%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE043+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 : n026.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 11.63s 2.64s
% Output : Refutation 13.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 149 ( 115 unt; 7 def)
% Number of atoms : 186 ( 113 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 38 ~; 32 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 122 !; 2 ?)
% 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(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(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(f17,conjecture,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(X0,star(X0)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(X0,star(X0)),X1)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1] : multiplication(star(X0),X1) != addition(X1,multiplication(multiplication(X0,star(X0)),X1)),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
multiplication(star(sK0),sK1) != addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f29,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
multiplication(star(sK0),sK1) != addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1)),
inference(cnf_transformation,[],[f23]) ).
fof(f42,definition,
sF2 = star(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f43,plain,
star(sK0) = sF2,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF3 = multiplication(sF2,sK1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f45,plain,
multiplication(sF2,sK1) = sF3,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF4 = multiplication(sK0,sF2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f47,plain,
multiplication(sK0,sF2) = sF4,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF5 = multiplication(sF4,sK1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f49,plain,
multiplication(sF4,sK1) = sF5,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF6 = addition(sK1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f51,plain,
addition(sK1,sF5) = sF6,
inference(reorient_equations,[],[f50]) ).
fof(f52,plain,
sF3 != sF6,
inference(definition_folding,[],[f41,f51,f49,f47,f43,f45,f43]) ).
fof(f56,plain,
! [X0] : multiplication(sF2,addition(X0,sK1)) = addition(multiplication(sF2,X0),sF3),
inference(superposition,[],[f31,f45]) ).
fof(f61,plain,
! [X0] : multiplication(sF4,X0) = multiplication(sK0,multiplication(sF2,X0)),
inference(superposition,[],[f28,f47]) ).
fof(f79,plain,
sF6 = addition(sF5,sK1),
inference(superposition,[],[f51,f24]) ).
fof(f80,plain,
! [X2,X0,X1] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(superposition,[],[f31,f24]) ).
fof(f81,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[],[f80,f31]) ).
fof(f85,plain,
! [X0] : multiplication(addition(sF2,X0),sK1) = addition(sF3,multiplication(X0,sK1)),
inference(superposition,[],[f32,f45]) ).
fof(f105,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f32,f30]) ).
fof(f106,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f32,f30]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| leq(multiplication(star(X1),X0),X2) ),
inference(superposition,[],[f39,f24]) ).
fof(f122,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f37,f35]) ).
fof(f127,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(forward_demodulation,[],[f122,f25]) ).
fof(f128,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[],[f127,f105]) ).
fof(f138,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(superposition,[],[f31,f29]) ).
fof(f196,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f25,f31]) ).
fof(f198,plain,
! [X0] : addition(sK1,addition(sF5,X0)) = addition(sF6,X0),
inference(superposition,[],[f25,f51]) ).
fof(f239,plain,
multiplication(addition(one,sK0),sF2) = addition(sF2,sF4),
inference(superposition,[],[f106,f47]) ).
fof(f270,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(resolution,[],[f38,f35]) ).
fof(f275,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(star(X0),X0),star(X0))),
inference(forward_demodulation,[],[f270,f25]) ).
fof(f276,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[],[f275,f138]) ).
fof(f328,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,[],[f196,f32]) ).
fof(f525,plain,
multiplication(addition(sF2,sF4),sK1) = addition(sF3,sF5),
inference(superposition,[],[f85,f49]) ).
fof(f527,plain,
multiplication(addition(sF2,one),sK1) = addition(sF3,sK1),
inference(superposition,[],[f85,f30]) ).
fof(f570,plain,
multiplication(sF4,sK1) = multiplication(sK0,sF3),
inference(superposition,[],[f61,f45]) ).
fof(f590,plain,
sF5 = multiplication(sK0,sF3),
inference(forward_demodulation,[],[f570,f49]) ).
fof(f598,plain,
! [X0] : multiplication(sK0,addition(sF3,X0)) = addition(sF5,multiplication(sK0,X0)),
inference(superposition,[],[f31,f590]) ).
fof(f602,plain,
! [X0] :
( ~ leq(addition(sF5,X0),sF3)
| leq(multiplication(star(sK0),X0),sF3) ),
inference(superposition,[],[f39,f590]) ).
fof(f609,plain,
! [X0] :
( ~ leq(addition(sF5,X0),sF3)
| leq(multiplication(sF2,X0),sF3) ),
inference(forward_demodulation,[],[f602,f43]) ).
fof(f620,definition,
( spl7_5
<=> leq(sF6,sF3) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f621,plain,
( leq(sF6,sF3)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f622,plain,
( ~ leq(sF6,sF3)
| spl7_5 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f666,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f25,f27]) ).
fof(f667,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f36,f27]) ).
fof(f669,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))),
inference(superposition,[],[f25,f27]) ).
fof(f676,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f667]) ).
fof(f712,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f666,f276]) ).
fof(f718,plain,
sF6 = addition(sF5,sF6),
inference(superposition,[],[f666,f79]) ).
fof(f781,plain,
sF2 = addition(one,sF2),
inference(superposition,[],[f712,f43]) ).
fof(f784,plain,
! [X2,X0,X1] : addition(multiplication(X1,one),multiplication(addition(X1,X2),star(X0))) = addition(multiplication(X1,star(X0)),multiplication(X2,star(X0))),
inference(superposition,[],[f328,f712]) ).
fof(f788,plain,
! [X2,X0,X1] : multiplication(addition(X1,X2),star(X0)) = addition(multiplication(X1,one),multiplication(addition(X1,X2),star(X0))),
inference(forward_demodulation,[],[f784,f32]) ).
fof(f789,plain,
! [X2,X0,X1] : multiplication(addition(X1,X2),star(X0)) = addition(X1,multiplication(addition(X1,X2),star(X0))),
inference(forward_demodulation,[],[f788,f29]) ).
fof(f790,plain,
! [X0] : addition(sF2,X0) = addition(one,addition(sF2,X0)),
inference(superposition,[],[f25,f781]) ).
fof(f1024,plain,
! [X0] : addition(sF6,X0) = addition(sK1,addition(X0,sF5)),
inference(superposition,[],[f198,f24]) ).
fof(f1042,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(superposition,[],[f128,f24]) ).
fof(f1058,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f1042,f789]) ).
fof(f1080,plain,
sF2 = multiplication(addition(one,sK0),sF2),
inference(superposition,[],[f1058,f43]) ).
fof(f1103,plain,
sF2 = addition(sF2,sF4),
inference(forward_demodulation,[],[f1080,f239]) ).
fof(f1119,plain,
! [X0] : addition(sF2,X0) = addition(sF2,addition(sF4,X0)),
inference(superposition,[],[f25,f1103]) ).
fof(f1166,plain,
! [X0] : addition(sF6,multiplication(sK0,X0)) = addition(sK1,multiplication(sK0,addition(sF3,X0))),
inference(superposition,[],[f198,f598]) ).
fof(f1321,plain,
! [X0,X1] :
( ~ leq(multiplication(addition(one,X0),X1),X1)
| leq(multiplication(star(X0),X1),X1) ),
inference(superposition,[],[f120,f106]) ).
fof(f1357,plain,
( ~ leq(sF6,sF3)
| leq(multiplication(sF2,sF6),sF3) ),
inference(superposition,[],[f609,f718]) ).
fof(f1358,plain,
! [X0] : addition(sF6,X0) = addition(sF5,addition(sF6,X0)),
inference(superposition,[],[f25,f718]) ).
fof(f1449,plain,
addition(sF5,sK1) = addition(sF5,addition(sF6,sK1)),
inference(superposition,[],[f669,f198]) ).
fof(f1494,plain,
addition(sF5,sK1) = addition(sF6,sK1),
inference(forward_demodulation,[],[f1449,f1358]) ).
fof(f1541,plain,
sF6 = addition(sF6,sK1),
inference(forward_demodulation,[],[f1494,f79]) ).
fof(f2996,plain,
multiplication(sF2,sK1) = addition(sF3,sF5),
inference(superposition,[],[f525,f1103]) ).
fof(f3007,plain,
multiplication(addition(addition(sF2,sF4),one),sK1) = addition(addition(sF3,sF5),sK1),
inference(superposition,[],[f105,f525]) ).
fof(f3008,plain,
multiplication(addition(one,addition(sF2,sF4)),sK1) = addition(sK1,addition(sF3,sF5)),
inference(superposition,[],[f106,f525]) ).
fof(f3029,plain,
addition(sF6,sF3) = multiplication(addition(one,addition(sF2,sF4)),sK1),
inference(forward_demodulation,[],[f3008,f1024]) ).
fof(f3030,plain,
multiplication(addition(addition(sF2,sF4),one),sK1) = addition(sF3,addition(sF5,sK1)),
inference(forward_demodulation,[],[f3007,f25]) ).
fof(f3041,plain,
sF3 = addition(sF3,sF5),
inference(forward_demodulation,[],[f2996,f45]) ).
fof(f3058,plain,
multiplication(addition(sF2,sF4),sK1) = addition(sF6,sF3),
inference(forward_demodulation,[],[f3029,f790]) ).
fof(f3059,plain,
addition(sF3,sF6) = multiplication(addition(addition(sF2,sF4),one),sK1),
inference(forward_demodulation,[],[f3030,f79]) ).
fof(f3074,plain,
addition(sF3,sF5) = addition(sF6,sF3),
inference(forward_demodulation,[],[f3058,f525]) ).
fof(f3075,plain,
addition(sF3,sF6) = multiplication(addition(sF2,addition(sF4,one)),sK1),
inference(forward_demodulation,[],[f3059,f25]) ).
fof(f3081,plain,
sF3 = addition(sF6,sF3),
inference(forward_demodulation,[],[f3074,f3041]) ).
fof(f3082,plain,
addition(sF3,sF6) = multiplication(addition(sF2,one),sK1),
inference(forward_demodulation,[],[f3075,f1119]) ).
fof(f3086,plain,
addition(sF3,sF6) = addition(sF3,sK1),
inference(forward_demodulation,[],[f3082,f527]) ).
fof(f3127,plain,
sF3 = addition(sF3,sF6),
inference(superposition,[],[f24,f3081]) ).
fof(f3129,plain,
( sF3 != sF3
| leq(sF6,sF3) ),
inference(superposition,[],[f36,f3081]) ).
fof(f3131,plain,
! [X0] : multiplication(X0,sF3) = multiplication(X0,addition(sF3,sF6)),
inference(superposition,[],[f81,f3081]) ).
fof(f3140,plain,
leq(sF6,sF3),
inference(trivial_inequality_removal,[],[f3129]) ).
fof(f3145,plain,
! [X0] : multiplication(X0,sF3) = multiplication(X0,addition(sF3,sK1)),
inference(forward_demodulation,[],[f3131,f3086]) ).
fof(f3147,plain,
( $false
| spl7_5 ),
inference(forward_subsumption_resolution,[],[f3140,f622]) ).
fof(f3148,plain,
spl7_5,
inference(avatar_contradiction_clause,[],[f3147]) ).
fof(f3150,plain,
sF3 = addition(sF3,sK1),
inference(forward_demodulation,[],[f3127,f3086]) ).
fof(f3154,plain,
( leq(multiplication(sF2,sF6),sF3)
| ~ spl7_5 ),
inference(forward_subsumption_resolution,[],[f1357,f621]) ).
fof(f3350,plain,
( sF3 = addition(multiplication(sF2,sF6),sF3)
| ~ spl7_5 ),
inference(resolution,[],[f3154,f35]) ).
fof(f3351,plain,
( sF3 = multiplication(sF2,addition(sF6,sK1))
| ~ spl7_5 ),
inference(forward_demodulation,[],[f3350,f56]) ).
fof(f3352,plain,
( sF3 = multiplication(sF2,sF6)
| ~ spl7_5 ),
inference(forward_demodulation,[],[f3351,f1541]) ).
fof(f3376,definition,
( spl7_34
<=> leq(sF3,sF6) ),
introduced(definition,[new_symbols(definition,[spl7_34])],[avatar_definition]) ).
fof(f3377,plain,
( leq(sF3,sF6)
| ~ spl7_34 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f3378,plain,
( ~ leq(sF3,sF6)
| spl7_34 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f4683,plain,
addition(sK1,multiplication(sK0,addition(sF3,sK1))) = addition(sF6,multiplication(sK0,sF6)),
inference(superposition,[],[f1166,f3086]) ).
fof(f4697,plain,
addition(sF6,multiplication(sK0,sK1)) = addition(sK1,multiplication(sK0,sF3)),
inference(superposition,[],[f1166,f3145]) ).
fof(f4722,plain,
addition(sK1,sF5) = addition(sF6,multiplication(sK0,sK1)),
inference(forward_demodulation,[],[f4697,f590]) ).
fof(f4729,plain,
addition(sK1,multiplication(sK0,addition(sF3,sK1))) = multiplication(addition(one,sK0),sF6),
inference(forward_demodulation,[],[f4683,f106]) ).
fof(f4739,plain,
sF6 = addition(sF6,multiplication(sK0,sK1)),
inference(forward_demodulation,[],[f4722,f51]) ).
fof(f4744,plain,
addition(sF6,multiplication(sK0,sK1)) = multiplication(addition(one,sK0),sF6),
inference(forward_demodulation,[],[f4729,f1166]) ).
fof(f4750,plain,
sF6 = multiplication(addition(one,sK0),sF6),
inference(forward_demodulation,[],[f4744,f4739]) ).
fof(f4820,plain,
( ~ leq(sF6,sF6)
| leq(multiplication(star(sK0),sF6),sF6) ),
inference(superposition,[],[f1321,f4750]) ).
fof(f4847,plain,
leq(multiplication(star(sK0),sF6),sF6),
inference(forward_subsumption_resolution,[],[f4820,f676]) ).
fof(f4852,plain,
leq(multiplication(sF2,sF6),sF6),
inference(forward_demodulation,[],[f4847,f43]) ).
fof(f4855,plain,
( leq(sF3,sF6)
| ~ spl7_5 ),
inference(forward_demodulation,[],[f4852,f3352]) ).
fof(f4856,plain,
( $false
| ~ spl7_5
| spl7_34 ),
inference(forward_subsumption_resolution,[],[f4855,f3378]) ).
fof(f4857,plain,
( ~ spl7_5
| spl7_34 ),
inference(avatar_contradiction_clause,[],[f4856]) ).
fof(f4858,plain,
( sF6 = addition(sF3,sF6)
| ~ spl7_34 ),
inference(resolution,[],[f3377,f35]) ).
fof(f4859,plain,
( sF6 = addition(sF3,sK1)
| ~ spl7_34 ),
inference(forward_demodulation,[],[f4858,f3086]) ).
fof(f4860,plain,
( sF3 = sF6
| ~ spl7_34 ),
inference(forward_demodulation,[],[f4859,f3150]) ).
fof(f4861,plain,
( $false
| ~ spl7_34 ),
inference(forward_subsumption_resolution,[],[f4860,f52]) ).
fof(f4862,plain,
~ spl7_34,
inference(avatar_contradiction_clause,[],[f4861]) ).
cnf(s22,plain,
spl7_5,
inference(sat_conversion,[],[f3148]) ).
cnf(s33,plain,
( ~ spl7_5
| spl7_34 ),
inference(sat_conversion,[],[f4857]) ).
cnf(s34,plain,
~ spl7_34,
inference(sat_conversion,[],[f4862]) ).
cnf(s35,plain,
~ spl7_5,
inference(rat,[],[s33,s34]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s22,s35]) ).
fof(f4863,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE043+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 13:07:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 11.63/2.64 % (2831686)Detected formulas, will run a generic FOF schedule.
% 11.63/2.64 % (2831730)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=1728784205:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.63/2.64 % (2831736)dis-21_1_sil=8000:lcm=predicate:random_seed=931487747: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)
% 11.63/2.64 % (2831736)Refutation not found, incomplete strategy
% 11.63/2.64 % (2831736)------------------------------
% 11.63/2.64 % (2831736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831736)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831736)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.64 % (2831736)Time elapsed: 0.003 s
% 11.63/2.64 % (2831736)Peak memory usage: 88 MB
% 11.63/2.64 % (2831736)Instructions burned: 1 (million)
% 11.63/2.64 % (2831733)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2409281985:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.63/2.64 % (2831733)Refutation not found, incomplete strategy
% 11.63/2.64 % (2831733)------------------------------
% 11.63/2.64 % (2831733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831733)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831733)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.64 % (2831733)Time elapsed: 0.002 s
% 11.63/2.64 % (2831733)Peak memory usage: 88 MB
% 11.63/2.64 % (2831731)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=1443453382:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.63/2.64 % (2831734)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2724121541:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.63/2.64 % (2831732)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=515726490:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.63/2.64 % (2831735)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3697038648:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.63/2.64 % (2831734)Instruction limit reached!
% 11.63/2.64 % (2831734)------------------------------
% 11.63/2.64 % (2831734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831734)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831734)Termination reason: Instruction limit
% 11.63/2.64 % (2831734)Termination phase: Saturation
% 11.63/2.64 % (2831734)Time elapsed: 0.110 s
% 11.63/2.64 % (2831734)Peak memory usage: 88 MB
% 11.63/2.64 % (2831734)Instructions burned: 119 (million)
% 11.63/2.64 % (2831735)Instruction limit reached!
% 11.63/2.64 % (2831735)------------------------------
% 11.63/2.64 % (2831735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831735)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831735)Termination reason: Instruction limit
% 11.63/2.64 % (2831735)Termination phase: Saturation
% 11.63/2.64 % (2831735)Time elapsed: 0.133 s
% 11.63/2.64 % (2831735)Peak memory usage: 90 MB
% 11.63/2.64 % (2831735)Instructions burned: 140 (million)
% 11.63/2.64 % (2831736)------------------------------
% 11.63/2.64 % (2831736)------------------------------
% 11.63/2.64 % (2831750)lrs+10_1_sil=8000:sp=occurrence:random_seed=1839072554:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 11.63/2.64 % (2831733)------------------------------
% 11.63/2.64 % (2831733)------------------------------
% 11.63/2.64 % (2831751)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3083876090:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 11.63/2.64 % (2831751)Instruction limit reached!
% 11.63/2.64 % (2831751)------------------------------
% 11.63/2.64 % (2831751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831751)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831751)Termination reason: Instruction limit
% 11.63/2.64 % (2831751)Termination phase: Saturation
% 11.63/2.64 % (2831751)Time elapsed: 0.149 s
% 11.63/2.64 % (2831751)Peak memory usage: 89 MB
% 11.63/2.64 % (2831751)Instructions burned: 157 (million)
% 11.63/2.64 % (2831754)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3187595647:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 11.63/2.64 % (2831756)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=4102362609:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 11.63/2.64 % (2831750)Instruction limit reached!
% 11.63/2.64 % (2831750)------------------------------
% 11.63/2.64 % (2831750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831750)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831750)Termination reason: Instruction limit
% 11.63/2.64 % (2831750)Termination phase: Saturation
% 11.63/2.64 % (2831750)Time elapsed: 0.287 s
% 11.63/2.64 % (2831750)Peak memory usage: 91 MB
% 11.63/2.64 % (2831750)Instructions burned: 286 (million)
% 11.63/2.64 % (2831756)Instruction limit reached!
% 11.63/2.64 % (2831756)------------------------------
% 11.63/2.64 % (2831756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831756)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831756)Termination reason: Instruction limit
% 11.63/2.64 % (2831756)Termination phase: Saturation
% 11.63/2.64 % (2831756)Time elapsed: 0.129 s
% 11.63/2.64 % (2831756)Peak memory usage: 91 MB
% 11.63/2.64 % (2831756)Instructions burned: 248 (million)
% 11.63/2.64 % (2831758)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3495418202:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 11.63/2.64 % (2831758)Refutation not found, incomplete strategy
% 11.63/2.64 % (2831758)------------------------------
% 11.63/2.64 % (2831758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831758)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831758)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.64 % (2831758)Time elapsed: 0.003 s
% 11.63/2.64 % (2831758)Peak memory usage: 88 MB
% 11.63/2.64 % (2831758)Instructions burned: 1 (million)
% 11.63/2.64 % (2831761)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2782870582:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 11.63/2.64 % (2831754)Instruction limit reached!
% 11.63/2.64 % (2831754)------------------------------
% 11.63/2.64 % (2831754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831754)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831754)Termination reason: Instruction limit
% 11.63/2.64 % (2831754)Termination phase: Saturation
% 11.63/2.64 % (2831754)Time elapsed: 0.324 s
% 11.63/2.64 % (2831754)Peak memory usage: 91 MB
% 11.63/2.64 % (2831754)Instructions burned: 326 (million)
% 11.63/2.64 % (2831764)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3897313240:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 11.63/2.64 % (2831732)Refutation not found, incomplete strategy
% 11.63/2.64 % (2831732)------------------------------
% 11.63/2.64 % (2831732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831732)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831764)Refutation not found, incomplete strategy
% 11.63/2.64 % (2831764)------------------------------
% 11.63/2.64 % (2831764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831732)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.64 % (2831732)Time elapsed: 0.972 s
% 11.63/2.64 % (2831732)Peak memory usage: 127 MB
% 11.63/2.64 % (2831732)Instructions burned: 894 (million)
% 11.63/2.64 % (2831764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831764)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831764)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.64 % (2831764)Time elapsed: 0.002 s
% 11.63/2.64 % (2831764)Peak memory usage: 88 MB
% 11.63/2.64 % (2831764)Instructions burned: 1 (million)
% 11.63/2.64 % (2831764)------------------------------
% 11.63/2.64 % (2831764)------------------------------
% 11.63/2.64 % (2831730)First to succeed.
% 11.63/2.64 % (2831730)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2831686"
% 11.63/2.64 % (2831769)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3057115200:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 11.63/2.64 % (2831769)Refutation not found, incomplete strategy
% 11.63/2.64 % (2831769)------------------------------
% 11.63/2.64 % (2831769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.64 % (2831769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.64 % (2831769)CaDiCaL version: 2.1.3
% 11.63/2.64 % (2831769)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.64 % (2831769)Time elapsed: 0.002 s
% 11.63/2.64 % (2831769)Peak memory usage: 88 MB
% 11.63/2.64 % (2831758)------------------------------
% 11.63/2.64 % (2831758)------------------------------
% 11.63/2.64 % (2831732)------------------------------
% 11.63/2.64 % (2831732)------------------------------
% 11.63/2.64 % (2831730)Refutation found. Thanks to Tanya!
% 11.63/2.64 % SZS status Theorem for theBenchmark
% 11.63/2.64 % SZS output start Proof for theBenchmark
% See solution above
% 13.01/2.87 % (2831730)------------------------------
% 13.01/2.87 % (2831730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.01/2.87 % (2831730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.01/2.87 % (2831730)CaDiCaL version: 2.1.3
% 13.01/2.87 % (2831730)Termination reason: Refutation
% 13.01/2.87 % (2831730)Time elapsed: 1.271 s
% 13.01/2.87 % (2831730)Peak memory usage: 136 MB
% 13.01/2.87 % (2831730)Instructions burned: 1629 (million)
% 13.01/2.87 % (2831730)------------------------------
% 13.01/2.87 % (2831730)------------------------------
% 13.01/2.87 % (2831686)Success in time 1.751 s
% 13.01/2.87 % Vampire exiting
%------------------------------------------------------------------------------