TSTP Solution File: GEO462+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO462+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Tue Apr 30 11:16:35 EDT 2024
% Result : Theorem 47.27s 7.70s
% Output : Refutation 47.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 22 unt; 0 def)
% Number of atoms : 185 ( 43 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 204 ( 71 ~; 54 |; 55 &)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 103 ( 91 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f123749,plain,
$false,
inference(resolution,[],[f123748,f15685]) ).
fof(f15685,plain,
p(s(bool,t)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
p(s(bool,t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aEXISTSu_UNIQUEu_DEF) ).
fof(f123748,plain,
~ p(s(bool,t)),
inference(forward_demodulation,[],[f123747,f28317]) ).
fof(f28317,plain,
s(bool,t) = s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),empty))),
inference(resolution,[],[f23182,f16390]) ).
fof(f16390,plain,
! [X0] :
( ~ p(s(bool,X0))
| s(bool,t) = s(bool,X0) ),
inference(cnf_transformation,[],[f9307]) ).
fof(f9307,plain,
! [X0] :
( ( s(bool,X0) = s(bool,f0)
| p(s(bool,X0)) )
& ( ~ p(s(bool,X0))
| s(bool,X0) != s(bool,f0) )
& ( s(bool,X0) = s(bool,f0)
| p(s(bool,X0)) )
& ( ~ p(s(bool,X0))
| s(bool,X0) != s(bool,f0) )
& ( s(bool,t) = s(bool,X0)
| ~ p(s(bool,X0)) )
& ( p(s(bool,X0))
| s(bool,t) != s(bool,X0) )
& ( s(bool,t) = s(bool,X0)
| ~ p(s(bool,X0)) )
& ( p(s(bool,X0))
| s(bool,t) != s(bool,X0) ) ),
inference(flattening,[],[f9306]) ).
fof(f9306,plain,
! [X0] :
( ( s(bool,X0) = s(bool,f0)
| p(s(bool,X0)) )
& ( ~ p(s(bool,X0))
| s(bool,X0) != s(bool,f0) )
& ( s(bool,X0) = s(bool,f0)
| p(s(bool,X0)) )
& ( ~ p(s(bool,X0))
| s(bool,X0) != s(bool,f0) )
& ( s(bool,t) = s(bool,X0)
| ~ p(s(bool,X0)) )
& ( p(s(bool,X0))
| s(bool,t) != s(bool,X0) )
& ( s(bool,t) = s(bool,X0)
| ~ p(s(bool,X0)) )
& ( p(s(bool,X0))
| s(bool,t) != s(bool,X0) ) ),
inference(nnf_transformation,[],[f3549]) ).
fof(f3549,plain,
! [X0] :
( ( s(bool,X0) = s(bool,f0)
<=> ~ p(s(bool,X0)) )
& ( s(bool,X0) = s(bool,f0)
<=> ~ p(s(bool,X0)) )
& ( s(bool,t) = s(bool,X0)
<=> p(s(bool,X0)) )
& ( s(bool,t) = s(bool,X0)
<=> p(s(bool,X0)) ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X14] :
( ( s(bool,f0) = s(bool,X14)
<=> ~ p(s(bool,X14)) )
& ( s(bool,f0) = s(bool,X14)
<=> ~ p(s(bool,X14)) )
& ( s(bool,t) = s(bool,X14)
<=> p(s(bool,X14)) )
& ( s(bool,t) = s(bool,X14)
<=> p(s(bool,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aEQu_CLAUSES) ).
fof(f23182,plain,
p(s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),empty)))),
inference(forward_demodulation,[],[f15682,f15683]) ).
fof(f15683,plain,
s(fun(cart(real,sK467),bool),sK468) = s(fun(cart(real,sK467),bool),empty),
inference(cnf_transformation,[],[f9141]) ).
fof(f9141,plain,
( s(fun(cart(real,sK467),bool),sK468) = s(fun(cart(real,sK467),bool),empty)
& p(s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),sK468)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK467,sK468])],[f6257,f9140]) ).
fof(f9140,plain,
( ? [X0,X1] :
( s(fun(cart(real,X0),bool),X1) = s(fun(cart(real,X0),bool),empty)
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) )
=> ( s(fun(cart(real,sK467),bool),sK468) = s(fun(cart(real,sK467),bool),empty)
& p(s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),sK468)))) ) ),
introduced(choice_axiom,[]) ).
fof(f6257,plain,
? [X0,X1] :
( s(fun(cart(real,X0),bool),X1) = s(fun(cart(real,X0),bool),empty)
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) ),
inference(ennf_transformation,[],[f3301]) ).
fof(f3301,plain,
~ ! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
=> s(fun(cart(real,X0),bool),X1) != s(fun(cart(real,X0),bool),empty) ),
inference(rectify,[],[f3300]) ).
fof(f3300,negated_conjecture,
~ ! [X1364,X96] :
( p(s(bool,i(s(fun(fun(cart(real,X1364),bool),bool),subspace),s(fun(cart(real,X1364),bool),X96))))
=> s(fun(cart(real,X1364),bool),X96) != s(fun(cart(real,X1364),bool),empty) ),
inference(negated_conjecture,[],[f3299]) ).
fof(f3299,conjecture,
! [X1364,X96] :
( p(s(bool,i(s(fun(fun(cart(real,X1364),bool),bool),subspace),s(fun(cart(real,X1364),bool),X96))))
=> s(fun(cart(real,X1364),bool),X96) != s(fun(cart(real,X1364),bool),empty) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSUBSPACEu_IMPu_NONEMPTY) ).
fof(f15682,plain,
p(s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),sK468)))),
inference(cnf_transformation,[],[f9141]) ).
fof(f123747,plain,
~ p(s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),empty)))),
inference(forward_demodulation,[],[f123746,f15683]) ).
fof(f123746,plain,
~ p(s(bool,i(s(fun(fun(cart(real,sK467),bool),bool),subspace),s(fun(cart(real,sK467),bool),sK468)))),
inference(resolution,[],[f123743,f18560]) ).
fof(f18560,plain,
! [X0,X1] :
( sP142(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) ),
inference(cnf_transformation,[],[f11327]) ).
fof(f11327,plain,
! [X0,X1] :
( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
| ~ sP142(X1,X0) )
& ( sP142(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) ) ),
inference(nnf_transformation,[],[f8640]) ).
fof(f8640,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> sP142(X1,X0) ),
inference(definition_folding,[],[f7021,f8639,f8638]) ).
fof(f8638,plain,
! [X1,X0] :
( sP141(X1,X0)
<=> ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X4))),s(fun(cart(real,X0),bool),X1)))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP141])]) ).
fof(f8639,plain,
! [X1,X0] :
( sP142(X1,X0)
<=> ( ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& sP141(X1,X0)
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP142])]) ).
fof(f7021,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X4))),s(fun(cart(real,X0),bool),X1)))) )
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) ) ),
inference(flattening,[],[f7020]) ).
fof(f7020,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X4))),s(fun(cart(real,X0),bool),X1)))) )
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) ) ),
inference(ennf_transformation,[],[f4583]) ).
fof(f4583,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1))))
=> p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X4))),s(fun(cart(real,X0),bool),X1)))) )
=> p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1)))) )
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) ) ),
inference(rectify,[],[f3294]) ).
fof(f3294,axiom,
! [X1360,X96] :
( p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),subspace),s(fun(cart(real,X1360),bool),X96))))
<=> ( ! [X94,X0] :
( p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),i(s(fun(cart(real,X1360),fun(fun(cart(real,X1360),bool),bool)),in),s(cart(real,X1360),X0))),s(fun(cart(real,X1360),bool),X96))))
=> p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),i(s(fun(cart(real,X1360),fun(fun(cart(real,X1360),bool),bool)),in),s(cart(real,X1360),i(s(fun(cart(real,X1360),cart(real,X1360)),i(s(fun(real,fun(cart(real,X1360),cart(real,X1360))),r_),s(real,X94))),s(cart(real,X1360),X0))))),s(fun(cart(real,X1360),bool),X96)))) )
& ! [X0,X7] :
( ( p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),i(s(fun(cart(real,X1360),fun(fun(cart(real,X1360),bool),bool)),in),s(cart(real,X1360),X7))),s(fun(cart(real,X1360),bool),X96))))
& p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),i(s(fun(cart(real,X1360),fun(fun(cart(real,X1360),bool),bool)),in),s(cart(real,X1360),X0))),s(fun(cart(real,X1360),bool),X96)))) )
=> p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),i(s(fun(cart(real,X1360),fun(fun(cart(real,X1360),bool),bool)),in),s(cart(real,X1360),i(s(fun(cart(real,X1360),cart(real,X1360)),i(s(fun(cart(real,X1360),fun(cart(real,X1360),cart(real,X1360))),vectoru_add),s(cart(real,X1360),X0))),s(cart(real,X1360),X7))))),s(fun(cart(real,X1360),bool),X96)))) )
& p(s(bool,i(s(fun(fun(cart(real,X1360),bool),bool),i(s(fun(cart(real,X1360),fun(fun(cart(real,X1360),bool),bool)),in),s(cart(real,X1360),i(s(fun(num,cart(real,X1360)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1360),bool),X96)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',asubspace) ).
fof(f123743,plain,
~ sP142(sK468,sK467),
inference(resolution,[],[f123739,f15684]) ).
fof(f15684,plain,
~ p(s(bool,f0)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
~ p(s(bool,f0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSsrboolo_notu_falseu_isu_true) ).
fof(f123739,plain,
( p(s(bool,f0))
| ~ sP142(sK468,sK467) ),
inference(forward_demodulation,[],[f123718,f17111]) ).
fof(f17111,plain,
! [X0,X1] : s(bool,f0) = s(bool,i(s(fun(X0,bool),empty),s(X0,X1))),
inference(cnf_transformation,[],[f3788]) ).
fof(f3788,plain,
! [X0,X1] : s(bool,f0) = s(bool,i(s(fun(X0,bool),empty),s(X0,X1))),
inference(rectify,[],[f1659]) ).
fof(f1659,axiom,
! [X3,X0] : s(bool,f0) = s(bool,i(s(fun(X3,bool),empty),s(X3,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aEMPTY) ).
fof(f123718,plain,
( p(s(bool,i(s(fun(cart(real,sK467),bool),empty),s(cart(real,sK467),i(s(fun(num,cart(real,sK467)),vec),s(num,u_0))))))
| ~ sP142(sK468,sK467) ),
inference(superposition,[],[f25568,f15683]) ).
fof(f25568,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(cart(real,X1),bool),X0),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,u_0))))))
| ~ sP142(X0,X1) ),
inference(backward_demodulation,[],[f24803,f19303]) ).
fof(f19303,plain,
! [X2,X0,X1] : s(bool,i(s(fun(X0,bool),X1),s(X0,X2))) = s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X2))),s(fun(X0,bool),X1))),
inference(cnf_transformation,[],[f4786]) ).
fof(f4786,plain,
! [X0,X1,X2] : s(bool,i(s(fun(X0,bool),X1),s(X0,X2))) = s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X2))),s(fun(X0,bool),X1))),
inference(rectify,[],[f1650]) ).
fof(f1650,axiom,
! [X3,X6,X0] : s(bool,i(s(fun(X3,bool),X6),s(X3,X0))) = s(bool,i(s(fun(fun(X3,bool),bool),i(s(fun(X3,fun(fun(X3,bool),bool)),in),s(X3,X0))),s(fun(X3,bool),X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aIN) ).
fof(f24803,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,u_0))))),s(fun(cart(real,X1),bool),X0))))
| ~ sP142(X0,X1) ),
inference(forward_demodulation,[],[f18551,f16053]) ).
fof(f16053,plain,
! [X0] : s(num,X0) = s(num,i(s(fun(num,num),numeral),s(num,X0))),
inference(cnf_transformation,[],[f3329]) ).
fof(f3329,plain,
! [X0] : s(num,X0) = s(num,i(s(fun(num,num),numeral),s(num,X0))),
inference(rectify,[],[f200]) ).
fof(f200,axiom,
! [X83] : s(num,X83) = s(num,i(s(fun(num,num),numeral),s(num,X83))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNUMERAL) ).
fof(f18551,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0))))
| ~ sP142(X0,X1) ),
inference(cnf_transformation,[],[f11322]) ).
fof(f11322,plain,
! [X0,X1] :
( ( sP142(X0,X1)
| ( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,sK1661(X0,X1)))),s(cart(real,X1),sK1662(X0,X1)))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),sK1662(X0,X1)))),s(fun(cart(real,X1),bool),X0)))) )
| ~ sP141(X0,X1)
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0)))) )
& ( ( ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X4))),s(cart(real,X1),X5))))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X5))),s(fun(cart(real,X1),bool),X0)))) )
& sP141(X0,X1)
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0)))) )
| ~ sP142(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1661,sK1662])],[f11320,f11321]) ).
fof(f11321,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X2))),s(cart(real,X1),X3))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X3))),s(fun(cart(real,X1),bool),X0)))) )
=> ( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,sK1661(X0,X1)))),s(cart(real,X1),sK1662(X0,X1)))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),sK1662(X0,X1)))),s(fun(cart(real,X1),bool),X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f11320,plain,
! [X0,X1] :
( ( sP142(X0,X1)
| ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X2))),s(cart(real,X1),X3))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X3))),s(fun(cart(real,X1),bool),X0)))) )
| ~ sP141(X0,X1)
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0)))) )
& ( ( ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X4))),s(cart(real,X1),X5))))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X5))),s(fun(cart(real,X1),bool),X0)))) )
& sP141(X0,X1)
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0)))) )
| ~ sP142(X0,X1) ) ),
inference(rectify,[],[f11319]) ).
fof(f11319,plain,
! [X1,X0] :
( ( sP142(X1,X0)
| ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
| ~ sP141(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) )
& ( ( ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& sP141(X1,X0)
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) )
| ~ sP142(X1,X0) ) ),
inference(flattening,[],[f11318]) ).
fof(f11318,plain,
! [X1,X0] :
( ( sP142(X1,X0)
| ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
| ~ sP141(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) )
& ( ( ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& sP141(X1,X0)
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) )
| ~ sP142(X1,X0) ) ),
inference(nnf_transformation,[],[f8639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO462+1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n006.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 : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:32:05 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (31728)Running in auto input_syntax mode. Trying TPTP
% 0.93/1.10 % (31971)WARNING: value z3 for option sas not known
% 0.93/1.10 % (31969)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.93/1.10 % (31972)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.93/1.10 % (31970)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.93/1.10 % (31971)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.93/1.10 % (31974)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.93/1.10 % (31973)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.93/1.10 % (31975)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 46.82/7.68 % (31974)First to succeed.
% 47.27/7.70 % (31974)Refutation found. Thanks to Tanya!
% 47.27/7.70 % SZS status Theorem for theBenchmark
% 47.27/7.70 % SZS output start Proof for theBenchmark
% See solution above
% 47.27/7.70 % (31974)------------------------------
% 47.27/7.70 % (31974)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 47.27/7.70 % (31974)Termination reason: Refutation
% 47.27/7.70
% 47.27/7.70 % (31974)Memory used [KB]: 94093
% 47.27/7.70 % (31974)Time elapsed: 6.583 s
% 47.27/7.70 % (31974)Instructions burned: 21474 (million)
% 47.27/7.70 % (31974)------------------------------
% 47.27/7.70 % (31974)------------------------------
% 47.27/7.70 % (31728)Success in time 7.257 s
%------------------------------------------------------------------------------