TSTP Solution File: COM133+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM133+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 : 600s
% DateTime : Fri Jul 15 01:44:42 EDT 2022
% Result : Theorem 1.14s 1.31s
% Output : Refutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 14 unt; 12 nHn; 30 RR)
% Number of literals : 64 ( 0 equ; 24 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
vtcheck(skc7,skc9,skc13),
file('COM133+1.p',unknown),
[] ).
cnf(52,axiom,
vtcheck(vbind(skc8,skc13,skc7),vabs(skc10,skc11,veabs),skc12),
file('COM133+1.p',unknown),
[] ).
cnf(56,axiom,
~ vtcheck(skc7,vsubst(skc8,skc9,vabs(skc10,skc11,veabs)),skc12),
file('COM133+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ equal(u,v)
| ~ visFreeVar(v,vabs(u,w,x)) ),
file('COM133+1.p',unknown),
[] ).
cnf(68,axiom,
equal(vsubst(u,v,vabs(u,w,x)),vabs(u,w,x)),
file('COM133+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ vtcheck(vbind(u,v,w),x,y)
| visFreeVar(u,x)
| vtcheck(w,x,y) ),
file('COM133+1.p',unknown),
[] ).
cnf(117,axiom,
( visFreeVar(u,v)
| equal(w,u)
| equal(vsubst(w,v,vabs(u,x,y)),vabs(u,x,vsubst(w,v,y))) ),
file('COM133+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ vtcheck(u,v,w)
| ~ vtcheck(vbind(x,w,u),vabs(y,z,veabs),x1)
| vtcheck(u,vsubst(x,v,vabs(y,z,veabs)),x1)
| equal(x,y)
| visFreeVar(y,v) ),
file('COM133+1.p',unknown),
[] ).
cnf(129,axiom,
( ~ visFreeVar(u,v)
| ~ vtcheck(w,v,x)
| ~ vtcheck(vbind(y,x,w),vabs(u,z,veabs),x1)
| equal(y,u)
| vtcheck(w,vsubst(y,v,vabs(u,z,veabs)),x1) ),
file('COM133+1.p',unknown),
[] ).
cnf(139,plain,
( ~ vtcheck(u,v,w)
| ~ vtcheck(vbind(x,w,u),vabs(y,z,veabs),x1)
| visFreeVar(y,v)
| equal(x,y)
| vtcheck(u,vabs(y,z,vsubst(x,v,veabs)),x1) ),
inference(rew,[status(thm),theory(equality)],[117,128]),
[iquote('0:Rew:117.0,128.2')] ).
cnf(158,plain,
( visFreeVar(skc8,vabs(skc10,skc11,veabs))
| vtcheck(skc7,vabs(skc10,skc11,veabs),skc12) ),
inference(res,[status(thm),theory(equality)],[52,88]),
[iquote('0:Res:52.0,88.0')] ).
cnf(160,plain,
( ~ vtcheck(skc7,u,skc13)
| visFreeVar(skc10,u)
| equal(skc10,skc8)
| vtcheck(skc7,vabs(skc10,skc11,vsubst(skc8,u,veabs)),skc12) ),
inference(res,[status(thm),theory(equality)],[52,139]),
[iquote('0:Res:52.0,139.1')] ).
cnf(162,plain,
( ~ vtcheck(skc7,skc9,u)
| ~ vtcheck(vbind(skc8,u,skc7),vabs(skc10,skc11,veabs),skc12)
| ~ visFreeVar(skc10,skc9)
| equal(skc10,skc8) ),
inference(res,[status(thm),theory(equality)],[129,56]),
[iquote('0:Res:129.3,56.0')] ).
cnf(165,plain,
( vtcheck(skc7,vabs(skc10,skc11,vsubst(skc8,skc9,veabs)),skc12)
| equal(skc10,skc8)
| visFreeVar(skc10,skc9) ),
inference(res,[status(thm),theory(equality)],[9,160]),
[iquote('0:Res:9.0,160.0')] ).
cnf(169,plain,
( ~ vtcheck(skc7,skc9,skc13)
| ~ visFreeVar(skc10,skc9)
| equal(skc10,skc8) ),
inference(res,[status(thm),theory(equality)],[52,162]),
[iquote('0:Res:52.0,162.1')] ).
cnf(172,plain,
( ~ visFreeVar(skc10,skc9)
| equal(skc10,skc8) ),
inference(mrr,[status(thm)],[169,9]),
[iquote('0:MRR:169.0,9.0')] ).
cnf(173,plain,
( equal(skc10,skc8)
| vtcheck(skc7,vabs(skc10,skc11,vsubst(skc8,skc9,veabs)),skc12) ),
inference(mrr,[status(thm)],[165,172]),
[iquote('0:MRR:165.2,172.0')] ).
cnf(174,plain,
equal(skc10,skc8),
inference(spt,[spt(split,[position(s1)])],[173]),
[iquote('1:Spt:173.0')] ).
cnf(175,plain,
~ vtcheck(skc7,vsubst(skc8,skc9,vabs(skc8,skc11,veabs)),skc12),
inference(rew,[status(thm),theory(equality)],[174,56]),
[iquote('1:Rew:174.0,56.0')] ).
cnf(178,plain,
( visFreeVar(skc8,vabs(skc8,skc11,veabs))
| vtcheck(skc7,vabs(skc10,skc11,veabs),skc12) ),
inference(rew,[status(thm),theory(equality)],[174,158]),
[iquote('1:Rew:174.0,158.0')] ).
cnf(180,plain,
~ vtcheck(skc7,vabs(skc8,skc11,veabs),skc12),
inference(rew,[status(thm),theory(equality)],[68,175]),
[iquote('1:Rew:68.0,175.0')] ).
cnf(181,plain,
( visFreeVar(skc8,vabs(skc8,skc11,veabs))
| vtcheck(skc7,vabs(skc8,skc11,veabs),skc12) ),
inference(rew,[status(thm),theory(equality)],[174,178]),
[iquote('1:Rew:174.0,178.1')] ).
cnf(182,plain,
visFreeVar(skc8,vabs(skc8,skc11,veabs)),
inference(mrr,[status(thm)],[181,180]),
[iquote('1:MRR:181.1,180.0')] ).
cnf(485,plain,
~ equal(skc8,skc8),
inference(res,[status(thm),theory(equality)],[182,59]),
[iquote('1:Res:182.0,59.1')] ).
cnf(486,plain,
$false,
inference(obv,[status(thm),theory(equality)],[485]),
[iquote('1:Obv:485.0')] ).
cnf(487,plain,
~ equal(skc10,skc8),
inference(spt,[spt(split,[position(sa)])],[486,174]),
[iquote('1:Spt:486.0,173.0,174.0')] ).
cnf(488,plain,
vtcheck(skc7,vabs(skc10,skc11,vsubst(skc8,skc9,veabs)),skc12),
inference(spt,[spt(split,[position(s2)])],[173]),
[iquote('1:Spt:486.0,173.1')] ).
cnf(489,plain,
~ visFreeVar(skc10,skc9),
inference(mrr,[status(thm)],[172,487]),
[iquote('1:MRR:172.1,487.0')] ).
cnf(3133,plain,
( ~ vtcheck(skc7,vabs(skc10,skc11,vsubst(skc8,skc9,veabs)),skc12)
| visFreeVar(skc10,skc9)
| equal(skc10,skc8) ),
inference(spl,[status(thm),theory(equality)],[117,56]),
[iquote('0:SpL:117.2,56.0')] ).
cnf(3142,plain,
$false,
inference(mrr,[status(thm)],[3133,488,489,487]),
[iquote('1:MRR:3133.0,3133.1,3133.2,488.0,489.0,487.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM133+1 : TPTP v8.1.0. Released v6.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 : 600
% 0.13/0.34 % DateTime : Thu Jun 16 19:19:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.14/1.31
% 1.14/1.31 SPASS V 3.9
% 1.14/1.31 SPASS beiseite: Proof found.
% 1.14/1.31 % SZS status Theorem
% 1.14/1.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.14/1.31 SPASS derived 2357 clauses, backtracked 10 clauses, performed 2 splits and kept 1326 clauses.
% 1.14/1.31 SPASS allocated 101219 KBytes.
% 1.14/1.31 SPASS spent 0:00:00.93 on the problem.
% 1.14/1.31 0:00:00.04 for the input.
% 1.14/1.31 0:00:00.37 for the FLOTTER CNF translation.
% 1.14/1.31 0:00:00.04 for inferences.
% 1.14/1.31 0:00:00.00 for the backtracking.
% 1.14/1.31 0:00:00.44 for the reduction.
% 1.14/1.31
% 1.14/1.31
% 1.14/1.31 Here is a proof with depth 3, length 30 :
% 1.14/1.31 % SZS output start Refutation
% See solution above
% 1.14/1.31 Formulae used in the proof : T_a45_subst_a45_abs isFreeVar1 subst3 T_a45_Strong subst5 T_a45_subst_a45_abs_a45_2 T_a45_subst_a45_abs_a45_3
% 1.14/1.31
%------------------------------------------------------------------------------