~![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))) | (Xp!2 = Xq!0) | (~s_m(Xr!1, Xa!3, Xq!0)) | (~s_m(Xr!1, Xa!3, Xp!2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 ((~![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))) | ((Xp!2 = Xq!0) | (~s_m(Xr!1, Xa!3, Xq!0)) | (~s_m(Xr!1, Xa!3, Xp!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 ((~![Xp: $i, Xa: $i, Xr: $i, Xq: $i] : ((Xr = Xq) | (~s_m(Xp, Xa, Xq)) | (~s_m(Xp, Xa, Xr)))) | (Xp!2 = Xq!0) | (~s_m(Xr!1, Xa!3, Xq!0)) | (~s_m(Xr!1, Xa!3, Xp!2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[65, 62, 52, 51, 39])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------