%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE034+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 11:40:09 AM UTC 2026
% Result : Theorem 11.27s 2.69s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 25
% Syntax : Number of formulae : 153 ( 89 unt; 11 def)
% Number of atoms : 271 ( 130 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 201 ( 83 ~; 75 |; 33 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 107 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f17,conjecture,
! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1,X2,X3,X4] :
( ~ leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero)
& test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2,X3,X4] :
( ~ leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero)
& test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
( ~ leq(multiplication(multiplication(multiplication(sK3,sK1),sK2),c(sK5)),zero)
& test(sK4)
& test(sK3)
& test(sK5)
& leq(multiplication(multiplication(sK3,sK1),c(sK4)),zero)
& leq(multiplication(multiplication(sK4,sK2),c(sK5)),zero) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5)],[f22]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
leq(multiplication(multiplication(sK4,sK2),c(sK5)),zero),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
leq(multiplication(multiplication(sK3,sK1),c(sK4)),zero),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
test(sK5),
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
test(sK3),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
test(sK4),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
~ leq(multiplication(multiplication(multiplication(sK3,sK1),sK2),c(sK5)),zero),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f50]) ).
fof(f60,definition,
sF6 = multiplication(sK3,sK1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f61,plain,
multiplication(sK3,sK1) = sF6,
inference(reorient_equations,[],[f60]) ).
fof(f62,definition,
sF7 = multiplication(sF6,sK2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f63,plain,
multiplication(sF6,sK2) = sF7,
inference(reorient_equations,[],[f62]) ).
fof(f64,definition,
sF8 = c(sK5),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f65,plain,
c(sK5) = sF8,
inference(reorient_equations,[],[f64]) ).
fof(f66,definition,
sF9 = multiplication(sF7,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f67,plain,
multiplication(sF7,sF8) = sF9,
inference(reorient_equations,[],[f66]) ).
fof(f68,plain,
~ leq(sF9,zero),
inference(definition_folding,[],[f58,f67,f65,f63,f61]) ).
fof(f69,definition,
sF10 = c(sK4),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f70,plain,
c(sK4) = sF10,
inference(reorient_equations,[],[f69]) ).
fof(f71,definition,
sF11 = multiplication(sF6,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f72,plain,
multiplication(sF6,sF10) = sF11,
inference(reorient_equations,[],[f71]) ).
fof(f73,plain,
leq(sF11,zero),
inference(definition_folding,[],[f54,f72,f70,f61]) ).
fof(f74,definition,
sF12 = multiplication(sK4,sK2),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f75,plain,
multiplication(sK4,sK2) = sF12,
inference(reorient_equations,[],[f74]) ).
fof(f76,definition,
sF13 = multiplication(sF12,sF8),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f77,plain,
multiplication(sF12,sF8) = sF13,
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
leq(sF13,zero),
inference(definition_folding,[],[f53,f77,f65,f75]) ).
fof(f79,plain,
zero = addition(sF11,zero),
inference(resolution,[],[f42,f73]) ).
fof(f80,plain,
zero = addition(sF13,zero),
inference(resolution,[],[f42,f78]) ).
fof(f81,plain,
zero = sF13,
inference(forward_demodulation,[],[f80,f33]) ).
fof(f82,plain,
zero = sF11,
inference(forward_demodulation,[],[f79,f33]) ).
fof(f83,plain,
! [X0] :
( ~ test(X0)
| one = addition(c(X0),X0) ),
inference(resolution,[],[f59,f46]) ).
fof(f84,plain,
( complement(sK5,sF8)
| ~ test(sK5) ),
inference(superposition,[],[f59,f65]) ).
fof(f85,plain,
( complement(sK4,sF10)
| ~ test(sK4) ),
inference(superposition,[],[f59,f70]) ).
fof(f86,plain,
complement(sK4,sF10),
inference(forward_subsumption_resolution,[],[f85,f57]) ).
fof(f87,plain,
complement(sK5,sF8),
inference(forward_subsumption_resolution,[],[f84,f55]) ).
fof(f88,plain,
leq(zero,zero),
inference(superposition,[],[f78,f81]) ).
fof(f95,plain,
! [X0] : multiplication(sF7,multiplication(sF8,X0)) = multiplication(sF9,X0),
inference(superposition,[],[f35,f67]) ).
fof(f119,plain,
! [X0] : multiplication(sF12,addition(sF8,X0)) = addition(sF13,multiplication(sF12,X0)),
inference(superposition,[],[f38,f77]) ).
fof(f128,plain,
! [X0] : multiplication(sF12,addition(X0,sF8)) = addition(multiplication(sF12,X0),sF13),
inference(superposition,[],[f38,f77]) ).
fof(f138,plain,
! [X0] : multiplication(sF12,addition(X0,sF8)) = addition(multiplication(sF12,X0),zero),
inference(forward_demodulation,[],[f128,f81]) ).
fof(f141,plain,
! [X0] : multiplication(sF12,addition(sF8,X0)) = addition(zero,multiplication(sF12,X0)),
inference(forward_demodulation,[],[f119,f81]) ).
fof(f144,plain,
! [X0] : multiplication(sF12,X0) = multiplication(sF12,addition(X0,sF8)),
inference(forward_demodulation,[],[f138,f33]) ).
fof(f150,plain,
one = addition(sF8,sK5),
inference(resolution,[],[f87,f46]) ).
fof(f151,plain,
one = addition(sF10,sK4),
inference(resolution,[],[f86,f46]) ).
fof(f206,plain,
zero = multiplication(sF8,sK5),
inference(resolution,[],[f48,f87]) ).
fof(f222,plain,
! [X0] : multiplication(sF12,X0) = multiplication(sF12,addition(sF8,X0)),
inference(superposition,[],[f144,f31]) ).
fof(f229,plain,
! [X0] : multiplication(sF12,X0) = addition(zero,multiplication(sF12,X0)),
inference(forward_demodulation,[],[f222,f141]) ).
fof(f253,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f31,f33]) ).
fof(f257,plain,
! [X0] : multiplication(addition(sK3,X0),sK1) = addition(sF6,multiplication(X0,sK1)),
inference(superposition,[],[f39,f61]) ).
fof(f265,plain,
! [X0] : multiplication(addition(sF6,X0),sK2) = addition(sF7,multiplication(X0,sK2)),
inference(superposition,[],[f39,f63]) ).
fof(f428,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f431,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f32,f38]) ).
fof(f1185,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X3,X2)),multiplication(X1,X2)) = addition(multiplication(X0,X3),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f431,f39]) ).
fof(f1366,plain,
! [X0,X1] : addition(multiplication(X0,sF8),multiplication(addition(X0,X1),sK5)) = addition(multiplication(X0,one),multiplication(X1,sK5)),
inference(superposition,[],[f1185,f150]) ).
fof(f1368,plain,
! [X0,X1] : addition(multiplication(X0,sF10),multiplication(addition(X0,X1),sK4)) = addition(multiplication(X0,one),multiplication(X1,sK4)),
inference(superposition,[],[f1185,f151]) ).
fof(f1555,plain,
! [X0,X1] : addition(multiplication(X0,sF10),multiplication(addition(X0,X1),sK4)) = addition(X0,multiplication(X1,sK4)),
inference(forward_demodulation,[],[f1368,f36]) ).
fof(f1557,plain,
! [X0,X1] : addition(multiplication(X0,sF8),multiplication(addition(X0,X1),sK5)) = addition(X0,multiplication(X1,sK5)),
inference(forward_demodulation,[],[f1366,f36]) ).
fof(f1840,plain,
multiplication(sF12,one) = addition(zero,multiplication(sF12,sK5)),
inference(superposition,[],[f141,f150]) ).
fof(f1877,plain,
multiplication(sF12,one) = multiplication(sF12,sK5),
inference(forward_demodulation,[],[f1840,f229]) ).
fof(f1889,plain,
sF12 = multiplication(sF12,sK5),
inference(forward_demodulation,[],[f1877,f36]) ).
fof(f2279,plain,
multiplication(sF7,zero) = multiplication(sF9,sK5),
inference(superposition,[],[f95,f206]) ).
fof(f2305,plain,
zero = multiplication(sF9,sK5),
inference(forward_demodulation,[],[f2279,f40]) ).
fof(f3607,plain,
one = addition(c(sK3),sK3),
inference(resolution,[],[f83,f56]) ).
fof(f3920,definition,
( spl14_21
<=> zero = sF9 ),
introduced(definition,[new_symbols(definition,[spl14_21])],[avatar_definition]) ).
fof(f3921,plain,
( zero = sF9
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f3922,plain,
( zero != sF9
| spl14_21 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f4107,definition,
( spl14_53
<=> one = addition(sK5,sF8) ),
introduced(definition,[new_symbols(definition,[spl14_53])],[avatar_definition]) ).
fof(f4108,plain,
( one = addition(sK5,sF8)
| ~ spl14_53 ),
inference(avatar_component_clause,[],[f4107]) ).
fof(f4109,plain,
( one != addition(sK5,sF8)
| spl14_53 ),
inference(avatar_component_clause,[],[f4107]) ).
fof(f5018,definition,
( spl14_61
<=> one = addition(sK3,c(sK3)) ),
introduced(definition,[new_symbols(definition,[spl14_61])],[avatar_definition]) ).
fof(f5019,plain,
( one = addition(sK3,c(sK3))
| ~ spl14_61 ),
inference(avatar_component_clause,[],[f5018]) ).
fof(f5020,plain,
( one != addition(sK3,c(sK3))
| spl14_61 ),
inference(avatar_component_clause,[],[f5018]) ).
fof(f8168,plain,
one = addition(sK3,c(sK3)),
inference(superposition,[],[f3607,f31]) ).
fof(f8218,plain,
( $false
| spl14_61 ),
inference(forward_subsumption_resolution,[],[f8168,f5020]) ).
fof(f8219,plain,
spl14_61,
inference(avatar_contradiction_clause,[],[f8218]) ).
fof(f8226,plain,
( one = addition(sK3,one)
| ~ spl14_61 ),
inference(superposition,[],[f428,f5019]) ).
fof(f8244,plain,
( multiplication(one,sK1) = addition(sF6,multiplication(one,sK1))
| ~ spl14_61 ),
inference(superposition,[],[f257,f8226]) ).
fof(f8274,plain,
( sK1 = addition(sF6,sK1)
| ~ spl14_61 ),
inference(forward_demodulation,[],[f8244,f37]) ).
fof(f8286,plain,
( addition(sF6,multiplication(sK1,sK4)) = addition(multiplication(sF6,sF10),multiplication(sK1,sK4))
| ~ spl14_61 ),
inference(superposition,[],[f1555,f8274]) ).
fof(f8294,plain,
( addition(sF6,multiplication(sK1,sK4)) = addition(sF11,multiplication(sK1,sK4))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f8286,f72]) ).
fof(f8306,plain,
( addition(sF6,multiplication(sK1,sK4)) = addition(zero,multiplication(sK1,sK4))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f8294,f82]) ).
fof(f8307,plain,
( multiplication(sK1,sK4) = addition(sF6,multiplication(sK1,sK4))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f8306,f253]) ).
fof(f8339,plain,
( multiplication(multiplication(sK1,sK4),sK2) = addition(sF7,multiplication(multiplication(sK1,sK4),sK2))
| ~ spl14_61 ),
inference(superposition,[],[f265,f8307]) ).
fof(f8370,plain,
( multiplication(sK1,multiplication(sK4,sK2)) = addition(sF7,multiplication(sK1,multiplication(sK4,sK2)))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f8339,f35]) ).
fof(f8373,plain,
( multiplication(sK1,sF12) = addition(sF7,multiplication(sK1,sF12))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f8370,f75]) ).
fof(f10900,plain,
( one != addition(sF8,sK5)
| spl14_53 ),
inference(superposition,[],[f4109,f31]) ).
fof(f10904,plain,
( $false
| spl14_53 ),
inference(forward_subsumption_resolution,[],[f10900,f150]) ).
fof(f10905,plain,
spl14_53,
inference(avatar_contradiction_clause,[],[f10904]) ).
fof(f10932,plain,
( ! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,sF8)) = addition(multiplication(X0,sK5),multiplication(addition(X0,X1),sF8))
| ~ spl14_53 ),
inference(superposition,[],[f1185,f4108]) ).
fof(f10945,plain,
( ! [X0,X1] : addition(X0,multiplication(X1,sF8)) = addition(multiplication(X0,sK5),multiplication(addition(X0,X1),sF8))
| ~ spl14_53 ),
inference(forward_demodulation,[],[f10932,f36]) ).
fof(f11345,plain,
( addition(sF7,multiplication(multiplication(sK1,sF12),sK5)) = addition(multiplication(sF7,sF8),multiplication(multiplication(sK1,sF12),sK5))
| ~ spl14_61 ),
inference(superposition,[],[f1557,f8373]) ).
fof(f11358,plain,
( addition(sF7,multiplication(sK1,multiplication(sF12,sK5))) = addition(multiplication(sF7,sF8),multiplication(sK1,multiplication(sF12,sK5)))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11345,f35]) ).
fof(f11374,plain,
( addition(sF7,multiplication(sK1,sF12)) = addition(multiplication(sF7,sF8),multiplication(sK1,sF12))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11358,f1889]) ).
fof(f11376,plain,
( addition(sF7,multiplication(sK1,sF12)) = addition(sF9,multiplication(sK1,sF12))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11374,f67]) ).
fof(f11378,plain,
( multiplication(sK1,sF12) = addition(sF9,multiplication(sK1,sF12))
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11376,f8373]) ).
fof(f11397,plain,
( addition(sF9,multiplication(multiplication(sK1,sF12),sF8)) = addition(multiplication(sF9,sK5),multiplication(multiplication(sK1,sF12),sF8))
| ~ spl14_53
| ~ spl14_61 ),
inference(superposition,[],[f10945,f11378]) ).
fof(f11401,plain,
( addition(sF9,multiplication(sK1,multiplication(sF12,sF8))) = addition(multiplication(sF9,sK5),multiplication(sK1,multiplication(sF12,sF8)))
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11397,f35]) ).
fof(f11419,plain,
( addition(sF9,multiplication(sK1,sF13)) = addition(multiplication(sF9,sK5),multiplication(sK1,sF13))
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11401,f77]) ).
fof(f11422,plain,
( addition(sF9,multiplication(sK1,zero)) = addition(multiplication(sF9,sK5),multiplication(sK1,zero))
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11419,f81]) ).
fof(f11424,plain,
( addition(sF9,zero) = addition(multiplication(sF9,sK5),zero)
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11422,f40]) ).
fof(f11425,plain,
( multiplication(sF9,sK5) = addition(sF9,zero)
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11424,f33]) ).
fof(f11426,plain,
( sF9 = multiplication(sF9,sK5)
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11425,f33]) ).
fof(f11427,plain,
( zero = sF9
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_demodulation,[],[f11426,f2305]) ).
fof(f11428,plain,
( $false
| spl14_21
| ~ spl14_53
| ~ spl14_61 ),
inference(forward_subsumption_resolution,[],[f11427,f3922]) ).
fof(f11429,plain,
( spl14_21
| ~ spl14_53
| ~ spl14_61 ),
inference(avatar_contradiction_clause,[],[f11428]) ).
fof(f11431,plain,
( ~ leq(zero,zero)
| ~ spl14_21 ),
inference(superposition,[],[f68,f3921]) ).
fof(f11442,plain,
( $false
| ~ spl14_21 ),
inference(forward_subsumption_resolution,[],[f11431,f88]) ).
fof(f11443,plain,
~ spl14_21,
inference(avatar_contradiction_clause,[],[f11442]) ).
cnf(s40,plain,
spl14_61,
inference(sat_conversion,[],[f8219]) ).
cnf(s46,plain,
spl14_53,
inference(sat_conversion,[],[f10905]) ).
cnf(s49,plain,
( spl14_21
| ~ spl14_53
| ~ spl14_61 ),
inference(sat_conversion,[],[f11429]) ).
cnf(s50,plain,
~ spl14_21,
inference(sat_conversion,[],[f11443]) ).
cnf(s51,plain,
( ~ spl14_53
| ~ spl14_61 ),
inference(rat,[],[s49,s50]) ).
cnf(s52,plain,
~ spl14_61,
inference(rat,[],[s51,s46]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s40,s52]) ).
fof(f11444,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE034+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n019.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 13:04:04 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.27/2.69 % (3076337)Detected formulas, will run a generic FOF schedule.
% 11.27/2.69 % (3076400)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1839374836:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.27/2.69 % (3076400)Refutation not found, incomplete strategy
% 11.27/2.69 % (3076400)------------------------------
% 11.27/2.69 % (3076400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076400)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076400)Termination reason: Refutation not found, incomplete strategy
% 11.27/2.69 % (3076400)Time elapsed: 0.001 s
% 11.27/2.69 % (3076400)Peak memory usage: 88 MB
% 11.27/2.69 % (3076400)Instructions burned: 1 (million)
% 11.27/2.69 % (3076398)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=4093917507:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.27/2.69 % (3076399)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=3284651626:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.27/2.69 % (3076397)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=1237787144:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.27/2.69 % (3076401)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3317629303:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.27/2.69 % (3076403)dis-21_1_sil=8000:lcm=predicate:random_seed=1306785388: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)
% 11.27/2.69 % (3076403)Refutation not found, incomplete strategy
% 11.27/2.69 % (3076403)------------------------------
% 11.27/2.69 % (3076403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076403)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076403)Termination reason: Refutation not found, incomplete strategy
% 11.27/2.69 % (3076403)Time elapsed: 0.003 s
% 11.27/2.69 % (3076403)Peak memory usage: 88 MB
% 11.27/2.69 % (3076403)Instructions burned: 2 (million)
% 11.27/2.69 % (3076401)Instruction limit reached!
% 11.27/2.69 % (3076401)------------------------------
% 11.27/2.69 % (3076401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076401)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076401)Termination reason: Instruction limit
% 11.27/2.69 % (3076401)Termination phase: Saturation
% 11.27/2.69 % (3076401)Time elapsed: 0.069 s
% 11.27/2.69 % (3076401)Peak memory usage: 88 MB
% 11.27/2.69 % (3076401)Instructions burned: 120 (million)
% 11.27/2.69 % (3076402)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3132591729:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.27/2.69 % (3076400)------------------------------
% 11.27/2.69 % (3076400)------------------------------
% 11.27/2.69 % (3076410)lrs+10_1_sil=8000:sp=occurrence:random_seed=3982092305:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.27/2.69 % (3076402)Instruction limit reached!
% 11.27/2.69 % (3076402)------------------------------
% 11.27/2.69 % (3076402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076402)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076402)Termination reason: Instruction limit
% 11.27/2.69 % (3076402)Termination phase: Saturation
% 11.27/2.69 % (3076402)Time elapsed: 0.137 s
% 11.27/2.69 % (3076402)Peak memory usage: 90 MB
% 11.27/2.69 % (3076402)Instructions burned: 139 (million)
% 11.27/2.69 % (3076412)lrs+10_1_sil=32000:urr=on:br=off:random_seed=218214185:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.27/2.69 % (3076403)------------------------------
% 11.27/2.69 % (3076403)------------------------------
% 11.27/2.69 % (3076412)Instruction limit reached!
% 11.27/2.69 % (3076412)------------------------------
% 11.27/2.69 % (3076412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076412)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076412)Termination reason: Instruction limit
% 11.27/2.69 % (3076412)Termination phase: Saturation
% 11.27/2.69 % (3076412)Time elapsed: 0.042 s
% 11.27/2.69 % (3076412)Peak memory usage: 89 MB
% 11.27/2.69 % (3076412)Instructions burned: 161 (million)
% 11.27/2.69 % (3076415)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1509399418:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 11.27/2.69 % (3076417)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3828007752:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.27/2.69 % (3076410)Instruction limit reached!
% 11.27/2.69 % (3076410)------------------------------
% 11.27/2.69 % (3076410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076410)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076410)Termination reason: Instruction limit
% 11.27/2.69 % (3076410)Termination phase: Saturation
% 11.27/2.69 % (3076410)Time elapsed: 0.179 s
% 11.27/2.69 % (3076410)Peak memory usage: 92 MB
% 11.27/2.69 % (3076410)Instructions burned: 286 (million)
% 11.27/2.69 % (3076416)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3022428005:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.27/2.69 % (3076417)Instruction limit reached!
% 11.27/2.69 % (3076417)------------------------------
% 11.27/2.69 % (3076417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076417)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076417)Termination reason: Instruction limit
% 11.27/2.69 % (3076417)Termination phase: Saturation
% 11.27/2.69 % (3076417)Time elapsed: 0.132 s
% 11.27/2.69 % (3076417)Peak memory usage: 89 MB
% 11.27/2.69 % (3076417)Instructions burned: 296 (million)
% 11.27/2.69 % (3076415)Instruction limit reached!
% 11.27/2.69 % (3076415)------------------------------
% 11.27/2.69 % (3076415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076415)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076415)Termination reason: Instruction limit
% 11.27/2.69 % (3076415)Termination phase: Saturation
% 11.27/2.69 % (3076415)Time elapsed: 0.262 s
% 11.27/2.69 % (3076415)Peak memory usage: 94 MB
% 11.27/2.69 % (3076415)Instructions burned: 325 (million)
% 11.27/2.69 % (3076428)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=274979088:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 11.27/2.69 % (3076416)Instruction limit reached!
% 11.27/2.69 % (3076416)------------------------------
% 11.27/2.69 % (3076416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076416)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076416)Termination reason: Instruction limit
% 11.27/2.69 % (3076416)Termination phase: Saturation
% 11.27/2.69 % (3076416)Time elapsed: 0.242 s
% 11.27/2.69 % (3076416)Peak memory usage: 92 MB
% 11.27/2.69 % (3076416)Instructions burned: 248 (million)
% 11.27/2.69 % (3076432)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1822864554:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 11.27/2.69 % (3076438)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2619973063:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 11.27/2.69 % (3076432)Instruction limit reached!
% 11.27/2.69 % (3076432)------------------------------
% 11.27/2.69 % (3076432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076432)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076432)Termination reason: Instruction limit
% 11.27/2.69 % (3076432)Termination phase: Saturation
% 11.27/2.69 % (3076432)Time elapsed: 0.121 s
% 11.27/2.69 % (3076432)Peak memory usage: 90 MB
% 11.27/2.69 % (3076432)Instructions burned: 114 (million)
% 11.27/2.69 % (3076442)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2668097403:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 11.27/2.69 % (3076442)Refutation not found, incomplete strategy
% 11.27/2.69 % (3076442)------------------------------
% 11.27/2.69 % (3076442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076442)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076442)Termination reason: Refutation not found, incomplete strategy
% 11.27/2.69 % (3076442)Time elapsed: 0.008 s
% 11.27/2.69 % (3076442)Peak memory usage: 89 MB
% 11.27/2.69 % (3076442)Instructions burned: 5 (million)
% 11.27/2.69 % (3076438)Instruction limit reached!
% 11.27/2.69 % (3076438)------------------------------
% 11.27/2.69 % (3076438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076438)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076438)Termination reason: Instruction limit
% 11.27/2.69 % (3076438)Termination phase: Saturation
% 11.27/2.69 % (3076438)Time elapsed: 0.091 s
% 11.27/2.69 % (3076438)Peak memory usage: 89 MB
% 11.27/2.69 % (3076438)Instructions burned: 127 (million)
% 11.27/2.69 % (3076453)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1998510264:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 11.27/2.69 % (3076449)lrs+10_1_sil=8000:sp=occurrence:random_seed=2460312055:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 11.27/2.69 % (3076453)Refutation not found, incomplete strategy
% 11.27/2.69 % (3076453)------------------------------
% 11.27/2.69 % (3076453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.27/2.69 % (3076453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.27/2.69 % (3076453)CaDiCaL version: 2.1.3
% 11.27/2.69 % (3076453)Termination reason: Refutation not found, incomplete strategy
% 11.27/2.69 % (3076453)Time elapsed: 0.004 s
% 11.27/2.69 % (3076453)Peak memory usage: 89 MB
% 11.27/2.69 % (3076453)Instructions burned: 2 (million)
% 11.27/2.69 % (3076397)First to succeed.
% 11.27/2.69 % (3076397)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3076337"
% 11.27/2.69 % (3076442)------------------------------
% 11.27/2.69 % (3076442)------------------------------
% 11.27/2.69 % (3076453)------------------------------
% 11.27/2.69 % (3076453)------------------------------
% 11.27/2.69 % (3076397)Refutation found. Thanks to Tanya!
% 11.27/2.69 % SZS status Theorem for theBenchmark
% 11.27/2.69 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/2.91 % (3076397)------------------------------
% 0.19/2.91 % (3076397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.91 % (3076397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.91 % (3076397)CaDiCaL version: 2.1.3
% 0.19/2.91 % (3076397)Termination reason: Refutation
% 0.19/2.91 % (3076397)Time elapsed: 1.375 s
% 0.19/2.91 % (3076397)Peak memory usage: 143 MB
% 0.19/2.91 % (3076397)Instructions burned: 2370 (million)
% 0.19/2.91 % (3076397)------------------------------
% 0.19/2.91 % (3076397)------------------------------
% 0.19/2.91 % (3076337)Success in time 1.806 s
% 0.19/2.91 % Vampire exiting
%------------------------------------------------------------------------------