TSTP Solution File: COM135+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM135+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 : 600s
% DateTime : Fri Jul 15 01:44:43 EDT 2022
% Result : Theorem 8.13s 8.40s
% Output : Refutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of clauses : 69 ( 28 unt; 12 nHn; 69 RR)
% Number of literals : 128 ( 0 equ; 50 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
vtcheck(skc6,skc8,skc11),
file('COM135+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(vsomeType(u),vnoType),
file('COM135+1.p',unknown),
[] ).
cnf(15,axiom,
equal(vgetSomeType(vsomeType(u)),u),
file('COM135+1.p',unknown),
[] ).
cnf(21,axiom,
~ equal(vvar(u),vapp(v,w)),
file('COM135+1.p',unknown),
[] ).
cnf(24,axiom,
equal(vsubst(u,v,vvar(u)),v),
file('COM135+1.p',unknown),
[] ).
cnf(25,axiom,
~ visFreeVar(skf55(u,v,w),u),
file('COM135+1.p',unknown),
[] ).
cnf(32,axiom,
vtcheck(vbind(skc7,skc11,skc6),vvar(skc9),skc10),
file('COM135+1.p',unknown),
[] ).
cnf(33,axiom,
~ equal(vvar(u),vabs(v,w,x)),
file('COM135+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ visFreeVar(u,vvar(v))
| equal(v,u) ),
file('COM135+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ skP7(u)
| equal(vvar(skf77(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(41,axiom,
~ vtcheck(skc6,vsubst(skc7,skc8,vvar(skc9)),skc10),
file('COM135+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ visFreeVar(u,v)
| visFreeVar(u,vapp(v,w)) ),
file('COM135+1.p',unknown),
[] ).
cnf(49,axiom,
equal(vlookup(u,vbind(u,v,w)),vsomeType(v)),
file('COM135+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ skP12(u)
| equal(vapp(skf96(u),skf97(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(60,axiom,
( equal(u,v)
| equal(vsubst(u,w,vvar(v)),vvar(v)) ),
file('COM135+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ skP8(u)
| equal(vabs(skf78(u),skf79(u),skf80(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ skP13(u,v,w)
| equal(vvar(skf101(w,x,y)),w) ),
file('COM135+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ skP13(u,v,w)
| equal(vlookup(skf101(w,u,v),v),vsomeType(u)) ),
file('COM135+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ vtcheck(vbind(u,v,w),x,y)
| visFreeVar(u,x)
| vtcheck(w,x,y) ),
file('COM135+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ vtcheck(u,v,w)
| visFreeVar(x,v)
| vtcheck(vbind(x,y,u),v,w) ),
file('COM135+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ skP9(u)
| equal(vapp(vabs(skf82(u),skf83(u),skf84(u)),skf81(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ skP10(u)
| equal(vapp(vabs(skf86(u),skf88(u),skf87(u)),skf85(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ skP11(u)
| equal(vapp(vabs(skf90(u),skf91(u),skf92(u)),skf89(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(97,axiom,
equal(vapp(vsubst(u,v,w),vsubst(u,v,x)),vsubst(u,v,vapp(w,x))),
file('COM135+1.p',unknown),
[] ).
cnf(110,axiom,
( skP12(u)
| skP11(u)
| skP10(u)
| skP9(u)
| skP8(u)
| skP7(u)
| equal(vapp(skf75(u),skf76(u)),u) ),
file('COM135+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ skP14(u,v,w)
| equal(vabs(skf104(w,u,v),skf103(v,u,w),skf105(w,u,v)),w) ),
file('COM135+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ vtcheck(u,v,w)
| equal(vapp(skf100(v,w,u),skf98(w,u,v)),v)
| skP14(u,w,v)
| skP13(w,u,v) ),
file('COM135+1.p',unknown),
[] ).
cnf(136,plain,
( visFreeVar(u,skc8)
| vtcheck(vbind(u,v,skc6),skc8,skc11) ),
inference(res,[status(thm),theory(equality)],[9,89]),
[iquote('0:Res:9.0,89.0')] ).
cnf(144,plain,
( visFreeVar(skc7,vvar(skc9))
| vtcheck(skc6,vvar(skc9),skc10) ),
inference(res,[status(thm),theory(equality)],[32,88]),
[iquote('0:Res:32.0,88.0')] ).
cnf(146,plain,
( ~ vtcheck(vbind(u,v,skc6),vsubst(skc7,skc8,vvar(skc9)),skc10)
| visFreeVar(u,vsubst(skc7,skc8,vvar(skc9))) ),
inference(res,[status(thm),theory(equality)],[88,41]),
[iquote('0:Res:88.2,41.0')] ).
cnf(178,plain,
( ~ skP7(u)
| equal(vsubst(skf77(u),v,u),v) ),
inference(spr,[status(thm),theory(equality)],[38,24]),
[iquote('0:SpR:38.1,24.0')] ).
cnf(296,plain,
~ visFreeVar(skf55(vapp(u,v),w,x),u),
inference(res,[status(thm),theory(equality)],[45,25]),
[iquote('0:Res:45.1,25.0')] ).
cnf(330,plain,
( ~ skP12(u)
| ~ equal(vvar(v),u) ),
inference(spl,[status(thm),theory(equality)],[55,21]),
[iquote('0:SpL:55.1,21.0')] ).
cnf(373,plain,
( ~ skP7(vvar(u))
| equal(skf77(vvar(u)),u)
| equal(vvar(u),v) ),
inference(spr,[status(thm),theory(equality)],[60,178]),
[iquote('0:SpR:60.1,178.1')] ).
cnf(377,plain,
( ~ vtcheck(skc6,vvar(skc9),skc10)
| equal(skc9,skc7) ),
inference(spl,[status(thm),theory(equality)],[60,41]),
[iquote('0:SpL:60.1,41.0')] ).
cnf(378,plain,
( ~ skP7(vvar(u))
| equal(skf77(vvar(u)),u) ),
inference(aed,[status(thm),theory(equality)],[14,373]),
[iquote('0:AED:14.0,373.2')] ).
cnf(381,plain,
( visFreeVar(skc7,vvar(skc9))
| equal(skc9,skc7) ),
inference(res,[status(thm),theory(equality)],[144,377]),
[iquote('0:Res:144.1,377.0')] ).
cnf(382,plain,
equal(skc9,skc7),
inference(mrr,[status(thm)],[381,35]),
[iquote('0:MRR:381.0,35.0')] ).
cnf(383,plain,
vtcheck(vbind(skc7,skc11,skc6),vvar(skc7),skc10),
inference(rew,[status(thm),theory(equality)],[382,32]),
[iquote('0:Rew:382.0,32.0')] ).
cnf(386,plain,
( ~ vtcheck(vbind(u,v,skc6),vsubst(skc7,skc8,vvar(skc7)),skc10)
| visFreeVar(u,vsubst(skc7,skc8,vvar(skc9))) ),
inference(rew,[status(thm),theory(equality)],[382,146]),
[iquote('0:Rew:382.0,146.0')] ).
cnf(394,plain,
( ~ vtcheck(vbind(u,v,skc6),skc8,skc10)
| visFreeVar(u,vsubst(skc7,skc8,vvar(skc9))) ),
inference(rew,[status(thm),theory(equality)],[24,386]),
[iquote('0:Rew:24.0,386.0')] ).
cnf(395,plain,
( ~ vtcheck(vbind(u,v,skc6),skc8,skc10)
| visFreeVar(u,vsubst(skc7,skc8,vvar(skc7))) ),
inference(rew,[status(thm),theory(equality)],[382,394]),
[iquote('0:Rew:382.0,394.1')] ).
cnf(396,plain,
( ~ vtcheck(vbind(u,v,skc6),skc8,skc10)
| visFreeVar(u,skc8) ),
inference(rew,[status(thm),theory(equality)],[24,395]),
[iquote('0:Rew:24.0,395.1')] ).
cnf(554,plain,
( ~ skP8(u)
| ~ equal(vvar(v),u) ),
inference(spl,[status(thm),theory(equality)],[72,33]),
[iquote('0:SpL:72.1,33.0')] ).
cnf(1025,plain,
( ~ skP11(u)
| ~ equal(vvar(v),u) ),
inference(spl,[status(thm),theory(equality)],[95,21]),
[iquote('0:SpL:95.1,21.0')] ).
cnf(1085,plain,
( ~ skP10(u)
| ~ equal(vvar(v),u) ),
inference(spl,[status(thm),theory(equality)],[94,21]),
[iquote('0:SpL:94.1,21.0')] ).
cnf(1151,plain,
( ~ skP9(u)
| ~ equal(vvar(v),u) ),
inference(spl,[status(thm),theory(equality)],[93,21]),
[iquote('0:SpL:93.1,21.0')] ).
cnf(1884,plain,
equal(vapp(u,vsubst(v,u,w)),vsubst(v,u,vapp(vvar(v),w))),
inference(spr,[status(thm),theory(equality)],[24,97]),
[iquote('0:SpR:24.0,97.0')] ).
cnf(2444,plain,
( ~ equal(vvar(u),v)
| skP12(v)
| skP11(v)
| skP10(v)
| skP9(v)
| skP8(v)
| skP7(v) ),
inference(spl,[status(thm),theory(equality)],[110,21]),
[iquote('0:SpL:110.6,21.0')] ).
cnf(2486,plain,
( ~ equal(vvar(u),v)
| skP7(v) ),
inference(mrr,[status(thm)],[2444,330,1025,1085,1151,554]),
[iquote('0:MRR:2444.1,2444.2,2444.3,2444.4,2444.5,330.0,1025.0,1085.0,1151.0,554.0')] ).
cnf(2539,plain,
skP7(vvar(u)),
inference(eqr,[status(thm),theory(equality)],[2486]),
[iquote('0:EqR:2486.0')] ).
cnf(2543,plain,
equal(skf77(vvar(u)),u),
inference(mrr,[status(thm)],[378,2539]),
[iquote('0:MRR:378.0,2539.0')] ).
cnf(2668,plain,
( ~ skP14(u,v,w)
| ~ equal(vvar(x),w) ),
inference(spl,[status(thm),theory(equality)],[112,33]),
[iquote('0:SpL:112.1,33.0')] ).
cnf(3201,plain,
( ~ vtcheck(u,v,w)
| ~ equal(vvar(x),v)
| skP14(u,w,v)
| skP13(w,u,v) ),
inference(spl,[status(thm),theory(equality)],[120,21]),
[iquote('0:SpL:120.1,21.0')] ).
cnf(3242,plain,
( ~ vtcheck(u,v,w)
| ~ equal(vvar(x),v)
| skP13(w,u,v) ),
inference(mrr,[status(thm)],[3201,2668]),
[iquote('0:MRR:3201.2,2668.0')] ).
cnf(8660,plain,
~ visFreeVar(skf55(vsubst(u,v,vapp(vvar(u),w)),x,y),v),
inference(spl,[status(thm),theory(equality)],[1884,296]),
[iquote('0:SpL:1884.0,296.0')] ).
cnf(9030,plain,
( ~ equal(vvar(u),vvar(skc7))
| skP13(skc10,vbind(skc7,skc11,skc6),vvar(skc7)) ),
inference(res,[status(thm),theory(equality)],[383,3242]),
[iquote('0:Res:383.0,3242.0')] ).
cnf(14369,plain,
skP13(skc10,vbind(skc7,skc11,skc6),vvar(skc7)),
inference(eqr,[status(thm),theory(equality)],[9030]),
[iquote('0:EqR:9030.0')] ).
cnf(14385,plain,
equal(vvar(skf101(vvar(skc7),u,v)),vvar(skc7)),
inference(res,[status(thm),theory(equality)],[14369,74]),
[iquote('0:Res:14369.0,74.0')] ).
cnf(14396,plain,
equal(skf101(vvar(skc7),u,v),skf77(vvar(skc7))),
inference(spr,[status(thm),theory(equality)],[14385,2543]),
[iquote('0:SpR:14385.0,2543.0')] ).
cnf(14511,plain,
equal(skf101(vvar(skc7),u,v),skc7),
inference(rew,[status(thm),theory(equality)],[2543,14396]),
[iquote('0:Rew:2543.0,14396.0')] ).
cnf(14644,plain,
( ~ skP13(u,v,vvar(skc7))
| equal(vlookup(skc7,v),vsomeType(u)) ),
inference(spr,[status(thm),theory(equality)],[14511,87]),
[iquote('0:SpR:14511.0,87.1')] ).
cnf(14867,plain,
equal(vlookup(skc7,vbind(skc7,skc11,skc6)),vsomeType(skc10)),
inference(res,[status(thm),theory(equality)],[14369,14644]),
[iquote('0:Res:14369.0,14644.0')] ).
cnf(14872,plain,
equal(vsomeType(skc11),vsomeType(skc10)),
inference(rew,[status(thm),theory(equality)],[49,14867]),
[iquote('0:Rew:49.0,14867.0')] ).
cnf(14930,plain,
equal(vgetSomeType(vsomeType(skc10)),skc11),
inference(spr,[status(thm),theory(equality)],[14872,15]),
[iquote('0:SpR:14872.0,15.0')] ).
cnf(14939,plain,
equal(skc11,skc10),
inference(rew,[status(thm),theory(equality)],[15,14930]),
[iquote('0:Rew:15.0,14930.0')] ).
cnf(14942,plain,
( visFreeVar(u,skc8)
| vtcheck(vbind(u,v,skc6),skc8,skc10) ),
inference(rew,[status(thm),theory(equality)],[14939,136]),
[iquote('0:Rew:14939.0,136.1')] ).
cnf(14983,plain,
visFreeVar(u,skc8),
inference(mrr,[status(thm)],[14942,396]),
[iquote('0:MRR:14942.1,396.0')] ).
cnf(14984,plain,
$false,
inference(unc,[status(thm)],[14983,8660]),
[iquote('0:UnC:14983.0,8660.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM135+1 : TPTP v8.1.0. Released v6.4.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n010.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 18:19:53 EDT 2022
% 0.14/0.35 % CPUTime :
% 8.13/8.40
% 8.13/8.40 SPASS V 3.9
% 8.13/8.40 SPASS beiseite: Proof found.
% 8.13/8.40 % SZS status Theorem
% 8.13/8.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.13/8.40 SPASS derived 12288 clauses, backtracked 0 clauses, performed 1 splits and kept 5484 clauses.
% 8.13/8.40 SPASS allocated 114299 KBytes.
% 8.13/8.40 SPASS spent 0:00:07.81 on the problem.
% 8.13/8.40 0:00:00.04 for the input.
% 8.13/8.40 0:00:00.28 for the FLOTTER CNF translation.
% 8.13/8.40 0:00:00.24 for inferences.
% 8.13/8.40 0:00:00.01 for the backtracking.
% 8.13/8.40 0:00:07.10 for the reduction.
% 8.13/8.40
% 8.13/8.40
% 8.13/8.40 Here is a proof with depth 8, length 69 :
% 8.13/8.40 % SZS output start Refutation
% See solution above
% 8.13/8.40 Formulae used in the proof : T_a45_subst_a45_var DIFF_a45_noType_a45_someType getSomeType0 DIFF_a45_var_a45_app subst0 subst_a45_INV gensym_a45_is_a45_fresh DIFF_a45_var_a45_abs isFreeVar0 reduce_a45_INV DIFF_a45_abs_a45_app isValue0 isValue1 isFreeVar2 lookup1 subst1 T_a45_inv T_a45_var T_a45_abs T_a45_Strong T_a45_Weak_a45_FreeVar subst2
% 8.13/8.40
%------------------------------------------------------------------------------