%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE044+2 : 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 : n006.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 11:40:11 AM UTC 2026
% Result : Theorem 4.79s 1.63s
% Output : Refutation 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 18
% Syntax : Number of formulae : 141 ( 69 unt; 4 def)
% Number of atoms : 247 ( 85 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 205 ( 99 ~; 96 |; 3 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 133 !; 1 ?)
% 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(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(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
fof(f17,conjecture,
! [X0] :
( leq(star(addition(one,X0)),star(X0))
& leq(star(X0),star(addition(one,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(star(addition(one,X0)),star(X0))
& leq(star(X0),star(addition(one,X0))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] :
( ~ leq(star(addition(one,X0)),star(X0))
| ~ leq(star(X0),star(addition(one,X0))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
( ~ leq(star(addition(one,sK0)),star(sK0))
| ~ leq(star(sK0),star(addition(one,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
( ~ leq(star(addition(one,sK0)),star(sK0))
| ~ leq(star(sK0),star(addition(one,sK0))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f25,plain,
! [X2,X0,X1] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f26,plain,
! [X2,X0,X1] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f27,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f40,definition,
( spl1_1
<=> leq(star(sK0),star(addition(one,sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f42,plain,
( ~ leq(star(sK0),star(addition(one,sK0)))
| spl1_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f44,definition,
( spl1_2
<=> leq(star(addition(one,sK0)),star(sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f46,plain,
( ~ leq(star(addition(one,sK0)),star(sK0))
| spl1_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f24,f44,f40]) ).
fof(f51,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f34,f36]) ).
fof(f58,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(resolution,[],[f27,f29]) ).
fof(f59,plain,
leq(addition(one,star(one)),star(one)),
inference(superposition,[],[f27,f38]) ).
fof(f60,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(star(X0),X0))),
inference(forward_demodulation,[],[f58,f36]) ).
fof(f61,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f28,f29]) ).
fof(f63,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f61,f36]) ).
fof(f64,plain,
star(one) = addition(addition(one,star(one)),star(one)),
inference(resolution,[],[f59,f29]) ).
fof(f65,plain,
star(one) = addition(star(one),addition(one,star(one))),
inference(forward_demodulation,[],[f64,f36]) ).
fof(f66,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f35,f33]) ).
fof(f69,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f35,f36]) ).
fof(f79,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f36,f35]) ).
fof(f84,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(superposition,[],[f66,f36]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| addition(multiplication(X2,star(X1)),X0) = X0 ),
inference(resolution,[],[f25,f29]) ).
fof(f100,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(multiplication(X1,X0),one),X1) ),
inference(superposition,[],[f25,f37]) ).
fof(f101,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(one,multiplication(X1,X0)),X1) ),
inference(forward_demodulation,[],[f100,f36]) ).
fof(f118,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(multiplication(X0,X1),one),X1) ),
inference(superposition,[],[f26,f38]) ).
fof(f119,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(one,multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[],[f118,f36]) ).
fof(f121,plain,
star(one) = addition(one,star(one)),
inference(superposition,[],[f84,f65]) ).
fof(f130,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f31,f37]) ).
fof(f154,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f32,f38]) ).
fof(f196,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f35,f69]) ).
fof(f586,plain,
! [X0,X1] :
( ~ leq(addition(one,multiplication(X0,X1)),X0)
| addition(star(X1),X0) = X0 ),
inference(resolution,[],[f101,f29]) ).
fof(f592,plain,
( ~ leq(addition(one,multiplication(sK0,star(addition(one,sK0)))),star(addition(one,sK0)))
| spl1_1 ),
inference(resolution,[],[f119,f42]) ).
fof(f609,plain,
! [X0] : multiplication(one,X0) = addition(X0,multiplication(zero,X0)),
inference(superposition,[],[f130,f34]) ).
fof(f642,plain,
! [X0] : addition(X0,multiplication(zero,X0)) = X0,
inference(forward_demodulation,[],[f609,f37]) ).
fof(f713,plain,
! [X0] : multiplication(X0,star(one)) = addition(X0,multiplication(X0,star(one))),
inference(superposition,[],[f154,f121]) ).
fof(f723,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,zero)),
inference(superposition,[],[f154,f34]) ).
fof(f768,plain,
! [X0] : addition(X0,multiplication(X0,zero)) = X0,
inference(forward_demodulation,[],[f723,f38]) ).
fof(f798,plain,
zero = multiplication(zero,zero),
inference(superposition,[],[f51,f642]) ).
fof(f923,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(star(X0),X0),star(X0))),
inference(superposition,[],[f79,f60]) ).
fof(f937,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(star(X0),X0))),
inference(forward_demodulation,[],[f923,f36]) ).
fof(f944,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),addition(one,X0))),
inference(forward_demodulation,[],[f937,f154]) ).
fof(f1025,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(superposition,[],[f79,f63]) ).
fof(f1039,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f1025,f36]) ).
fof(f1046,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f1039,f130]) ).
fof(f1371,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(superposition,[],[f79,f196]) ).
fof(f1842,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(multiplication(X1,star(one)),X0) = X0 ),
inference(superposition,[],[f99,f38]) ).
fof(f1847,plain,
! [X0] :
( ~ leq(addition(zero,X0),zero)
| zero = addition(multiplication(X0,star(zero)),zero) ),
inference(superposition,[],[f99,f798]) ).
fof(f1889,plain,
! [X0] :
( ~ leq(X0,zero)
| zero = addition(multiplication(X0,star(zero)),zero) ),
inference(forward_demodulation,[],[f1847,f51]) ).
fof(f1896,plain,
! [X0] :
( zero = addition(zero,multiplication(X0,star(zero)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[],[f1889,f36]) ).
fof(f1899,plain,
! [X0] :
( ~ leq(X0,zero)
| zero = multiplication(X0,star(zero)) ),
inference(forward_demodulation,[],[f1896,f51]) ).
fof(f1900,plain,
! [X0] :
( zero = multiplication(X0,star(zero))
| zero != addition(X0,zero) ),
inference(resolution,[],[f1899,f30]) ).
fof(f1905,plain,
! [X0] :
( zero != X0
| zero = multiplication(X0,star(zero)) ),
inference(forward_demodulation,[],[f1900,f34]) ).
fof(f2199,plain,
zero = multiplication(zero,star(zero)),
inference(equality_resolution,[],[f1905]) ).
fof(f2437,plain,
star(zero) = addition(star(zero),addition(one,zero)),
inference(superposition,[],[f63,f2199]) ).
fof(f2474,plain,
star(zero) = addition(zero,addition(star(zero),one)),
inference(forward_demodulation,[],[f2437,f79]) ).
fof(f2485,plain,
star(zero) = addition(zero,addition(one,star(zero))),
inference(forward_demodulation,[],[f2474,f1371]) ).
fof(f2491,plain,
star(zero) = addition(one,star(zero)),
inference(forward_demodulation,[],[f2485,f51]) ).
fof(f3049,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f66,f944]) ).
fof(f3094,plain,
! [X0,X1] : addition(X1,star(X0)) = addition(one,addition(star(X0),X1)),
inference(superposition,[],[f79,f3049]) ).
fof(f3144,plain,
! [X0] : star(X0) = addition(multiplication(addition(one,X0),star(X0)),star(X0)),
inference(superposition,[],[f84,f1046]) ).
fof(f3155,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f3144,f36]) ).
fof(f3168,plain,
! [X0] : star(X0) = multiplication(addition(one,addition(one,X0)),star(X0)),
inference(forward_demodulation,[],[f3155,f130]) ).
fof(f3172,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f3168,f66]) ).
fof(f4213,plain,
! [X0] : star(addition(one,X0)) = multiplication(addition(one,X0),star(addition(one,X0))),
inference(superposition,[],[f3172,f66]) ).
fof(f4326,plain,
( ~ leq(one,one)
| one = addition(star(zero),one) ),
inference(superposition,[],[f586,f768]) ).
fof(f4329,plain,
( one = addition(one,star(zero))
| ~ leq(one,one) ),
inference(forward_demodulation,[],[f4326,f36]) ).
fof(f4343,plain,
( one = star(zero)
| ~ leq(one,one) ),
inference(forward_demodulation,[],[f4329,f2491]) ).
fof(f4364,definition,
( spl1_5
<=> leq(one,one) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f4365,plain,
( leq(one,one)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f4364]) ).
fof(f4366,plain,
( ~ leq(one,one)
| spl1_5 ),
inference(avatar_component_clause,[],[f4364]) ).
fof(f4368,definition,
( spl1_6
<=> one = star(zero) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f4370,plain,
( one = star(zero)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f4368]) ).
fof(f4371,plain,
( ~ spl1_5
| spl1_6 ),
inference(avatar_split_clause,[],[f4343,f4368,f4364]) ).
fof(f4442,plain,
( one != addition(one,one)
| spl1_5 ),
inference(resolution,[],[f4366,f30]) ).
fof(f4443,plain,
( $false
| spl1_5 ),
inference(forward_subsumption_resolution,[],[f4442,f33]) ).
fof(f4444,plain,
spl1_5,
inference(avatar_contradiction_clause,[],[f4443]) ).
fof(f4767,plain,
( ~ leq(star(zero),one)
| one = addition(multiplication(star(zero),star(one)),one) ),
inference(superposition,[],[f1842,f2491]) ).
fof(f4780,plain,
( ~ leq(one,one)
| one = addition(multiplication(star(zero),star(one)),one)
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4767,f4370]) ).
fof(f4804,plain,
( one = addition(multiplication(star(zero),star(one)),one)
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f4780,f4365]) ).
fof(f4810,plain,
( one = addition(one,multiplication(star(zero),star(one)))
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4804,f36]) ).
fof(f4812,plain,
( one = addition(one,multiplication(one,star(one)))
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4810,f4370]) ).
fof(f4814,plain,
( one = multiplication(one,star(one))
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4812,f713]) ).
fof(f4816,plain,
( one = star(one)
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4814,f37]) ).
fof(f4898,plain,
( ! [X0,X1] :
( leq(multiplication(one,X0),X1)
| ~ leq(addition(multiplication(one,X1),X0),X1) )
| ~ spl1_5
| ~ spl1_6 ),
inference(superposition,[],[f26,f4816]) ).
fof(f4921,plain,
( ! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(multiplication(one,X1),X0),X1) )
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4898,f37]) ).
fof(f4932,plain,
( ! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X1,X0),X1) )
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f4921,f37]) ).
fof(f7321,plain,
( ~ leq(addition(star(addition(one,sK0)),addition(one,multiplication(sK0,star(addition(one,sK0))))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(resolution,[],[f4932,f592]) ).
fof(f7342,plain,
( ~ leq(addition(one,addition(multiplication(sK0,star(addition(one,sK0))),star(addition(one,sK0)))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f7321,f79]) ).
fof(f7347,plain,
( ~ leq(addition(one,addition(star(addition(one,sK0)),multiplication(sK0,star(addition(one,sK0))))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f7342,f1371]) ).
fof(f7349,plain,
( ~ leq(addition(multiplication(sK0,star(addition(one,sK0))),star(addition(one,sK0))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f7347,f3094]) ).
fof(f7351,plain,
( ~ leq(addition(star(addition(one,sK0)),multiplication(sK0,star(addition(one,sK0)))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f7349,f36]) ).
fof(f7353,plain,
( ~ leq(multiplication(addition(one,sK0),star(addition(one,sK0))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f7351,f130]) ).
fof(f7355,plain,
( ~ leq(star(addition(one,sK0)),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_demodulation,[],[f7353,f4213]) ).
fof(f8318,plain,
( ~ leq(addition(one,multiplication(addition(one,sK0),star(addition(one,sK0)))),star(addition(one,sK0)))
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(resolution,[],[f7355,f119]) ).
fof(f8327,plain,
( $false
| spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f8318,f28]) ).
fof(f8328,plain,
( spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f8327]) ).
fof(f8331,plain,
( ~ leq(addition(one,multiplication(star(sK0),addition(one,sK0))),star(sK0))
| spl1_2 ),
inference(resolution,[],[f46,f101]) ).
fof(f8336,plain,
( ~ leq(star(sK0),star(sK0))
| spl1_2 ),
inference(forward_demodulation,[],[f8331,f944]) ).
fof(f8339,plain,
( ~ leq(addition(one,multiplication(sK0,star(sK0))),star(sK0))
| spl1_2 ),
inference(resolution,[],[f8336,f119]) ).
fof(f8348,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f8339,f28]) ).
fof(f8349,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f8348]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( ~ spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f4371]) ).
cnf(s6,plain,
spl1_5,
inference(sat_conversion,[],[f4444]) ).
cnf(s9,plain,
( spl1_1
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f8328]) ).
cnf(s12,plain,
spl1_2,
inference(sat_conversion,[],[f8349]) ).
cnf(s13,plain,
spl1_6,
inference(rat,[],[s3,s6]) ).
cnf(s14,plain,
spl1_1,
inference(rat,[],[s9,s6,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s12,s14]) ).
fof(f8350,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 13:06:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 4.79/1.63 % (2965946)Detected formulas, will run a generic FOF schedule.
% 4.79/1.63 % (2965955)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3432014562:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.79/1.63 % (2965953)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=494052898:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.79/1.63 % (2965957)dis-21_1_sil=8000:lcm=predicate:random_seed=4274126829: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)
% 4.79/1.63 % (2965954)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3441740504:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.79/1.63 % (2965952)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=2679830914:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.79/1.63 % (2965951)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=1276965898:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.79/1.63 % (2965956)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1526927068:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.79/1.63 % (2965954)Refutation not found, incomplete strategy
% 4.79/1.63 % (2965954)------------------------------
% 4.79/1.63 % (2965954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965957)Refutation not found, incomplete strategy
% 4.79/1.63 % (2965957)------------------------------
% 4.79/1.63 % (2965957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965957)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965954)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965957)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.63 % (2965957)Time elapsed: 0.002 s
% 4.79/1.63 % (2965954)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.63 % (2965954)Time elapsed: 0.002 s
% 4.79/1.63 % (2965954)Peak memory usage: 88 MB
% 4.79/1.63 % (2965957)Peak memory usage: 88 MB
% 4.79/1.63 % (2965957)Instructions burned: 1 (million)
% 4.79/1.63 % (2965955)Instruction limit reached!
% 4.79/1.63 % (2965955)------------------------------
% 4.79/1.63 % (2965955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965955)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965955)Termination reason: Instruction limit
% 4.79/1.63 % (2965955)Termination phase: Saturation
% 4.79/1.63 % (2965955)Time elapsed: 0.038 s
% 4.79/1.63 % (2965955)Peak memory usage: 89 MB
% 4.79/1.63 % (2965955)Instructions burned: 120 (million)
% 4.79/1.63 % (2965956)Instruction limit reached!
% 4.79/1.63 % (2965956)------------------------------
% 4.79/1.63 % (2965956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965956)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965956)Termination reason: Instruction limit
% 4.79/1.63 % (2965956)Termination phase: Saturation
% 4.79/1.63 % (2965956)Time elapsed: 0.082 s
% 4.79/1.63 % (2965956)Peak memory usage: 89 MB
% 4.79/1.63 % (2965956)Instructions burned: 141 (million)
% 4.79/1.63 % (2965965)lrs+10_1_sil=8000:sp=occurrence:random_seed=3557388357:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.79/1.63 % (2965965)Instruction limit reached!
% 4.79/1.63 % (2965965)------------------------------
% 4.79/1.63 % (2965965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965965)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965965)Termination reason: Instruction limit
% 4.79/1.63 % (2965965)Termination phase: Saturation
% 4.79/1.63 % (2965965)Time elapsed: 0.097 s
% 4.79/1.63 % (2965965)Peak memory usage: 91 MB
% 4.79/1.63 % (2965965)Instructions burned: 287 (million)
% 4.79/1.63 % (2965954)------------------------------
% 4.79/1.63 % (2965954)------------------------------
% 4.79/1.63 % (2965957)------------------------------
% 4.79/1.63 % (2965957)------------------------------
% 4.79/1.63 % (2965966)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1825257763:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.79/1.63 % (2965968)lrs+1011_1_sil=32000:sp=occurrence:random_seed=347403652:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.79/1.63 % (2965966)Instruction limit reached!
% 4.79/1.63 % (2965966)------------------------------
% 4.79/1.63 % (2965966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965966)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965966)Termination reason: Instruction limit
% 4.79/1.63 % (2965966)Termination phase: Saturation
% 4.79/1.63 % (2965966)Time elapsed: 0.097 s
% 4.79/1.63 % (2965966)Peak memory usage: 90 MB
% 4.79/1.63 % (2965966)Instructions burned: 158 (million)
% 4.79/1.63 % (2965971)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=832902643:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.79/1.63 % (2965970)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=122449005:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.79/1.63 % (2965971)Refutation not found, incomplete strategy
% 4.79/1.63 % (2965971)------------------------------
% 4.79/1.63 % (2965971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965971)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965971)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.63 % (2965971)Time elapsed: 0.002 s
% 4.79/1.63 % (2965971)Peak memory usage: 88 MB
% 4.79/1.63 % (2965971)Instructions burned: 1 (million)
% 4.79/1.63 % (2965968)First to succeed.
% 4.79/1.63 % (2965968)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2965946"
% 4.79/1.63 % (2965973)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3005893861:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.79/1.63 % (2965970)Instruction limit reached!
% 4.79/1.63 % (2965970)------------------------------
% 4.79/1.63 % (2965970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.63 % (2965970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.63 % (2965970)CaDiCaL version: 2.1.3
% 4.79/1.63 % (2965970)Termination reason: Instruction limit
% 4.79/1.63 % (2965970)Termination phase: Saturation
% 4.79/1.63 % (2965970)Time elapsed: 0.154 s
% 4.79/1.63 % (2965970)Peak memory usage: 91 MB
% 4.79/1.63 % (2965970)Instructions burned: 248 (million)
% 4.79/1.63 % (2965968)Refutation found. Thanks to Tanya!
% 4.79/1.63 % SZS status Theorem for theBenchmark
% 4.79/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 6.04/1.82 % (2965968)------------------------------
% 6.04/1.82 % (2965968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/1.82 % (2965968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.82 % (2965968)CaDiCaL version: 2.1.3
% 6.04/1.82 % (2965968)Termination reason: Refutation
% 6.04/1.82 % (2965968)Time elapsed: 0.101 s
% 6.04/1.82 % (2965968)Peak memory usage: 92 MB
% 6.04/1.82 % (2965968)Instructions burned: 326 (million)
% 6.04/1.82 % (2965968)------------------------------
% 6.04/1.82 % (2965968)------------------------------
% 6.04/1.82 % (2965946)Success in time 0.768 s
% 6.04/1.82 % Vampire exiting
%------------------------------------------------------------------------------