TSTP Solution File: LCL656+1.001 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : LCL656+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n026.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 : Wed Aug 31 17:49:12 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 456 ( 0 equ)
% Maximal formula atoms : 52 ( 13 avg)
% Number of connectives : 746 ( 324 ~; 258 |; 161 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 116 ( 94 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70,plain,
$false,
inference(subsumption_resolution,[],[f69,f33]) ).
fof(f33,plain,
~ p101(sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ~ p101(sK3)
& ! [X1] :
( ~ r1(sK3,X1)
| ( ( ( ( p2(X1)
| ! [X2] :
( ~ p101(X2)
| ~ p2(X2)
| ~ r1(X1,X2) ) )
& ( ~ p2(X1)
| ! [X3] :
( p2(X3)
| ~ p101(X3)
| ~ r1(X1,X3) ) ) )
| ~ p101(X1) )
& ( p100(X1)
| ~ p101(X1) )
& sP0(X1)
& ( ( ( p1(X1)
| ! [X4] :
( ~ p1(X4)
| ~ p100(X4)
| ~ r1(X1,X4) ) )
& ( ! [X5] :
( ~ r1(X1,X5)
| p1(X5)
| ~ p100(X5) )
| ~ p1(X1) ) )
| ~ p100(X1) ) ) )
& p100(sK3)
& ! [X6] :
( ~ r1(sK3,X6)
| p2(X6) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f17]) ).
fof(f17,plain,
( ? [X0] :
( ~ p101(X0)
& ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ( p2(X1)
| ! [X2] :
( ~ p101(X2)
| ~ p2(X2)
| ~ r1(X1,X2) ) )
& ( ~ p2(X1)
| ! [X3] :
( p2(X3)
| ~ p101(X3)
| ~ r1(X1,X3) ) ) )
| ~ p101(X1) )
& ( p100(X1)
| ~ p101(X1) )
& sP0(X1)
& ( ( ( p1(X1)
| ! [X4] :
( ~ p1(X4)
| ~ p100(X4)
| ~ r1(X1,X4) ) )
& ( ! [X5] :
( ~ r1(X1,X5)
| p1(X5)
| ~ p100(X5) )
| ~ p1(X1) ) )
| ~ p100(X1) ) ) )
& p100(X0)
& ! [X6] :
( ~ r1(X0,X6)
| p2(X6) ) )
=> ( ~ p101(sK3)
& ! [X1] :
( ~ r1(sK3,X1)
| ( ( ( ( p2(X1)
| ! [X2] :
( ~ p101(X2)
| ~ p2(X2)
| ~ r1(X1,X2) ) )
& ( ~ p2(X1)
| ! [X3] :
( p2(X3)
| ~ p101(X3)
| ~ r1(X1,X3) ) ) )
| ~ p101(X1) )
& ( p100(X1)
| ~ p101(X1) )
& sP0(X1)
& ( ( ( p1(X1)
| ! [X4] :
( ~ p1(X4)
| ~ p100(X4)
| ~ r1(X1,X4) ) )
& ( ! [X5] :
( ~ r1(X1,X5)
| p1(X5)
| ~ p100(X5) )
| ~ p1(X1) ) )
| ~ p100(X1) ) ) )
& p100(sK3)
& ! [X6] :
( ~ r1(sK3,X6)
| p2(X6) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0] :
( ~ p101(X0)
& ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ( p2(X1)
| ! [X2] :
( ~ p101(X2)
| ~ p2(X2)
| ~ r1(X1,X2) ) )
& ( ~ p2(X1)
| ! [X3] :
( p2(X3)
| ~ p101(X3)
| ~ r1(X1,X3) ) ) )
| ~ p101(X1) )
& ( p100(X1)
| ~ p101(X1) )
& sP0(X1)
& ( ( ( p1(X1)
| ! [X4] :
( ~ p1(X4)
| ~ p100(X4)
| ~ r1(X1,X4) ) )
& ( ! [X5] :
( ~ r1(X1,X5)
| p1(X5)
| ~ p100(X5) )
| ~ p1(X1) ) )
| ~ p100(X1) ) ) )
& p100(X0)
& ! [X6] :
( ~ r1(X0,X6)
| p2(X6) ) ),
inference(rectify,[],[f10]) ).
fof(f10,plain,
? [X0] :
( ~ p101(X0)
& ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ( p2(X1)
| ! [X6] :
( ~ p101(X6)
| ~ p2(X6)
| ~ r1(X1,X6) ) )
& ( ~ p2(X1)
| ! [X7] :
( p2(X7)
| ~ p101(X7)
| ~ r1(X1,X7) ) ) )
| ~ p101(X1) )
& ( p100(X1)
| ~ p101(X1) )
& sP0(X1)
& ( ( ( p1(X1)
| ! [X3] :
( ~ p1(X3)
| ~ p100(X3)
| ~ r1(X1,X3) ) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) ) ) )
& p100(X0)
& ! [X8] :
( ~ r1(X0,X8)
| p2(X8) ) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f9,plain,
! [X1] :
( p101(X1)
| ( ? [X5] :
( p101(X5)
& r1(X1,X5)
& ~ p2(X5) )
& ? [X4] :
( p101(X4)
& r1(X1,X4)
& p2(X4) ) )
| ~ p100(X1)
| ~ sP0(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f8,plain,
? [X0] :
( ~ p101(X0)
& ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ( p2(X1)
| ! [X6] :
( ~ p101(X6)
| ~ p2(X6)
| ~ r1(X1,X6) ) )
& ( ~ p2(X1)
| ! [X7] :
( p2(X7)
| ~ p101(X7)
| ~ r1(X1,X7) ) ) )
| ~ p101(X1) )
& ( p100(X1)
| ~ p101(X1) )
& ( p101(X1)
| ( ? [X5] :
( p101(X5)
& r1(X1,X5)
& ~ p2(X5) )
& ? [X4] :
( p101(X4)
& r1(X1,X4)
& p2(X4) ) )
| ~ p100(X1) )
& ( ( ( p1(X1)
| ! [X3] :
( ~ p1(X3)
| ~ p100(X3)
| ~ r1(X1,X3) ) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) ) ) )
& p100(X0)
& ! [X8] :
( ~ r1(X0,X8)
| p2(X8) ) ),
inference(flattening,[],[f7]) ).
fof(f7,plain,
? [X0] :
( p100(X0)
& ! [X1] :
( ( ( p100(X1)
| ~ p101(X1) )
& ( p101(X1)
| ~ p100(X1)
| ( ? [X4] :
( r1(X1,X4)
& p2(X4)
& p101(X4) )
& ? [X5] :
( r1(X1,X5)
& p101(X5)
& ~ p2(X5) ) ) )
& ( ( ( p1(X1)
| ! [X3] :
( ~ p1(X3)
| ~ p100(X3)
| ~ r1(X1,X3) ) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( ( ( p2(X1)
| ! [X6] :
( ~ p101(X6)
| ~ p2(X6)
| ~ r1(X1,X6) ) )
& ( ~ p2(X1)
| ! [X7] :
( p2(X7)
| ~ p101(X7)
| ~ r1(X1,X7) ) ) )
| ~ p101(X1) ) )
| ~ r1(X0,X1) )
& ~ p101(X0)
& ! [X8] :
( ~ r1(X0,X8)
| p2(X8) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ( p100(X0)
& ! [X1] :
( ( ( p100(X1)
| ~ p101(X1) )
& ( ~ ( ~ p101(X1)
& p100(X1) )
| ( ~ ! [X4] :
( ~ r1(X1,X4)
| ~ ( p2(X4)
& p101(X4) ) )
& ~ ! [X5] :
( ~ r1(X1,X5)
| ~ ( p101(X5)
& ~ p2(X5) ) ) ) )
& ( ( ( p1(X1)
| ! [X3] :
( ~ p1(X3)
| ~ p100(X3)
| ~ r1(X1,X3) ) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( ( ( p2(X1)
| ! [X6] :
( ~ p101(X6)
| ~ p2(X6)
| ~ r1(X1,X6) ) )
& ( ~ p2(X1)
| ! [X7] :
( p2(X7)
| ~ p101(X7)
| ~ r1(X1,X7) ) ) )
| ~ p101(X1) ) )
| ~ r1(X0,X1) )
& ~ p101(X0) )
| ~ ! [X8] :
( ~ r1(X0,X8)
| p2(X8) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ( p100(X0)
& ! [X1] :
( ( ( p100(X1)
| ~ p101(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( ~ ( ~ p101(X1)
& p100(X1) )
| ( ~ ! [X4] :
( ~ r1(X1,X4)
| ~ ( ~ p102(X4)
& p2(X4)
& p101(X4) ) )
& ~ ! [X5] :
( ~ r1(X1,X5)
| ~ ( p101(X5)
& ~ p2(X5)
& ~ p102(X5) ) ) ) )
& ( ( ( p1(X1)
| ! [X3] :
( ~ p1(X3)
| ~ p100(X3)
| ~ r1(X1,X3) ) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( ( ( p2(X1)
| ! [X6] :
( ~ p101(X6)
| ~ p2(X6)
| ~ r1(X1,X6) ) )
& ( ~ p2(X1)
| ! [X7] :
( p2(X7)
| ~ p101(X7)
| ~ r1(X1,X7) ) ) )
| ~ p101(X1) ) )
| ~ r1(X0,X1) )
& ~ p101(X0) )
| ~ ! [X8] :
( ~ r1(X0,X8)
| p2(X8) ) ),
inference(flattening,[],[f4]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ( p100(X0)
& ! [X1] :
( ( ( p100(X1)
| ~ p101(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( ~ ( ~ p101(X1)
& p100(X1) )
| ( ~ ! [X4] :
( ~ r1(X1,X4)
| ~ ( ~ p102(X4)
& p2(X4)
& p101(X4) ) )
& ~ ! [X5] :
( ~ r1(X1,X5)
| ~ ( p101(X5)
& ~ p2(X5)
& ~ p102(X5) ) ) ) )
& ( ( ( p1(X1)
| ! [X3] :
( ~ p1(X3)
| ~ p100(X3)
| ~ r1(X1,X3) ) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( ( ( p2(X1)
| ! [X6] :
( ~ p101(X6)
| ~ p2(X6)
| ~ r1(X1,X6) ) )
& ( ~ p2(X1)
| ! [X7] :
( p2(X7)
| ~ p101(X7)
| ~ r1(X1,X7) ) ) )
| ~ p101(X1) ) )
| ~ r1(X0,X1) )
& ~ p101(X0) )
| ~ ! [X8] :
( ~ r1(X0,X8)
| p2(X8) ) ),
inference(rectify,[],[f3]) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ( ~ p101(X0)
& ! [X1] :
( ( ( p100(X1)
| ~ p101(X1) )
& ( ( ( ! [X0] :
( p1(X0)
| ~ r1(X1,X0)
| ~ p100(X0) )
| ~ p1(X1) )
& ( p1(X1)
| ! [X0] :
( ~ p100(X0)
| ~ r1(X1,X0)
| ~ p1(X0) ) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( ~ ( ~ p101(X1)
& p100(X1) )
| ( ~ ! [X0] :
( ~ ( ~ p102(X0)
& p101(X0)
& p2(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( ~ p2(X0)
& ~ p102(X0)
& p101(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ p101(X1)
| ( ( p2(X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ p101(X0)
| ~ p2(X0) ) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ p101(X0) )
| ~ p2(X1) ) ) ) )
| ~ r1(X0,X1) )
& p100(X0) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f2]) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ( ~ p101(X0)
& ! [X1] :
( ( ( p100(X1)
| ~ p101(X1) )
& ( ( ( ! [X0] :
( p1(X0)
| ~ r1(X1,X0)
| ~ p100(X0) )
| ~ p1(X1) )
& ( p1(X1)
| ! [X0] :
( ~ p100(X0)
| ~ r1(X1,X0)
| ~ p1(X0) ) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( ~ ( ~ p101(X1)
& p100(X1) )
| ( ~ ! [X0] :
( ~ ( ~ p102(X0)
& p101(X0)
& p2(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( ~ p2(X0)
& ~ p102(X0)
& p101(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ p101(X1)
| ( ( p2(X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ p101(X0)
| ~ p2(X0) ) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ p101(X0) )
| ~ p2(X1) ) ) ) )
| ~ r1(X0,X1) )
& p100(X0) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f69,plain,
p101(sK3),
inference(subsumption_resolution,[],[f68,f40]) ).
fof(f40,plain,
sP0(sK3),
inference(resolution,[],[f34,f29]) ).
fof(f29,plain,
! [X1] :
( ~ r1(sK3,X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f68,plain,
( ~ sP0(sK3)
| p101(sK3) ),
inference(subsumption_resolution,[],[f67,f26]) ).
fof(f26,plain,
p100(sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f67,plain,
( ~ p100(sK3)
| ~ sP0(sK3)
| p101(sK3) ),
inference(resolution,[],[f60,f22]) ).
fof(f22,plain,
! [X0] :
( ~ p2(sK1(X0))
| ~ p100(X0)
| p101(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( p101(X0)
| ( p101(sK1(X0))
& r1(X0,sK1(X0))
& ~ p2(sK1(X0))
& p101(sK2(X0))
& r1(X0,sK2(X0))
& p2(sK2(X0)) )
| ~ p100(X0)
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f12,f14,f13]) ).
fof(f13,plain,
! [X0] :
( ? [X1] :
( p101(X1)
& r1(X0,X1)
& ~ p2(X1) )
=> ( p101(sK1(X0))
& r1(X0,sK1(X0))
& ~ p2(sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ? [X2] :
( p101(X2)
& r1(X0,X2)
& p2(X2) )
=> ( p101(sK2(X0))
& r1(X0,sK2(X0))
& p2(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
! [X0] :
( p101(X0)
| ( ? [X1] :
( p101(X1)
& r1(X0,X1)
& ~ p2(X1) )
& ? [X2] :
( p101(X2)
& r1(X0,X2)
& p2(X2) ) )
| ~ p100(X0)
| ~ sP0(X0) ),
inference(rectify,[],[f11]) ).
fof(f11,plain,
! [X1] :
( p101(X1)
| ( ? [X5] :
( p101(X5)
& r1(X1,X5)
& ~ p2(X5) )
& ? [X4] :
( p101(X4)
& r1(X1,X4)
& p2(X4) ) )
| ~ p100(X1)
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f9]) ).
fof(f60,plain,
p2(sK1(sK3)),
inference(resolution,[],[f59,f25]) ).
fof(f25,plain,
! [X6] :
( ~ r1(sK3,X6)
| p2(X6) ),
inference(cnf_transformation,[],[f18]) ).
fof(f59,plain,
r1(sK3,sK1(sK3)),
inference(subsumption_resolution,[],[f58,f26]) ).
fof(f58,plain,
( ~ p100(sK3)
| r1(sK3,sK1(sK3)) ),
inference(subsumption_resolution,[],[f56,f33]) ).
fof(f56,plain,
( p101(sK3)
| r1(sK3,sK1(sK3))
| ~ p100(sK3) ),
inference(resolution,[],[f23,f40]) ).
fof(f23,plain,
! [X0] :
( ~ sP0(X0)
| p101(X0)
| r1(X0,sK1(X0))
| ~ p100(X0) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL656+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n026.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 : Tue Aug 30 02:30:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50 % (31234)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.50 % (31234)First to succeed.
% 0.19/0.51 % (31235)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (31234)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (31234)------------------------------
% 0.19/0.51 % (31234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (31234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (31234)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (31234)Memory used [KB]: 1023
% 0.19/0.51 % (31234)Time elapsed: 0.097 s
% 0.19/0.51 % (31234)Instructions burned: 3 (million)
% 0.19/0.51 % (31234)------------------------------
% 0.19/0.51 % (31234)------------------------------
% 0.19/0.51 % (31231)Success in time 0.157 s
%------------------------------------------------------------------------------