%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:27:04 PM UTC 2026
% Result : Theorem 0.36s 0.48s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 31 unt; 3 def)
% Number of atoms : 493 ( 33 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 785 ( 377 ~; 337 |; 68 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 413 ( 0 sgn 360 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(f12,conjecture,
? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r2(X8,X7)
& ? [X9] :
( r2(X9,X8)
& ? [X10] :
( r1(X10)
& r2(X10,X9) ) ) ) ) ) ) ) ) ) )
& ? [X11] :
( ? [X12] :
( r3(X11,X12,X0)
& ? [X13] :
( r2(X13,X12)
& ? [X14] :
( r1(X14)
& r2(X14,X13) ) ) )
& ? [X15] :
( r2(X15,X11)
& ? [X16] :
( r2(X16,X15)
& ? [X17] :
( r2(X17,X16)
& ? [X18] :
( r2(X18,X17)
& ? [X19] :
( r2(X19,X18)
& ? [X20] :
( r2(X20,X19)
& ? [X21] :
( r1(X21)
& r2(X21,X20) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sevenplustwoeqnine) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r2(X8,X7)
& ? [X9] :
( r2(X9,X8)
& ? [X10] :
( r1(X10)
& r2(X10,X9) ) ) ) ) ) ) ) ) ) )
& ? [X11] :
( ? [X12] :
( r3(X11,X12,X0)
& ? [X13] :
( r2(X13,X12)
& ? [X14] :
( r1(X14)
& r2(X14,X13) ) ) )
& ? [X15] :
( r2(X15,X11)
& ? [X16] :
( r2(X16,X15)
& ? [X17] :
( r2(X17,X16)
& ? [X18] :
( r2(X18,X17)
& ? [X19] :
( r2(X19,X18)
& ? [X20] :
( r2(X20,X19)
& ? [X21] :
( r1(X21)
& r2(X21,X20) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r2(X6,X5)
| ! [X7] :
( ~ r2(X7,X6)
| ! [X8] :
( ~ r2(X8,X7)
| ! [X9] :
( ~ r2(X9,X8)
| ! [X10] :
( ~ r1(X10)
| ~ r2(X10,X9) ) ) ) ) ) ) ) ) ) )
| ! [X11] :
( ! [X12] :
( ~ r3(X11,X12,X0)
| ! [X13] :
( ~ r2(X13,X12)
| ! [X14] :
( ~ r1(X14)
| ~ r2(X14,X13) ) ) )
| ! [X15] :
( ~ r2(X15,X11)
| ! [X16] :
( ~ r2(X16,X15)
| ! [X17] :
( ~ r2(X17,X16)
| ! [X18] :
( ~ r2(X18,X17)
| ! [X19] :
( ~ r2(X19,X18)
| ! [X20] :
( ~ r2(X20,X19)
| ! [X21] :
( ~ r1(X21)
| ~ r2(X21,X20) ) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f17,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK2(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK2(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK6(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,X1,sK7(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
fof(f21,plain,
! [X0] :
( r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0))
& sK12(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f63,plain,
! [X2,X21,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X19,X17,X15,X5,X12,X13,X20] :
( X0 != X1
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r3(X11,X12,X0)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X14,X13)
| ~ r2(X15,X11)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r2(X18,X17)
| ~ r2(X19,X18)
| ~ r2(X20,X19)
| ~ r1(X21)
| ~ r2(X21,X20) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f41,f42]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X2,X21,X3,X10,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X19,X17,X15,X5,X12,X13,X20] :
( ~ r3(X11,X12,X1)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r2(X2,X1)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X14,X13)
| ~ r2(X15,X11)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r2(X18,X17)
| ~ r2(X19,X18)
| ~ r2(X20,X19)
| ~ r1(X21)
| ~ r2(X21,X20) ),
inference(equality_resolution,[],[f63]) ).
fof(f79,definition,
( spl20_1
<=> ! [X2] : ~ r1(X2) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] : ~ r1(X2)
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f84,plain,
( $false
| ~ spl20_1 ),
inference(forward_subsumption_resolution,[],[f67,f80]) ).
fof(f85,plain,
~ spl20_1,
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f96,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f120,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f121,plain,
! [X0] : r3(X0,sK0,X0),
inference(forward_demodulation,[],[f120,f96]) ).
fof(f143,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f30,f44]) ).
fof(f196,plain,
! [X0,X1] : r3(X0,sK1(X1),sK5(X0,X1)),
inference(forward_demodulation,[],[f43,f143]) ).
fof(f197,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X19,X17,X15,X5,X12,X13] :
( ~ r2(X1,sK5(X9,X10))
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7)
| ~ r2(X0,X1)
| ~ r2(X11,sK1(X10))
| ~ r1(X12)
| ~ r2(X12,X11)
| ~ r2(X13,X9)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r2(X18,X17)
| ~ r1(X19)
| ~ r2(X19,X18) ),
inference(resolution,[],[f196,f77]) ).
fof(f204,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X17,X15,X5,X12,X13] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X1,sK7(X8,X9))
| ~ r2(X10,sK1(X9))
| ~ r1(X11)
| ~ r2(X11,X10)
| ~ r2(X12,X8)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r1(X18)
| ~ r2(X18,X17) ),
inference(resolution,[],[f197,f64]) ).
fof(f224,plain,
! [X0,X1] : sK2(X0,X1) = sK7(X0,X1),
inference(resolution,[],[f34,f40]) ).
fof(f226,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(resolution,[],[f34,f121]) ).
fof(f325,plain,
! [X0,X1] : r2(sK2(X0,X1),sK5(X0,X1)),
inference(superposition,[],[f64,f224]) ).
fof(f330,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X17,X15,X5,X12,X13] :
( ~ r2(X1,sK2(X8,X9))
| ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X10,sK1(X9))
| ~ r1(X11)
| ~ r2(X11,X10)
| ~ r2(X12,X8)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r1(X18)
| ~ r2(X18,X17) ),
inference(forward_demodulation,[],[f204,f224]) ).
fof(f348,plain,
! [X0] : r2(X0,sK5(X0,sK0)),
inference(superposition,[],[f325,f226]) ).
fof(f350,plain,
! [X0] : sK1(X0) = sK5(X0,sK0),
inference(resolution,[],[f348,f30]) ).
fof(f355,plain,
! [X0] : r3(X0,sK1(sK0),sK1(X0)),
inference(superposition,[],[f196,f350]) ).
fof(f361,plain,
! [X0] : sK1(X0) = sK2(X0,sK1(sK0)),
inference(resolution,[],[f355,f34]) ).
fof(f366,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X17,X15,X5,X12,X13] :
( ~ r2(X1,sK1(X0))
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7)
| ~ r2(X9,sK1(sK1(sK0)))
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r2(X11,X0)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r1(X17)
| ~ r2(X17,X16) ),
inference(superposition,[],[f330,f361]) ).
fof(f373,definition,
( spl20_22
<=> ! [X9,X10] :
( ~ r2(X9,sK1(sK1(sK0)))
| ~ r1(X10)
| ~ r2(X10,X9) ) ),
introduced(definition,[new_symbols(definition,[spl20_22])],[avatar_definition]) ).
fof(f374,plain,
( ! [X10,X9] :
( ~ r2(X9,sK1(sK1(sK0)))
| ~ r1(X10)
| ~ r2(X10,X9) )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f376,definition,
( spl20_23
<=> ! [X7,X2,X3,X0,X11,X1,X8,X6,X16,X14,X4,X17,X15,X5,X12,X13] :
( ~ r2(X1,sK1(X0))
| ~ r1(X17)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X0)
| ~ r1(X8)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition]) ).
fof(f377,plain,
( ! [X2,X3,X0,X11,X1,X8,X6,X16,X14,X7,X4,X17,X15,X5,X12,X13] :
( ~ r2(X1,sK1(X0))
| ~ r1(X17)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X0)
| ~ r1(X8)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1) )
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( spl20_22
| spl20_23 ),
inference(avatar_split_clause,[],[f366,f376,f373]) ).
fof(f381,plain,
( ! [X0] :
( ~ r2(X0,sK1(sK0))
| ~ r1(X0) )
| ~ spl20_22 ),
inference(resolution,[],[f374,f69]) ).
fof(f382,plain,
( ~ r1(sK0)
| ~ spl20_22 ),
inference(resolution,[],[f381,f69]) ).
fof(f383,plain,
( $false
| ~ spl20_22 ),
inference(forward_subsumption_resolution,[],[f382,f67]) ).
fof(f384,plain,
~ spl20_22,
inference(avatar_contradiction_clause,[],[f383]) ).
fof(f385,plain,
( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X14,X7)
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r1(X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X12)
| ~ r2(X12,X13)
| ~ r2(X13,X14)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f377,f69]) ).
fof(f388,plain,
( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12,X13] :
( ~ r2(X6,sK1(X7))
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r2(X5,X6)
| ~ r2(X0,X1)
| ~ r1(X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X12)
| ~ r2(X12,X13)
| ~ r2(X13,X7)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f385,f69]) ).
fof(f398,plain,
( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12] :
( ~ r2(X12,X5)
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r2(X6,X0)
| ~ r1(X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X12)
| ~ r2(X0,X1)
| ~ r1(X6) )
| ~ spl20_23 ),
inference(resolution,[],[f388,f69]) ).
fof(f401,plain,
( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(X3,sK1(X4))
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X0,X1)
| ~ r2(X5,X6)
| ~ r1(X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X4)
| ~ r2(X6,X0)
| ~ r1(X5) )
| ~ spl20_23 ),
inference(resolution,[],[f398,f69]) ).
fof(f411,plain,
( ! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(X10,X2)
| ~ r2(X1,X2)
| ~ r2(X3,X0)
| ~ r2(X4,X5)
| ~ r1(X6)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X0,X1)
| ~ r2(X5,X3)
| ~ r1(X4) )
| ~ spl20_23 ),
inference(resolution,[],[f401,f69]) ).
fof(f414,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(X0,sK1(X1))
| ~ r2(X2,X3)
| ~ r2(X4,X5)
| ~ r1(X6)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X1)
| ~ r2(X3,X0)
| ~ r2(X5,X2)
| ~ r1(X4) )
| ~ spl20_23 ),
inference(resolution,[],[f411,f69]) ).
fof(f424,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ r2(X7,X8)
| ~ r2(X2,X3)
| ~ r1(X4)
| ~ r2(X4,X5)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X0,X1)
| ~ r2(X1,X8)
| ~ r2(X3,X0)
| ~ r1(X2) )
| ~ spl20_23 ),
inference(resolution,[],[f414,f69]) ).
fof(f427,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(X7,sK1(X5))
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r2(X6,X7)
| ~ r2(X0,X1)
| ~ r2(X1,X6)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f424,f69]) ).
fof(f437,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X6,X4)
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X6)
| ~ r1(X0)
| ~ r1(X5) )
| ~ spl20_23 ),
inference(resolution,[],[f427,f69]) ).
fof(f440,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ r2(sK1(X4),X3)
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X0,X1)
| ~ r2(X5,X4)
| ~ r1(X0)
| ~ r1(X5) )
| ~ spl20_23 ),
inference(resolution,[],[f437,f69]) ).
fof(f453,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ r2(X1,sK1(sK1(X2)))
| ~ r2(X0,X1)
| ~ r2(X3,X0)
| ~ r2(X4,X2)
| ~ r1(X3)
| ~ r1(X4) )
| ~ spl20_23 ),
inference(resolution,[],[f440,f69]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X0,sK1(X1))
| ~ r2(X2,X0)
| ~ r2(X3,X1)
| ~ r1(X2)
| ~ r1(X3) )
| ~ spl20_23 ),
inference(resolution,[],[f453,f69]) ).
fof(f480,plain,
( ! [X2,X0,X1] :
( ~ r2(X2,X1)
| ~ r2(X0,X1)
| ~ r1(X0)
| ~ r1(X2) )
| ~ spl20_23 ),
inference(resolution,[],[f474,f69]) ).
fof(f483,plain,
( ! [X0,X1] :
( ~ r2(X0,sK1(X1))
| ~ r1(X0)
| ~ r1(X1) )
| ~ spl20_23 ),
inference(resolution,[],[f480,f69]) ).
fof(f493,plain,
( ! [X0] :
( ~ r1(X0)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f483,f69]) ).
fof(f495,plain,
( ! [X0] : ~ r1(X0)
| ~ spl20_23 ),
inference(duplicate_literal_removal,[],[f493]) ).
fof(f498,plain,
( spl20_1
| ~ spl20_23 ),
inference(avatar_split_clause,[],[f495,f376,f79]) ).
cnf(s35,plain,
~ spl20_1,
inference(sat_conversion,[],[f85]) ).
cnf(s241,plain,
( spl20_22
| spl20_23 ),
inference(sat_conversion,[],[f378]) ).
cnf(s249,plain,
~ spl20_22,
inference(sat_conversion,[],[f384]) ).
cnf(s336,plain,
( spl20_1
| ~ spl20_23 ),
inference(sat_conversion,[],[f498]) ).
cnf(s337,plain,
spl20_23,
inference(rat,[],[s241,s249]) ).
cnf(s338,plain,
spl20_1,
inference(rat,[],[s336,s337]) ).
cnf(s341,plain,
$false,
inference(rat,[],[s35,s338]) ).
fof(f499,plain,
$false,
inference(avatar_sat_refutation,[],[s341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.36 % Computer : n007.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 21:55:25 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.48 % (1814200)Will run a generic schedule for satisfiability detection.
% 0.36/0.48 % (1814210)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=704350923:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.48 % (1814206)% WARNING: option uhcvi not known.
% 0.36/0.48 % (1814211)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3483543155:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.48 % (1814205)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4064922540_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.48 % (1814208)dis+10_1_sil=32000:sp=arity:random_seed=823641076:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.48 % (1814207)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2527932894:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.48 % (1814209)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=566938525:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.48 % TRYING [1]
% 0.36/0.48 % (1814206)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2005824221:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.48 % TRYING [2]
% 0.36/0.48 % TRYING [3]
% 0.36/0.48 % TRYING [4]
% 0.36/0.48 % TRYING [5]
% 0.36/0.48 % TRYING [6]
% 0.36/0.48 % (1814210)Instruction limit reached!
% 0.36/0.48 % (1814210)------------------------------
% 0.36/0.48 % (1814210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (1814210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (1814210)CaDiCaL version: 2.1.3
% 0.36/0.48 % (1814210)Termination reason: Instruction limit
% 0.36/0.48 % (1814210)Termination phase: Saturation
% 0.36/0.48 % (1814210)Time elapsed: 0.028 s
% 0.36/0.48 % (1814210)Peak memory usage: 12 MB
% 0.36/0.48 % (1814210)Instructions burned: 136 (million)
% 0.36/0.48 % (1814219)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1776478627:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.36/0.48 % TRYING [1]
% 0.36/0.48 % TRYING [2]
% 0.36/0.48 % (1814208)Instruction limit reached!
% 0.36/0.48 % (1814208)------------------------------
% 0.36/0.48 % (1814208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (1814208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (1814208)CaDiCaL version: 2.1.3
% 0.36/0.48 % (1814208)Termination reason: Instruction limit
% 0.36/0.48 % (1814208)Termination phase: Saturation
% 0.36/0.48 % (1814208)Time elapsed: 0.036 s
% 0.36/0.48 % (1814208)Peak memory usage: 11 MB
% 0.36/0.48 % (1814208)Instructions burned: 104 (million)
% 0.36/0.48 % TRYING [3]
% 0.36/0.48 % TRYING [4]
% 0.36/0.48 % TRYING [7]
% 0.36/0.48 % (1814207) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1814200-1814207"...
% 0.36/0.48 % (1814209)Instruction limit reached!
% 0.36/0.48 % (1814209)------------------------------
% 0.36/0.48 % (1814209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (1814209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (1814209)CaDiCaL version: 2.1.3
% 0.36/0.48 % (1814209)Termination reason: Instruction limit
% 0.36/0.48 % (1814209)Termination phase: Saturation
% 0.36/0.48 % (1814209)Time elapsed: 0.041 s
% 0.36/0.48 % (1814209)Peak memory usage: 11 MB
% 0.36/0.48 % (1814209)Instructions burned: 118 (million)
% 0.36/0.48 % (1814207)...printing done.
% 0.36/0.48 % TRYING [5]
% 0.36/0.48 % (1814207)Refutation found. Thanks to Tanya!
% 0.36/0.48 % SZS status Theorem for theBenchmark
% 0.36/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.48 % (1814207)------------------------------
% 0.36/0.48 % (1814207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (1814207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (1814207)CaDiCaL version: 2.1.3
% 0.36/0.48 % (1814207)Termination reason: Refutation
% 0.36/0.48 % (1814207)Time elapsed: 0.041 s
% 0.36/0.48 % (1814207)Peak memory usage: 13 MB
% 0.36/0.48 % (1814207)Instructions burned: 100 (million)
% 0.36/0.48 % (1814200)Success in time 0.074 s
% 0.36/0.48 % Vampire exiting
%------------------------------------------------------------------------------