%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE110+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:40:22 AM UTC 2026
% Result : Theorem 20.71s 4.63s
% Output : Refutation 25.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 42
% Syntax : Number of formulae : 259 ( 259 unt; 19 def)
% Number of atoms : 259 ( 258 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 20 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 23 con; 0-2 aty)
% Number of variables : 204 ( 202 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
fof(f18,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_diamond) ).
fof(f26,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_box) ).
fof(f27,conjecture,
! [X0,X1] : addition(domain(X0),backward_box(X1,forward_diamond(X1,domain(X0)))) = backward_box(X1,forward_diamond(X1,domain(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] : addition(domain(X0),backward_box(X1,forward_diamond(X1,domain(X0)))) = backward_box(X1,forward_diamond(X1,domain(X0))),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1] : backward_box(X1,forward_diamond(X1,domain(X0))) != addition(domain(X0),backward_box(X1,forward_diamond(X1,domain(X0)))),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
backward_box(sK1,forward_diamond(sK1,domain(sK0))) != addition(domain(sK0),backward_box(sK1,forward_diamond(sK1,domain(sK0)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f29]) ).
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(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f47,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f18]) ).
fof(f48,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f50,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f53,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f55,plain,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f26]) ).
fof(f56,plain,
backward_box(sK1,forward_diamond(sK1,domain(sK0))) != addition(domain(sK0),backward_box(sK1,forward_diamond(sK1,domain(sK0)))),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0] : c(X0) = antidomain(antidomain(antidomain(X0))),
inference(definition_unfolding,[],[f50,f45]) ).
fof(f58,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f53,f49,f49]) ).
fof(f59,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X0)))))),
inference(definition_unfolding,[],[f55,f57,f58,f57]) ).
fof(f61,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f63,plain,
antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK0)))))))))))),sK1)))))) != addition(antidomain(antidomain(sK0)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK0)))))))))))),sK1))))))),
inference(definition_unfolding,[],[f56,f59,f61,f45,f45,f59,f61,f45]) ).
fof(f64,definition,
sF2 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f65,plain,
antidomain(sK0) = sF2,
inference(reorient_equations,[],[f64]) ).
fof(f66,definition,
sF3 = antidomain(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f67,plain,
antidomain(sF2) = sF3,
inference(reorient_equations,[],[f66]) ).
fof(f68,definition,
sF4 = antidomain(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f69,plain,
antidomain(sF3) = sF4,
inference(reorient_equations,[],[f68]) ).
fof(f70,definition,
sF5 = antidomain(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f71,plain,
antidomain(sF4) = sF5,
inference(reorient_equations,[],[f70]) ).
fof(f72,definition,
sF6 = multiplication(sK1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f73,plain,
multiplication(sK1,sF5) = sF6,
inference(reorient_equations,[],[f72]) ).
fof(f74,definition,
sF7 = antidomain(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f75,plain,
antidomain(sF6) = sF7,
inference(reorient_equations,[],[f74]) ).
fof(f76,definition,
sF8 = antidomain(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f77,plain,
antidomain(sF7) = sF8,
inference(reorient_equations,[],[f76]) ).
fof(f78,definition,
sF9 = antidomain(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f79,plain,
antidomain(sF8) = sF9,
inference(reorient_equations,[],[f78]) ).
fof(f80,definition,
sF10 = antidomain(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f81,plain,
antidomain(sF9) = sF10,
inference(reorient_equations,[],[f80]) ).
fof(f82,definition,
sF11 = antidomain(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f83,plain,
antidomain(sF10) = sF11,
inference(reorient_equations,[],[f82]) ).
fof(f84,definition,
sF12 = coantidomain(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f85,plain,
coantidomain(sF11) = sF12,
inference(reorient_equations,[],[f84]) ).
fof(f86,definition,
sF13 = coantidomain(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f87,plain,
coantidomain(sF12) = sF13,
inference(reorient_equations,[],[f86]) ).
fof(f88,definition,
sF14 = multiplication(sF13,sK1),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f89,plain,
multiplication(sF13,sK1) = sF14,
inference(reorient_equations,[],[f88]) ).
fof(f90,definition,
sF15 = coantidomain(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f91,plain,
coantidomain(sF14) = sF15,
inference(reorient_equations,[],[f90]) ).
fof(f92,definition,
sF16 = coantidomain(sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f93,plain,
coantidomain(sF15) = sF16,
inference(reorient_equations,[],[f92]) ).
fof(f94,definition,
sF17 = antidomain(sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f95,plain,
antidomain(sF16) = sF17,
inference(reorient_equations,[],[f94]) ).
fof(f96,definition,
sF18 = antidomain(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f97,plain,
antidomain(sF17) = sF18,
inference(reorient_equations,[],[f96]) ).
fof(f98,definition,
sF19 = antidomain(sF18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f99,plain,
antidomain(sF18) = sF19,
inference(reorient_equations,[],[f98]) ).
fof(f100,definition,
sF20 = addition(sF3,sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f101,plain,
addition(sF3,sF19) = sF20,
inference(reorient_equations,[],[f100]) ).
fof(f102,plain,
sF19 != sF20,
inference(definition_folding,[],[f63,f101,f99,f97,f95,f93,f91,f89,f87,f85,f83,f81,f79,f77,f75,f73,f71,f69,f67,f65,f67,f65,f99,f97,f95,f93,f91,f89,f87,f85,f83,f81,f79,f77,f75,f73,f71,f69,f67,f65]) ).
fof(f119,plain,
one = addition(antidomain(sF2),sF2),
inference(superposition,[],[f44,f65]) ).
fof(f125,plain,
one = addition(antidomain(sF9),sF9),
inference(superposition,[],[f44,f79]) ).
fof(f134,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f31,f44]) ).
fof(f138,plain,
one = addition(sF10,sF9),
inference(forward_demodulation,[],[f125,f81]) ).
fof(f143,plain,
one = addition(sF3,sF2),
inference(forward_demodulation,[],[f119,f67]) ).
fof(f149,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f39,f37]) ).
fof(f164,plain,
one = addition(coantidomain(sF15),sF15),
inference(superposition,[],[f48,f91]) ).
fof(f169,plain,
! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
inference(superposition,[],[f31,f48]) ).
fof(f170,plain,
one = addition(sF16,sF15),
inference(forward_demodulation,[],[f164,f93]) ).
fof(f176,plain,
zero = multiplication(sF7,sF6),
inference(superposition,[],[f42,f75]) ).
fof(f184,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(superposition,[],[f39,f42]) ).
fof(f185,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[],[f39,f42]) ).
fof(f186,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f38,f42]) ).
fof(f187,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[],[f38,f42]) ).
fof(f188,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[],[f186,f33]) ).
fof(f189,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f184,f33]) ).
fof(f203,plain,
! [X0,X1] : multiplication(X1,X0) = multiplication(addition(antidomain(X0),X1),X0),
inference(superposition,[],[f189,f31]) ).
fof(f204,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f189,f44]) ).
fof(f211,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f204,f37]) ).
fof(f212,plain,
! [X0,X1] : multiplication(X1,X0) = addition(zero,multiplication(X1,X0)),
inference(forward_demodulation,[],[f203,f185]) ).
fof(f247,plain,
! [X0,X1] : addition(one,X1) = addition(antidomain(antidomain(X0)),addition(antidomain(X0),X1)),
inference(superposition,[],[f32,f44]) ).
fof(f248,plain,
! [X0,X1] : addition(one,X1) = addition(coantidomain(coantidomain(X0)),addition(coantidomain(X0),X1)),
inference(superposition,[],[f32,f48]) ).
fof(f264,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(superposition,[],[f39,f46]) ).
fof(f265,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(superposition,[],[f39,f46]) ).
fof(f266,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(superposition,[],[f38,f46]) ).
fof(f268,plain,
zero = coantidomain(one),
inference(superposition,[],[f37,f46]) ).
fof(f270,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(forward_demodulation,[],[f266,f33]) ).
fof(f271,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[],[f265,f212]) ).
fof(f272,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[],[f264,f33]) ).
fof(f280,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,coantidomain(coantidomain(X0))),
inference(superposition,[],[f270,f48]) ).
fof(f291,plain,
! [X0] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f280,f36]) ).
fof(f310,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,X1)) = multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f188,f38]) ).
fof(f364,plain,
one = addition(coantidomain(zero),zero),
inference(superposition,[],[f48,f268]) ).
fof(f365,plain,
one = coantidomain(zero),
inference(forward_demodulation,[],[f364,f33]) ).
fof(f379,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(superposition,[],[f38,f36]) ).
fof(f380,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f38,f36]) ).
fof(f383,plain,
zero = antidomain(one),
inference(superposition,[],[f42,f36]) ).
fof(f439,plain,
! [X0,X1] : multiplication(zero,X1) = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(superposition,[],[f35,f42]) ).
fof(f444,plain,
! [X0] : multiplication(sF14,X0) = multiplication(sF13,multiplication(sK1,X0)),
inference(superposition,[],[f35,f89]) ).
fof(f464,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(forward_demodulation,[],[f439,f41]) ).
fof(f480,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f505,plain,
! [X0,X1] : multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(X0,X1))) = multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(superposition,[],[f270,f47]) ).
fof(f511,plain,
! [X0,X1] : zero = multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f505,f46]) ).
fof(f523,plain,
! [X0,X1] : zero = multiplication(coantidomain(coantidomain(X0)),multiplication(X1,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f511,f35]) ).
fof(f656,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),multiplication(X0,coantidomain(zero))),
inference(superposition,[],[f523,f42]) ).
fof(f689,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),multiplication(X0,one)),
inference(forward_demodulation,[],[f656,f365]) ).
fof(f700,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),X0),
inference(forward_demodulation,[],[f689,f36]) ).
fof(f725,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,coantidomain(coantidomain(antidomain(X1)))),X1),
inference(superposition,[],[f39,f700]) ).
fof(f739,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,coantidomain(coantidomain(antidomain(X1)))),X1),
inference(forward_demodulation,[],[f725,f33]) ).
fof(f806,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f189,f43]) ).
fof(f814,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f806,f42]) ).
fof(f1241,plain,
! [X0,X1] : multiplication(X0,coantidomain(addition(X0,X1))) = multiplication(addition(X0,X1),coantidomain(addition(X0,X1))),
inference(superposition,[],[f272,f480]) ).
fof(f1250,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X0,X1))),
inference(forward_demodulation,[],[f1241,f46]) ).
fof(f1290,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f187,f44]) ).
fof(f1382,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))),
inference(forward_demodulation,[],[f1290,f36]) ).
fof(f1413,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f1382,f212]) ).
fof(f1423,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f1413,f211]) ).
fof(f1431,plain,
sF3 = antidomain(antidomain(sF3)),
inference(superposition,[],[f1423,f67]) ).
fof(f1434,plain,
sF7 = antidomain(antidomain(sF7)),
inference(superposition,[],[f1423,f75]) ).
fof(f1435,plain,
sF8 = antidomain(antidomain(sF8)),
inference(superposition,[],[f1423,f77]) ).
fof(f1436,plain,
sF9 = antidomain(antidomain(sF9)),
inference(superposition,[],[f1423,f79]) ).
fof(f1439,plain,
sF17 = antidomain(antidomain(sF17)),
inference(superposition,[],[f1423,f95]) ).
fof(f1459,plain,
sF17 = antidomain(sF18),
inference(forward_demodulation,[],[f1439,f97]) ).
fof(f1461,plain,
sF9 = antidomain(sF10),
inference(forward_demodulation,[],[f1436,f81]) ).
fof(f1462,plain,
sF8 = antidomain(sF9),
inference(forward_demodulation,[],[f1435,f79]) ).
fof(f1463,plain,
sF7 = antidomain(sF8),
inference(forward_demodulation,[],[f1434,f77]) ).
fof(f1465,plain,
sF3 = antidomain(sF4),
inference(forward_demodulation,[],[f1431,f69]) ).
fof(f1467,plain,
sF17 = sF19,
inference(forward_demodulation,[],[f1459,f99]) ).
fof(f1468,plain,
sF9 = sF11,
inference(forward_demodulation,[],[f1461,f83]) ).
fof(f1469,plain,
sF8 = sF10,
inference(forward_demodulation,[],[f1462,f81]) ).
fof(f1470,plain,
sF7 = sF9,
inference(forward_demodulation,[],[f1463,f79]) ).
fof(f1471,plain,
sF3 = sF5,
inference(forward_demodulation,[],[f1465,f71]) ).
fof(f1476,plain,
sF20 = addition(sF3,sF17),
inference(superposition,[],[f101,f1467]) ).
fof(f1480,plain,
sF6 = multiplication(sK1,sF3),
inference(superposition,[],[f73,f1471]) ).
fof(f1486,plain,
sF12 = coantidomain(sF9),
inference(superposition,[],[f85,f1468]) ).
fof(f1487,plain,
sF12 = coantidomain(sF7),
inference(forward_demodulation,[],[f1486,f1470]) ).
fof(f1604,plain,
sF7 = multiplication(sF7,coantidomain(sF12)),
inference(superposition,[],[f291,f1487]) ).
fof(f1607,plain,
sF7 = multiplication(sF7,sF13),
inference(forward_demodulation,[],[f1604,f87]) ).
fof(f1959,plain,
one = multiplication(antidomain(zero),one),
inference(superposition,[],[f211,f383]) ).
fof(f1965,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f1959,f36]) ).
fof(f2000,plain,
one = addition(sF2,antidomain(sF2)),
inference(superposition,[],[f134,f65]) ).
fof(f2005,plain,
one = addition(sF7,antidomain(sF7)),
inference(superposition,[],[f134,f75]) ).
fof(f2023,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(superposition,[],[f480,f134]) ).
fof(f2041,plain,
one = addition(sF7,sF8),
inference(forward_demodulation,[],[f2005,f77]) ).
fof(f2046,plain,
one = addition(sF2,sF3),
inference(forward_demodulation,[],[f2000,f67]) ).
fof(f2150,plain,
! [X0,X1] : zero = multiplication(antidomain(zero),multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1))))),
inference(superposition,[],[f814,f464]) ).
fof(f2151,plain,
! [X0,X1] : zero = multiplication(one,multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f2150,f1965]) ).
fof(f2183,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f2151,f37]) ).
fof(f2689,plain,
! [X0] : multiplication(coantidomain(X0),coantidomain(coantidomain(coantidomain(X0)))) = multiplication(one,coantidomain(coantidomain(coantidomain(X0)))),
inference(superposition,[],[f272,f169]) ).
fof(f2697,plain,
! [X0] : coantidomain(coantidomain(coantidomain(X0))) = multiplication(coantidomain(X0),coantidomain(coantidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f2689,f37]) ).
fof(f2706,plain,
! [X0] : coantidomain(X0) = coantidomain(coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f2697,f291]) ).
fof(f2712,plain,
sF12 = coantidomain(coantidomain(sF12)),
inference(superposition,[],[f2706,f85]) ).
fof(f2730,plain,
sF12 = coantidomain(sF13),
inference(forward_demodulation,[],[f2712,f87]) ).
fof(f4613,plain,
one = addition(sF3,one),
inference(superposition,[],[f480,f143]) ).
fof(f4985,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = addition(one,antidomain(X0)),
inference(superposition,[],[f247,f34]) ).
fof(f5015,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f4985,f44]) ).
fof(f5060,plain,
one = addition(one,sF8),
inference(superposition,[],[f5015,f77]) ).
fof(f5355,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,one)) = multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f310,f44]) ).
fof(f5443,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(X1))),X0),
inference(forward_demodulation,[],[f5355,f36]) ).
fof(f5650,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = addition(one,coantidomain(X0)),
inference(superposition,[],[f248,f34]) ).
fof(f5678,plain,
! [X0] : one = addition(one,coantidomain(X0)),
inference(forward_demodulation,[],[f5650,f48]) ).
fof(f5697,plain,
one = addition(one,sF12),
inference(superposition,[],[f5678,f2730]) ).
fof(f6482,plain,
multiplication(sF8,coantidomain(sF7)) = multiplication(one,coantidomain(sF7)),
inference(superposition,[],[f271,f2041]) ).
fof(f6548,plain,
coantidomain(sF7) = multiplication(sF8,coantidomain(sF7)),
inference(forward_demodulation,[],[f6482,f37]) ).
fof(f6588,plain,
sF12 = multiplication(sF8,sF12),
inference(forward_demodulation,[],[f6548,f1487]) ).
fof(f6622,plain,
multiplication(sF8,addition(one,sF12)) = addition(sF8,sF12),
inference(superposition,[],[f380,f6588]) ).
fof(f6633,plain,
multiplication(sF8,one) = addition(sF8,sF12),
inference(forward_demodulation,[],[f6622,f5697]) ).
fof(f6641,plain,
sF8 = addition(sF8,sF12),
inference(forward_demodulation,[],[f6633,f36]) ).
fof(f7148,plain,
! [X0] : multiplication(one,X0) = multiplication(coantidomain(antidomain(X0)),X0),
inference(superposition,[],[f739,f169]) ).
fof(f7224,plain,
! [X0] : multiplication(coantidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f7148,f37]) ).
fof(f7314,plain,
sF10 = multiplication(coantidomain(sF11),sF10),
inference(superposition,[],[f7224,f83]) ).
fof(f7377,plain,
sF8 = multiplication(coantidomain(sF11),sF8),
inference(forward_demodulation,[],[f7314,f1469]) ).
fof(f7393,plain,
sF8 = multiplication(sF12,sF8),
inference(forward_demodulation,[],[f7377,f85]) ).
fof(f7414,plain,
multiplication(sF12,addition(one,sF8)) = addition(sF12,sF8),
inference(superposition,[],[f380,f7393]) ).
fof(f7425,plain,
addition(sF12,sF8) = multiplication(sF12,one),
inference(forward_demodulation,[],[f7414,f5060]) ).
fof(f7436,plain,
sF12 = addition(sF12,sF8),
inference(forward_demodulation,[],[f7425,f36]) ).
fof(f8313,plain,
sF12 = addition(sF8,sF12),
inference(superposition,[],[f31,f7436]) ).
fof(f8335,plain,
sF8 = sF12,
inference(forward_demodulation,[],[f8313,f6641]) ).
fof(f8365,plain,
sF13 = coantidomain(sF8),
inference(superposition,[],[f87,f8335]) ).
fof(f8769,plain,
multiplication(one,coantidomain(sF10)) = multiplication(sF9,coantidomain(sF10)),
inference(superposition,[],[f271,f138]) ).
fof(f8802,plain,
multiplication(one,coantidomain(sF8)) = multiplication(sF9,coantidomain(sF8)),
inference(forward_demodulation,[],[f8769,f1469]) ).
fof(f8824,plain,
multiplication(sF9,sF13) = multiplication(one,sF13),
inference(forward_demodulation,[],[f8802,f8365]) ).
fof(f8839,plain,
sF13 = multiplication(sF9,sF13),
inference(forward_demodulation,[],[f8824,f37]) ).
fof(f8844,plain,
sF13 = multiplication(sF7,sF13),
inference(forward_demodulation,[],[f8839,f1470]) ).
fof(f8848,plain,
sF7 = sF13,
inference(forward_demodulation,[],[f8844,f1607]) ).
fof(f11645,plain,
multiplication(sF14,sF3) = multiplication(sF13,sF6),
inference(superposition,[],[f444,f1480]) ).
fof(f11721,plain,
multiplication(sF7,sF6) = multiplication(sF14,sF3),
inference(forward_demodulation,[],[f11645,f8848]) ).
fof(f11735,plain,
zero = multiplication(sF14,sF3),
inference(forward_demodulation,[],[f11721,f176]) ).
fof(f11761,plain,
zero = multiplication(coantidomain(coantidomain(sF14)),multiplication(sF3,coantidomain(zero))),
inference(superposition,[],[f523,f11735]) ).
fof(f11770,plain,
zero = multiplication(coantidomain(coantidomain(sF14)),multiplication(sF3,one)),
inference(forward_demodulation,[],[f11761,f365]) ).
fof(f11790,plain,
zero = multiplication(coantidomain(coantidomain(sF14)),sF3),
inference(forward_demodulation,[],[f11770,f36]) ).
fof(f11799,plain,
zero = multiplication(coantidomain(sF15),sF3),
inference(forward_demodulation,[],[f11790,f91]) ).
fof(f11806,plain,
zero = multiplication(sF16,sF3),
inference(forward_demodulation,[],[f11799,f93]) ).
fof(f11814,plain,
! [X0] : addition(zero,multiplication(X0,sF3)) = multiplication(addition(sF16,X0),sF3),
inference(superposition,[],[f39,f11806]) ).
fof(f11851,plain,
! [X0] : multiplication(X0,sF3) = multiplication(addition(sF16,X0),sF3),
inference(forward_demodulation,[],[f11814,f212]) ).
fof(f11878,plain,
multiplication(one,sF3) = multiplication(sF15,sF3),
inference(superposition,[],[f11851,f170]) ).
fof(f11939,plain,
sF3 = multiplication(sF15,sF3),
inference(forward_demodulation,[],[f11878,f37]) ).
fof(f11976,plain,
multiplication(sF15,addition(sF3,one)) = addition(sF3,sF15),
inference(superposition,[],[f379,f11939]) ).
fof(f11990,plain,
multiplication(sF15,one) = addition(sF3,sF15),
inference(forward_demodulation,[],[f11976,f4613]) ).
fof(f12002,plain,
sF15 = addition(sF3,sF15),
inference(forward_demodulation,[],[f11990,f36]) ).
fof(f12029,plain,
zero = multiplication(sF3,coantidomain(sF15)),
inference(superposition,[],[f1250,f12002]) ).
fof(f12044,plain,
zero = multiplication(sF3,sF16),
inference(forward_demodulation,[],[f12029,f93]) ).
fof(f12264,plain,
! [X0,X1] : multiplication(antidomain(zero),antidomain(X0)) = multiplication(antidomain(zero),multiplication(antidomain(X0),antidomain(antidomain(antidomain(multiplication(X0,X1)))))),
inference(superposition,[],[f5443,f2183]) ).
fof(f12313,plain,
! [X0,X1] : multiplication(antidomain(zero),antidomain(X0)) = multiplication(antidomain(zero),multiplication(antidomain(X0),antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f12264,f1423]) ).
fof(f12391,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = multiplication(one,multiplication(antidomain(X0),antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f12313,f1965]) ).
fof(f12423,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = multiplication(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f12391,f37]) ).
fof(f12430,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f12423,f37]) ).
fof(f12553,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),antidomain(multiplication(X0,X1))) = addition(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(superposition,[],[f149,f12430]) ).
fof(f12574,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,X1))) = multiplication(one,antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f12553,f2023]) ).
fof(f12641,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = addition(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f12574,f37]) ).
fof(f15689,plain,
zero = multiplication(antidomain(zero),multiplication(sF3,antidomain(antidomain(sF16)))),
inference(superposition,[],[f814,f12044]) ).
fof(f15702,plain,
zero = multiplication(antidomain(zero),multiplication(sF3,antidomain(sF17))),
inference(forward_demodulation,[],[f15689,f95]) ).
fof(f15725,plain,
zero = multiplication(antidomain(zero),multiplication(sF3,sF18)),
inference(forward_demodulation,[],[f15702,f97]) ).
fof(f15740,plain,
zero = multiplication(one,multiplication(sF3,sF18)),
inference(forward_demodulation,[],[f15725,f1965]) ).
fof(f15747,plain,
zero = multiplication(sF3,sF18),
inference(forward_demodulation,[],[f15740,f37]) ).
fof(f15753,plain,
! [X0] : addition(multiplication(X0,sF18),zero) = multiplication(addition(X0,sF3),sF18),
inference(superposition,[],[f39,f15747]) ).
fof(f15802,plain,
! [X0] : multiplication(X0,sF18) = multiplication(addition(X0,sF3),sF18),
inference(forward_demodulation,[],[f15753,f33]) ).
fof(f15835,plain,
multiplication(one,sF18) = multiplication(sF2,sF18),
inference(superposition,[],[f15802,f2046]) ).
fof(f15892,plain,
sF18 = multiplication(sF2,sF18),
inference(forward_demodulation,[],[f15835,f37]) ).
fof(f15946,plain,
antidomain(sF18) = addition(antidomain(sF2),antidomain(sF18)),
inference(superposition,[],[f12641,f15892]) ).
fof(f15951,plain,
sF19 = addition(antidomain(sF2),sF19),
inference(forward_demodulation,[],[f15946,f99]) ).
fof(f15970,plain,
sF17 = addition(antidomain(sF2),sF17),
inference(forward_demodulation,[],[f15951,f1467]) ).
fof(f15983,plain,
sF17 = addition(sF3,sF17),
inference(forward_demodulation,[],[f15970,f67]) ).
fof(f15990,plain,
sF17 = sF20,
inference(forward_demodulation,[],[f15983,f1476]) ).
fof(f15995,plain,
sF17 != sF19,
inference(superposition,[],[f102,f15990]) ).
fof(f15996,plain,
$false,
inference(forward_subsumption_resolution,[],[f15995,f1467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE110+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:13:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.74/4.09 % (3518614)Detected formulas, will run a generic FOF schedule.
% 20.74/4.09 % (3518619)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=1060465197:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 20.74/4.09 % (3518620)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=394399579:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 20.74/4.09 % (3518621)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=3653647661:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 20.74/4.09 % (3518622)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3476960360:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 20.74/4.09 % (3518623)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=444121247:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 20.74/4.09 % (3518622)Refutation not found, incomplete strategy
% 20.74/4.09 % (3518622)------------------------------
% 20.74/4.09 % (3518622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.74/4.09 % (3518622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.74/4.09 % (3518622)CaDiCaL version: 2.1.3
% 20.74/4.09 % (3518622)Termination reason: Refutation not found, incomplete strategy
% 20.74/4.09 % (3518622)Time elapsed: 0.002 s
% 20.74/4.09 % (3518622)Peak memory usage: 88 MB
% 20.74/4.09 % (3518625)dis-21_1_sil=8000:lcm=predicate:random_seed=1817353784: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)
% 20.74/4.09 % (3518624)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=454864127:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 20.74/4.09 % (3518625)Refutation not found, incomplete strategy
% 20.74/4.09 % (3518625)------------------------------
% 20.74/4.09 % (3518625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.74/4.09 % (3518625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.74/4.09 % (3518625)CaDiCaL version: 2.1.3
% 20.74/4.09 % (3518625)Termination reason: Refutation not found, incomplete strategy
% 20.74/4.09 % (3518625)Time elapsed: 0.003 s
% 20.74/4.09 % (3518625)Peak memory usage: 88 MB
% 20.74/4.09 % (3518625)Instructions burned: 1 (million)
% 20.74/4.09 % (3518623)Instruction limit reached!
% 20.74/4.09 % (3518623)------------------------------
% 20.74/4.09 % (3518623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.74/4.09 % (3518623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.74/4.09 % (3518623)CaDiCaL version: 2.1.3
% 20.74/4.09 % (3518623)Termination reason: Instruction limit
% 20.74/4.09 % (3518623)Termination phase: Saturation
% 20.74/4.09 % (3518623)Time elapsed: 0.122 s
% 20.74/4.09 % (3518623)Peak memory usage: 89 MB
% 20.74/4.09 % (3518623)Instructions burned: 130 (million)
% 20.74/4.09 % (3518624)Instruction limit reached!
% 20.74/4.09 % (3518624)------------------------------
% 20.74/4.09 % (3518624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.74/4.09 % (3518624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.74/4.09 % (3518624)CaDiCaL version: 2.1.3
% 20.74/4.09 % (3518624)Termination reason: Instruction limit
% 20.74/4.09 % (3518624)Termination phase: Saturation
% 20.74/4.09 % (3518624)Time elapsed: 0.136 s
% 20.74/4.09 % (3518624)Peak memory usage: 89 MB
% 20.74/4.09 % (3518624)Instructions burned: 139 (million)
% 20.74/4.09 % (3518622)------------------------------
% 20.74/4.09 % (3518622)------------------------------
% 20.74/4.09 % (3518625)------------------------------
% 20.74/4.09 % (3518625)------------------------------
% 20.74/4.09 % (3518633)lrs+10_1_sil=8000:sp=occurrence:random_seed=4038121681:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 20.74/4.09 % (3518634)lrs+10_1_sil=32000:urr=on:br=off:random_seed=865771636:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 20.74/4.09 % (3518634)Instruction limit reached!
% 20.74/4.09 % (3518634)------------------------------
% 20.74/4.09 % (3518634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.74/4.09 % (3518634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518634)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518634)Termination reason: Instruction limit
% 20.71/4.63 % (3518634)Termination phase: Saturation
% 20.71/4.63 % (3518634)Time elapsed: 0.143 s
% 20.71/4.63 % (3518634)Peak memory usage: 89 MB
% 20.71/4.63 % (3518634)Instructions burned: 157 (million)
% 20.71/4.63 % (3518633)Instruction limit reached!
% 20.71/4.63 % (3518633)------------------------------
% 20.71/4.63 % (3518633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518633)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518633)Termination reason: Instruction limit
% 20.71/4.63 % (3518633)Termination phase: Saturation
% 20.71/4.63 % (3518633)Time elapsed: 0.154 s
% 20.71/4.63 % (3518633)Peak memory usage: 91 MB
% 20.71/4.63 % (3518633)Instructions burned: 287 (million)
% 20.71/4.63 % (3518635)lrs+1011_1_sil=32000:sp=occurrence:random_seed=126423281:i=325:sd=1:ss=axioms:sgt=32_2992 on theBenchmark for (2992ds/325Mi)
% 20.71/4.63 % (3518636)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=2450140903:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 20.71/4.63 % (3518640)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2859486794:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 20.71/4.63 % (3518639)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4067393706:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 20.71/4.63 % (3518639)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518639)------------------------------
% 20.71/4.63 % (3518639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518639)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518639)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518639)Time elapsed: 0.004 s
% 20.71/4.63 % (3518639)Peak memory usage: 88 MB
% 20.71/4.63 % (3518639)Instructions burned: 2 (million)
% 20.71/4.63 % (3518636)Instruction limit reached!
% 20.71/4.63 % (3518636)------------------------------
% 20.71/4.63 % (3518636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518636)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518636)Termination reason: Instruction limit
% 20.71/4.63 % (3518636)Termination phase: Saturation
% 20.71/4.63 % (3518636)Time elapsed: 0.242 s
% 20.71/4.63 % (3518636)Peak memory usage: 91 MB
% 20.71/4.63 % (3518636)Instructions burned: 248 (million)
% 20.71/4.63 % (3518621)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518621)------------------------------
% 20.71/4.63 % (3518621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518621)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518621)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518621)Time elapsed: 0.991 s
% 20.71/4.63 % (3518621)Peak memory usage: 127 MB
% 20.71/4.63 % (3518621)Instructions burned: 889 (million)
% 20.71/4.63 % (3518635)Instruction limit reached!
% 20.71/4.63 % (3518635)------------------------------
% 20.71/4.63 % (3518635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518635)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518635)Termination reason: Instruction limit
% 20.71/4.63 % (3518635)Termination phase: Saturation
% 20.71/4.63 % (3518635)Time elapsed: 0.325 s
% 20.71/4.63 % (3518635)Peak memory usage: 92 MB
% 20.71/4.63 % (3518635)Instructions burned: 325 (million)
% 20.71/4.63 % (3518645)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=869473705:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 20.71/4.63 % (3518645)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518645)------------------------------
% 20.71/4.63 % (3518645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518645)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518645)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518645)Time elapsed: 0.003 s
% 20.71/4.63 % (3518645)Peak memory usage: 88 MB
% 20.71/4.63 % (3518645)Instructions burned: 1 (million)
% 20.71/4.63 % (3518639)------------------------------
% 20.71/4.63 % (3518639)------------------------------
% 20.71/4.63 % (3518646)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3060793717:i=127:av=off:fsr=off:sup=off_2986 on theBenchmark for (2986ds/127Mi)
% 20.71/4.63 % (3518646)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518646)------------------------------
% 20.71/4.63 % (3518646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518646)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518646)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518646)Time elapsed: 0.002 s
% 20.71/4.63 % (3518646)Peak memory usage: 88 MB
% 20.71/4.63 % (3518646)Instructions burned: 1 (million)
% 20.71/4.63 % (3518621)------------------------------
% 20.71/4.63 % (3518621)------------------------------
% 20.71/4.63 % (3518648)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3359584592:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2983 on theBenchmark for (2983ds/114Mi)
% 20.71/4.63 % (3518648)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518648)------------------------------
% 20.71/4.63 % (3518648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518648)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518648)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518648)Time elapsed: 0.002 s
% 20.71/4.63 % (3518648)Peak memory usage: 88 MB
% 20.71/4.63 % (3518648)Instructions burned: 1 (million)
% 20.71/4.63 % (3518645)------------------------------
% 20.71/4.63 % (3518645)------------------------------
% 20.71/4.63 % (3518650)lrs+10_1_sil=8000:sp=occurrence:random_seed=1344790097:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2983 on theBenchmark for (2983ds/907Mi)
% 20.71/4.63 % (3518646)------------------------------
% 20.71/4.63 % (3518646)------------------------------
% 20.71/4.63 % (3518648)------------------------------
% 20.71/4.63 % (3518648)------------------------------
% 20.71/4.63 % (3518652)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2070841782:i=437:sd=1:aac=none:ss=included_2980 on theBenchmark for (2980ds/437Mi)
% 20.71/4.63 % (3518652)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518652)------------------------------
% 20.71/4.63 % (3518652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518652)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518652)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518652)Time elapsed: 0.002 s
% 20.71/4.63 % (3518652)Peak memory usage: 88 MB
% 20.71/4.63 % (3518655)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4231411100:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2979 on theBenchmark for (2979ds/134Mi)
% 20.71/4.63 % (3518655)Refutation not found, incomplete strategy
% 20.71/4.63 % (3518655)------------------------------
% 20.71/4.63 % (3518655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518655)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518655)Termination reason: Refutation not found, incomplete strategy
% 20.71/4.63 % (3518655)Time elapsed: 0.002 s
% 20.71/4.63 % (3518655)Peak memory usage: 88 MB
% 20.71/4.63 % (3518655)Instructions burned: 1 (million)
% 20.71/4.63 % (3518654)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3908139907:i=5202:ss=axioms:sgt=16_2979 on theBenchmark for (2979ds/5202Mi)
% 20.71/4.63 % (3518655)------------------------------
% 20.71/4.63 % (3518655)------------------------------
% 20.71/4.63 % (3518652)------------------------------
% 20.71/4.63 % (3518652)------------------------------
% 20.71/4.63 % (3518659)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3169221763:st=8:i=592:sd=3:ep=RST:ss=axioms_2974 on theBenchmark for (2974ds/592Mi)
% 20.71/4.63 % (3518650)Instruction limit reached!
% 20.71/4.63 % (3518650)------------------------------
% 20.71/4.63 % (3518650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518650)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518650)Termination reason: Instruction limit
% 20.71/4.63 % (3518650)Termination phase: Saturation
% 20.71/4.63 % (3518650)Time elapsed: 0.887 s
% 20.71/4.63 % (3518650)Peak memory usage: 97 MB
% 20.71/4.63 % (3518650)Instructions burned: 907 (million)
% 20.71/4.63 % (3518660)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1819096566:st=3:i=13193:sd=3:ss=axioms_2973 on theBenchmark for (2973ds/13193Mi)
% 20.71/4.63 % (3518619)First to succeed.
% 20.71/4.63 % (3518619)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3518614"
% 20.71/4.63 % (3518659)Instruction limit reached!
% 20.71/4.63 % (3518659)------------------------------
% 20.71/4.63 % (3518659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518659)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518659)Termination reason: Instruction limit
% 20.71/4.63 % (3518659)Termination phase: Saturation
% 20.71/4.63 % (3518659)Time elapsed: 0.286 s
% 20.71/4.63 % (3518659)Peak memory usage: 95 MB
% 20.71/4.63 % (3518659)Instructions burned: 594 (million)
% 20.71/4.63 % (3518662)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2552570984:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2971 on theBenchmark for (2971ds/125Mi)
% 20.71/4.63 % (3518640)Instruction limit reached!
% 20.71/4.63 % (3518640)------------------------------
% 20.71/4.63 % (3518640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518640)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518640)Termination reason: Instruction limit
% 20.71/4.63 % (3518640)Termination phase: Saturation
% 20.71/4.63 % (3518640)Time elapsed: 2.120 s
% 20.71/4.63 % (3518640)Peak memory usage: 143 MB
% 20.71/4.63 % (3518640)Instructions burned: 2351 (million)
% 20.71/4.63 % (3518662)Instruction limit reached!
% 20.71/4.63 % (3518662)------------------------------
% 20.71/4.63 % (3518662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.71/4.63 % (3518662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.71/4.63 % (3518662)CaDiCaL version: 2.1.3
% 20.71/4.63 % (3518662)Termination reason: Instruction limit
% 20.71/4.63 % (3518662)Termination phase: Saturation
% 20.71/4.63 % (3518662)Time elapsed: 0.136 s
% 20.71/4.63 % (3518662)Peak memory usage: 90 MB
% 20.71/4.63 % (3518662)Instructions burned: 126 (million)
% 20.71/4.63 % (3518664)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3552580139:i=134:gtgl=5:slsql=off:gtg=exists_sym_2969 on theBenchmark for (2969ds/134Mi)
% 20.71/4.63 % (3518619)Refutation found. Thanks to Tanya!
% 20.71/4.63 % SZS status Theorem for theBenchmark
% 20.71/4.63 % SZS output start Proof for theBenchmark
% See solution above
% 25.01/4.99 % (3518619)------------------------------
% 25.01/4.99 % (3518619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.01/4.99 % (3518619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.01/4.99 % (3518619)CaDiCaL version: 2.1.3
% 25.01/4.99 % (3518619)Termination reason: Refutation
% 25.01/4.99 % (3518619)Time elapsed: 2.768 s
% 25.01/4.99 % (3518619)Peak memory usage: 150 MB
% 25.01/4.99 % (3518619)Instructions burned: 2935 (million)
% 25.01/4.99 % (3518619)------------------------------
% 25.01/4.99 % (3518619)------------------------------
% 25.01/4.99 % (3518614)Success in time 3.419 s
% 25.01/4.99 % Vampire exiting
%------------------------------------------------------------------------------