%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM462+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:17 PM UTC 2026
% Result : Theorem 2.62s 1.32s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 9 unt; 0 def)
% Number of atoms : 431 ( 80 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 649 ( 310 ~; 290 |; 34 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 122 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f25,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__897) ).
fof(f26,axiom,
( xm != sz00
& xl != xn
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__897_03) ).
fof(f27,conjecture,
( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
( sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f35,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f35]) ).
fof(f43,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f49,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f56]) ).
fof(f64,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f67]) ).
fof(f69,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f25]) ).
fof(f70,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f25]) ).
fof(f71,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f72,plain,
sdtlseqdt0(xl,xn),
inference(cnf_transformation,[],[f26]) ).
fof(f73,plain,
xl != xn,
inference(cnf_transformation,[],[f26]) ).
fof(f74,plain,
sz00 != xm,
inference(cnf_transformation,[],[f26]) ).
fof(f75,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(cnf_transformation,[],[f30]) ).
fof(f79,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f92,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f94,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f95,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f96,plain,
! [X0,X1] :
( aNaturalNumber0(sK0(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f98,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f101,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f102,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f107,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f109,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f97]) ).
fof(f185,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f109,f107]) ).
fof(f239,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[],[f92,f75]) ).
fof(f253,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f239,f101]) ).
fof(f254,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f253,f102]) ).
fof(f258,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f254,f71]) ).
fof(f262,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xn,xm) ),
inference(forward_subsumption_resolution,[],[f258,f69]) ).
fof(f270,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f262,f101]) ).
fof(f271,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(duplicate_literal_removal,[],[f270]) ).
fof(f273,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f271,f102]) ).
fof(f275,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f273,f71]) ).
fof(f277,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) ),
inference(forward_subsumption_resolution,[],[f275,f70]) ).
fof(f310,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) ),
inference(factoring,[],[f277]) ).
fof(f311,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) ),
inference(forward_subsumption_resolution,[],[f310,f94]) ).
fof(f341,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f311,f92]) ).
fof(f344,plain,
! [X0] :
( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f341]) ).
fof(f476,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X1) ),
inference(superposition,[],[f79,f344]) ).
fof(f480,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f476,f69]) ).
fof(f484,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f480,f74]) ).
fof(f487,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f484,f71]) ).
fof(f554,plain,
! [X0] :
( xl = xn
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f487]) ).
fof(f557,plain,
! [X0] :
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f554,f73]) ).
fof(f561,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f557,f70]) ).
fof(f566,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm)) ),
inference(resolution,[],[f561,f185]) ).
fof(f569,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f566]) ).
fof(f574,plain,
! [X0] :
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f569,f107]) ).
fof(f666,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f574,f98]) ).
fof(f711,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f666,f102]) ).
fof(f737,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f711,f102]) ).
fof(f741,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f737,f71]) ).
fof(f743,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f741,f70]) ).
fof(f873,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0(xl,X0))
| ~ sdtlseqdt0(xl,X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f743,f95]) ).
fof(f884,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0(xl,X0))
| ~ sdtlseqdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f873,f70]) ).
fof(f2025,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0(xl,xn))
| ~ sdtlseqdt0(xl,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f884,f94]) ).
fof(f2040,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0(xl,xn))
| ~ sdtlseqdt0(xl,xn)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f2025]) ).
fof(f2045,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0(xl,xn))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f2040,f72]) ).
fof(f2048,plain,
( ~ aNaturalNumber0(sK0(xl,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f2045,f69]) ).
fof(f2073,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xl,xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f2048,f96]) ).
fof(f2074,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f2073,f72]) ).
fof(f2075,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f2074,f70]) ).
fof(f2076,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[],[f2075,f69]) ).
fof(f2185,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f2076,f102]) ).
fof(f2188,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[],[f2185,f69]) ).
fof(f2189,plain,
$false,
inference(forward_subsumption_resolution,[],[f2188,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM462+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:05:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.62/1.32 % (2959174)Detected formulas, will run a generic FOF schedule.
% 2.62/1.32 % (2959181)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=401290076:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.32 % (2959182)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1818505055:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.32 % (2959180)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1017782020:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.32 % (2959183)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=942913315:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.32 % (2959185)dis-21_1_sil=8000:lcm=predicate:random_seed=2945990992:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.62/1.32 % (2959179)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3692240804:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.32 % (2959184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3985083086:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.32 % (2959183)First to succeed.
% 2.62/1.32 % (2959183)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2959174"
% 2.62/1.32 % (2959182)Instruction limit reached!
% 2.62/1.32 % (2959182)------------------------------
% 2.62/1.32 % (2959182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (2959182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (2959182)CaDiCaL version: 2.1.3
% 2.62/1.32 % (2959182)Termination reason: Instruction limit
% 2.62/1.32 % (2959182)Termination phase: Saturation
% 2.62/1.32 % (2959182)Time elapsed: 0.064 s
% 2.62/1.32 % (2959182)Peak memory usage: 89 MB
% 2.62/1.32 % (2959182)Instructions burned: 110 (million)
% 2.62/1.32 % (2959185)Instruction limit reached!
% 2.62/1.32 % (2959185)------------------------------
% 2.62/1.32 % (2959185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (2959185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (2959185)CaDiCaL version: 2.1.3
% 2.62/1.32 % (2959185)Termination reason: Instruction limit
% 2.62/1.32 % (2959185)Termination phase: Saturation
% 2.62/1.32 % (2959185)Time elapsed: 0.080 s
% 2.62/1.32 % (2959185)Peak memory usage: 90 MB
% 2.62/1.32 % (2959185)Instructions burned: 130 (million)
% 2.62/1.32 % (2959184)Instruction limit reached!
% 2.62/1.32 % (2959184)------------------------------
% 2.62/1.32 % (2959184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (2959184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (2959184)CaDiCaL version: 2.1.3
% 2.62/1.32 % (2959184)Termination reason: Instruction limit
% 2.62/1.32 % (2959184)Termination phase: Saturation
% 2.62/1.32 % (2959184)Time elapsed: 0.090 s
% 2.62/1.32 % (2959184)Peak memory usage: 90 MB
% 2.62/1.32 % (2959184)Instructions burned: 140 (million)
% 2.62/1.32 % (2959193)lrs+10_1_sil=8000:sp=occurrence:random_seed=4286189406:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.62/1.32 % (2959195)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2982432551:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.62/1.32 % (2959194)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1051886066:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.62/1.32 % (2959183)Refutation found. Thanks to Tanya!
% 2.62/1.32 % SZS status Theorem for theBenchmark
% 2.62/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.96/1.52 % (2959183)------------------------------
% 3.96/1.52 % (2959183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.52 % (2959183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.52 % (2959183)CaDiCaL version: 2.1.3
% 3.96/1.52 % (2959183)Termination reason: Refutation
% 3.96/1.52 % (2959183)Time elapsed: 0.040 s
% 3.96/1.52 % (2959183)Peak memory usage: 88 MB
% 3.96/1.52 % (2959183)Instructions burned: 65 (million)
% 3.96/1.52 % (2959183)------------------------------
% 3.96/1.52 % (2959183)------------------------------
% 3.96/1.52 % (2959174)Success in time 0.469 s
% 3.96/1.52 % Vampire exiting
%------------------------------------------------------------------------------