%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE109+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 : n004.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 11:40:21 AM UTC 2026
% Result : Theorem 25.22s 4.57s
% Output : Refutation 26.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 42
% Syntax : Number of formulae : 278 ( 278 unt; 19 def)
% Number of atoms : 278 ( 277 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 213 ( 211 !; 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',codomain2) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
fof(f26,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_box) ).
fof(f27,conjecture,
! [X0,X1] : addition(forward_diamond(X0,backward_box(X0,domain(X1))),domain(X1)) = domain(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] : addition(forward_diamond(X0,backward_box(X0,domain(X1))),domain(X1)) = domain(X1),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1] : domain(X1) != addition(forward_diamond(X0,backward_box(X0,domain(X1))),domain(X1)),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
domain(sK1) != addition(forward_diamond(sK0,backward_box(sK0,domain(sK1))),domain(sK1)),
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,
domain(sK1) != addition(forward_diamond(sK0,backward_box(sK0,domain(sK1))),domain(sK1)),
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(sK1)) != addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1))))))),sK0))))))))))),antidomain(antidomain(sK1))),
inference(definition_unfolding,[],[f56,f45,f61,f59,f45,f45]) ).
fof(f64,definition,
sF2 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f65,plain,
antidomain(sK1) = 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 = antidomain(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f73,plain,
antidomain(sF5) = sF6,
inference(reorient_equations,[],[f72]) ).
fof(f74,definition,
sF7 = coantidomain(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f75,plain,
coantidomain(sF6) = sF7,
inference(reorient_equations,[],[f74]) ).
fof(f76,definition,
sF8 = coantidomain(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f77,plain,
coantidomain(sF7) = sF8,
inference(reorient_equations,[],[f76]) ).
fof(f78,definition,
sF9 = multiplication(sF8,sK0),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f79,plain,
multiplication(sF8,sK0) = sF9,
inference(reorient_equations,[],[f78]) ).
fof(f80,definition,
sF10 = coantidomain(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f81,plain,
coantidomain(sF9) = sF10,
inference(reorient_equations,[],[f80]) ).
fof(f82,definition,
sF11 = coantidomain(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f83,plain,
coantidomain(sF10) = sF11,
inference(reorient_equations,[],[f82]) ).
fof(f84,definition,
sF12 = antidomain(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f85,plain,
antidomain(sF11) = sF12,
inference(reorient_equations,[],[f84]) ).
fof(f86,definition,
sF13 = antidomain(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f87,plain,
antidomain(sF12) = sF13,
inference(reorient_equations,[],[f86]) ).
fof(f88,definition,
sF14 = antidomain(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f89,plain,
antidomain(sF13) = sF14,
inference(reorient_equations,[],[f88]) ).
fof(f90,definition,
sF15 = antidomain(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f91,plain,
antidomain(sF14) = sF15,
inference(reorient_equations,[],[f90]) ).
fof(f92,definition,
sF16 = antidomain(sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f93,plain,
antidomain(sF15) = sF16,
inference(reorient_equations,[],[f92]) ).
fof(f94,definition,
sF17 = multiplication(sK0,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f95,plain,
multiplication(sK0,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(sF19,sF3),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f101,plain,
addition(sF19,sF3) = sF20,
inference(reorient_equations,[],[f100]) ).
fof(f102,plain,
sF3 != sF20,
inference(definition_folding,[],[f63,f101,f67,f65,f99,f97,f95,f93,f91,f89,f87,f85,f83,f81,f79,f77,f75,f73,f71,f69,f67,f65,f67,f65]) ).
fof(f119,plain,
one = addition(antidomain(sF2),sF2),
inference(superposition,[],[f44,f65]) ).
fof(f120,plain,
one = addition(antidomain(sF3),sF3),
inference(superposition,[],[f44,f67]) ).
fof(f134,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f31,f44]) ).
fof(f142,plain,
one = addition(sF4,sF3),
inference(forward_demodulation,[],[f120,f69]) ).
fof(f143,plain,
one = addition(sF3,sF2),
inference(forward_demodulation,[],[f119,f67]) ).
fof(f144,plain,
one = addition(coantidomain(sF7),sF7),
inference(superposition,[],[f48,f75]) ).
fof(f151,plain,
! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
inference(superposition,[],[f31,f48]) ).
fof(f153,plain,
one = addition(sF8,sF7),
inference(forward_demodulation,[],[f144,f77]) ).
fof(f156,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f39,f37]) ).
fof(f159,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f39,f37]) ).
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(f215,plain,
sK1 = multiplication(antidomain(sF2),sK1),
inference(superposition,[],[f211,f65]) ).
fof(f241,plain,
sK1 = multiplication(sF3,sK1),
inference(forward_demodulation,[],[f215,f67]) ).
fof(f244,plain,
zero = multiplication(sF9,sF10),
inference(superposition,[],[f46,f81]) ).
fof(f247,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(superposition,[],[f39,f46]) ).
fof(f249,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(superposition,[],[f38,f46]) ).
fof(f251,plain,
zero = coantidomain(one),
inference(superposition,[],[f37,f46]) ).
fof(f253,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(forward_demodulation,[],[f249,f33]) ).
fof(f255,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[],[f247,f33]) ).
fof(f262,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,coantidomain(coantidomain(X0))),
inference(superposition,[],[f253,f48]) ).
fof(f273,plain,
! [X0] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f262,f36]) ).
fof(f291,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(f346,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f32,f38]) ).
fof(f374,plain,
one = addition(coantidomain(zero),zero),
inference(superposition,[],[f48,f251]) ).
fof(f375,plain,
one = coantidomain(zero),
inference(forward_demodulation,[],[f374,f33]) ).
fof(f390,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f38,f36]) ).
fof(f393,plain,
zero = antidomain(one),
inference(superposition,[],[f42,f36]) ).
fof(f447,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f451,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = multiplication(zero,X1),
inference(superposition,[],[f35,f46]) ).
fof(f463,plain,
! [X0] : multiplication(sF9,X0) = multiplication(sF8,multiplication(sK0,X0)),
inference(superposition,[],[f35,f79]) ).
fof(f487,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X0),X1)),
inference(forward_demodulation,[],[f451,f41]) ).
fof(f556,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,[],[f253,f47]) ).
fof(f564,plain,
! [X0,X1] : zero = multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f556,f46]) ).
fof(f576,plain,
! [X0,X1] : zero = multiplication(coantidomain(coantidomain(X0)),multiplication(X1,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f564,f35]) ).
fof(f584,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f31,f33]) ).
fof(f619,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),multiplication(X0,coantidomain(zero))),
inference(superposition,[],[f576,f42]) ).
fof(f652,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),multiplication(X0,one)),
inference(forward_demodulation,[],[f619,f375]) ).
fof(f663,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),X0),
inference(forward_demodulation,[],[f652,f36]) ).
fof(f675,plain,
zero = multiplication(coantidomain(coantidomain(sF6)),sF5),
inference(superposition,[],[f663,f73]) ).
fof(f706,plain,
zero = multiplication(coantidomain(sF7),sF5),
inference(forward_demodulation,[],[f675,f75]) ).
fof(f711,plain,
zero = multiplication(sF8,sF5),
inference(forward_demodulation,[],[f706,f77]) ).
fof(f766,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(f774,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f766,f42]) ).
fof(f938,plain,
sF6 = multiplication(sF6,coantidomain(sF7)),
inference(superposition,[],[f273,f75]) ).
fof(f968,plain,
sF6 = multiplication(sF6,sF8),
inference(forward_demodulation,[],[f938,f77]) ).
fof(f975,plain,
multiplication(antidomain(sF2),sF3) = multiplication(antidomain(sF2),one),
inference(superposition,[],[f188,f143]) ).
fof(f978,plain,
antidomain(sF2) = multiplication(antidomain(sF2),sF3),
inference(forward_demodulation,[],[f975,f36]) ).
fof(f981,plain,
sF3 = multiplication(sF3,sF3),
inference(forward_demodulation,[],[f978,f67]) ).
fof(f1015,plain,
zero = multiplication(antidomain(sK1),multiplication(sF3,antidomain(antidomain(sK1)))),
inference(superposition,[],[f774,f241]) ).
fof(f1016,plain,
zero = multiplication(sF2,multiplication(sF3,antidomain(sF2))),
inference(forward_demodulation,[],[f1015,f65]) ).
fof(f1023,plain,
zero = multiplication(sF2,multiplication(sF3,sF3)),
inference(forward_demodulation,[],[f1016,f67]) ).
fof(f1025,plain,
zero = multiplication(sF2,sF3),
inference(forward_demodulation,[],[f1023,f981]) ).
fof(f1115,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,[],[f346,f39]) ).
fof(f1319,plain,
one = addition(sF3,one),
inference(superposition,[],[f447,f143]) ).
fof(f1320,plain,
one = addition(sF4,one),
inference(superposition,[],[f447,f142]) ).
fof(f1326,plain,
! [X0,X1] : multiplication(X0,coantidomain(addition(X0,X1))) = multiplication(addition(X0,X1),coantidomain(addition(X0,X1))),
inference(superposition,[],[f255,f447]) ).
fof(f1335,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X0,X1))),
inference(forward_demodulation,[],[f1326,f46]) ).
fof(f1679,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f187,f44]) ).
fof(f1779,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))),
inference(forward_demodulation,[],[f1679,f36]) ).
fof(f1813,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f1779,f212]) ).
fof(f1824,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f1813,f211]) ).
fof(f1832,plain,
sF2 = antidomain(antidomain(sF2)),
inference(superposition,[],[f1824,f65]) ).
fof(f1833,plain,
sF3 = antidomain(antidomain(sF3)),
inference(superposition,[],[f1824,f67]) ).
fof(f1834,plain,
sF4 = antidomain(antidomain(sF4)),
inference(superposition,[],[f1824,f69]) ).
fof(f1837,plain,
sF12 = antidomain(antidomain(sF12)),
inference(superposition,[],[f1824,f85]) ).
fof(f1839,plain,
sF14 = antidomain(antidomain(sF14)),
inference(superposition,[],[f1824,f89]) ).
fof(f1842,plain,
sF18 = antidomain(antidomain(sF18)),
inference(superposition,[],[f1824,f97]) ).
fof(f1860,plain,
sF18 = antidomain(sF19),
inference(forward_demodulation,[],[f1842,f99]) ).
fof(f1862,plain,
sF14 = antidomain(sF15),
inference(forward_demodulation,[],[f1839,f91]) ).
fof(f1864,plain,
sF12 = antidomain(sF13),
inference(forward_demodulation,[],[f1837,f87]) ).
fof(f1866,plain,
sF4 = antidomain(sF5),
inference(forward_demodulation,[],[f1834,f71]) ).
fof(f1867,plain,
sF3 = antidomain(sF4),
inference(forward_demodulation,[],[f1833,f69]) ).
fof(f1868,plain,
sF2 = antidomain(sF3),
inference(forward_demodulation,[],[f1832,f67]) ).
fof(f1869,plain,
sF14 = sF16,
inference(forward_demodulation,[],[f1862,f93]) ).
fof(f1871,plain,
sF12 = sF14,
inference(forward_demodulation,[],[f1864,f89]) ).
fof(f1872,plain,
sF4 = sF6,
inference(forward_demodulation,[],[f1866,f73]) ).
fof(f1873,plain,
sF3 = sF5,
inference(forward_demodulation,[],[f1867,f71]) ).
fof(f1874,plain,
sF2 = sF4,
inference(forward_demodulation,[],[f1868,f69]) ).
fof(f1876,plain,
sF20 = addition(sF19,sF5),
inference(superposition,[],[f101,f1873]) ).
fof(f1878,plain,
one = addition(sF5,sF2),
inference(superposition,[],[f143,f1873]) ).
fof(f1882,plain,
zero = multiplication(sF2,sF5),
inference(superposition,[],[f1025,f1873]) ).
fof(f1883,plain,
one = addition(sF5,one),
inference(superposition,[],[f1319,f1873]) ).
fof(f1887,plain,
one = addition(sF2,one),
inference(superposition,[],[f1320,f1874]) ).
fof(f1892,plain,
sF4 = multiplication(sF4,sF8),
inference(superposition,[],[f968,f1872]) ).
fof(f1895,plain,
sF2 = multiplication(sF2,sF8),
inference(forward_demodulation,[],[f1892,f1874]) ).
fof(f1900,plain,
sF17 = multiplication(sK0,sF14),
inference(superposition,[],[f95,f1869]) ).
fof(f1901,plain,
sF17 = multiplication(sK0,sF12),
inference(forward_demodulation,[],[f1900,f1871]) ).
fof(f1905,plain,
sF20 = addition(sF5,sF19),
inference(superposition,[],[f31,f1876]) ).
fof(f2113,plain,
one = addition(sF12,antidomain(sF12)),
inference(superposition,[],[f134,f85]) ).
fof(f2121,plain,
one = addition(sF18,antidomain(sF18)),
inference(superposition,[],[f134,f1860]) ).
fof(f2139,plain,
one = addition(sF18,sF19),
inference(forward_demodulation,[],[f2121,f99]) ).
fof(f2147,plain,
one = addition(sF12,sF13),
inference(forward_demodulation,[],[f2113,f87]) ).
fof(f2180,plain,
one = addition(sF12,one),
inference(superposition,[],[f447,f2147]) ).
fof(f2465,plain,
one = multiplication(antidomain(zero),one),
inference(superposition,[],[f211,f393]) ).
fof(f2472,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f2465,f36]) ).
fof(f2609,plain,
one = addition(sF10,coantidomain(sF10)),
inference(superposition,[],[f151,f81]) ).
fof(f2625,plain,
one = addition(sF10,sF11),
inference(forward_demodulation,[],[f2609,f83]) ).
fof(f2762,plain,
multiplication(antidomain(sF11),sF10) = multiplication(antidomain(sF11),one),
inference(superposition,[],[f188,f2625]) ).
fof(f2765,plain,
one = addition(sF10,one),
inference(superposition,[],[f447,f2625]) ).
fof(f2770,plain,
antidomain(sF11) = multiplication(antidomain(sF11),sF10),
inference(forward_demodulation,[],[f2762,f36]) ).
fof(f2772,plain,
sF12 = multiplication(sF12,sF10),
inference(forward_demodulation,[],[f2770,f85]) ).
fof(f2879,plain,
one = addition(sF8,one),
inference(superposition,[],[f447,f153]) ).
fof(f2889,plain,
one = addition(one,sF8),
inference(superposition,[],[f31,f2879]) ).
fof(f3037,plain,
multiplication(addition(sF2,one),sF8) = addition(sF2,sF8),
inference(superposition,[],[f159,f1895]) ).
fof(f3053,plain,
multiplication(addition(sF12,one),sF10) = addition(sF12,sF10),
inference(superposition,[],[f159,f2772]) ).
fof(f3098,plain,
addition(sF12,sF10) = multiplication(one,sF10),
inference(forward_demodulation,[],[f3053,f2180]) ).
fof(f3114,plain,
addition(sF2,sF8) = multiplication(one,sF8),
inference(forward_demodulation,[],[f3037,f1887]) ).
fof(f3144,plain,
sF10 = addition(sF12,sF10),
inference(forward_demodulation,[],[f3098,f37]) ).
fof(f3160,plain,
sF8 = addition(sF2,sF8),
inference(forward_demodulation,[],[f3114,f37]) ).
fof(f3901,plain,
! [X0,X1] : zero = multiplication(X1,coantidomain(addition(X0,X1))),
inference(superposition,[],[f1335,f31]) ).
fof(f4154,plain,
! [X2,X0,X1] : addition(multiplication(X0,coantidomain(coantidomain(X1))),multiplication(addition(X0,X2),coantidomain(X1))) = addition(multiplication(X0,one),multiplication(X2,coantidomain(X1))),
inference(superposition,[],[f1115,f48]) ).
fof(f4161,plain,
! [X0,X1] : addition(multiplication(X0,sF3),multiplication(addition(X0,X1),sF2)) = addition(multiplication(X0,one),multiplication(X1,sF2)),
inference(superposition,[],[f1115,f143]) ).
fof(f4172,plain,
! [X0,X1] : addition(multiplication(X0,sF18),multiplication(addition(X0,X1),sF19)) = addition(multiplication(X0,one),multiplication(X1,sF19)),
inference(superposition,[],[f1115,f2139]) ).
fof(f4449,plain,
! [X0,X1] : addition(multiplication(X0,sF18),multiplication(addition(X0,X1),sF19)) = addition(X0,multiplication(X1,sF19)),
inference(forward_demodulation,[],[f4172,f36]) ).
fof(f4459,plain,
! [X0,X1] : addition(multiplication(X0,sF3),multiplication(addition(X0,X1),sF2)) = addition(X0,multiplication(X1,sF2)),
inference(forward_demodulation,[],[f4161,f36]) ).
fof(f4466,plain,
! [X2,X0,X1] : addition(multiplication(X0,coantidomain(coantidomain(X1))),multiplication(addition(X0,X2),coantidomain(X1))) = addition(X0,multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[],[f4154,f36]) ).
fof(f4556,plain,
! [X0,X1] : addition(X0,multiplication(X1,sF2)) = addition(multiplication(X0,sF5),multiplication(addition(X0,X1),sF2)),
inference(forward_demodulation,[],[f4459,f1873]) ).
fof(f4684,plain,
! [X0,X1] : addition(X0,multiplication(X1,coantidomain(addition(X0,X1)))) = addition(multiplication(X0,coantidomain(coantidomain(addition(X0,X1)))),zero),
inference(superposition,[],[f4466,f46]) ).
fof(f4712,plain,
! [X0,X1] : multiplication(X0,coantidomain(coantidomain(addition(X0,X1)))) = addition(X0,multiplication(X1,coantidomain(addition(X0,X1)))),
inference(forward_demodulation,[],[f4684,f33]) ).
fof(f4774,plain,
! [X0,X1] : addition(X0,zero) = multiplication(X0,coantidomain(coantidomain(addition(X0,X1)))),
inference(forward_demodulation,[],[f4712,f3901]) ).
fof(f4807,plain,
! [X0,X1] : multiplication(X0,coantidomain(coantidomain(addition(X0,X1)))) = X0,
inference(forward_demodulation,[],[f4774,f33]) ).
fof(f5259,plain,
! [X0] : addition(X0,multiplication(X0,sF2)) = addition(multiplication(X0,sF5),multiplication(X0,sF2)),
inference(superposition,[],[f4556,f34]) ).
fof(f5289,plain,
addition(sF2,multiplication(sF8,sF2)) = addition(multiplication(sF2,sF5),multiplication(sF8,sF2)),
inference(superposition,[],[f4556,f3160]) ).
fof(f5297,plain,
addition(multiplication(sF8,sF5),multiplication(one,sF2)) = addition(sF8,multiplication(one,sF2)),
inference(superposition,[],[f4556,f2879]) ).
fof(f5347,plain,
addition(sF8,sF2) = addition(multiplication(sF8,sF5),sF2),
inference(forward_demodulation,[],[f5297,f37]) ).
fof(f5355,plain,
addition(sF2,multiplication(sF8,sF2)) = addition(zero,multiplication(sF8,sF2)),
inference(forward_demodulation,[],[f5289,f1882]) ).
fof(f5380,plain,
! [X0] : addition(X0,multiplication(X0,sF2)) = multiplication(X0,addition(sF5,sF2)),
inference(forward_demodulation,[],[f5259,f38]) ).
fof(f5399,plain,
addition(sF8,sF2) = addition(zero,sF2),
inference(forward_demodulation,[],[f5347,f711]) ).
fof(f5405,plain,
multiplication(sF8,sF2) = addition(sF2,multiplication(sF8,sF2)),
inference(forward_demodulation,[],[f5355,f212]) ).
fof(f5422,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sF2)),
inference(forward_demodulation,[],[f5380,f1878]) ).
fof(f5433,plain,
sF2 = addition(sF8,sF2),
inference(forward_demodulation,[],[f5399,f584]) ).
fof(f5438,plain,
multiplication(sF8,sF2) = multiplication(addition(one,sF8),sF2),
inference(forward_demodulation,[],[f5405,f156]) ).
fof(f5449,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,addition(one,sF2)),
inference(forward_demodulation,[],[f5422,f390]) ).
fof(f5459,plain,
multiplication(one,sF2) = multiplication(sF8,sF2),
inference(forward_demodulation,[],[f5438,f2889]) ).
fof(f5469,plain,
! [X0] : multiplication(X0,addition(one,sF2)) = X0,
inference(forward_demodulation,[],[f5449,f36]) ).
fof(f5477,plain,
sF2 = multiplication(sF8,sF2),
inference(forward_demodulation,[],[f5459,f37]) ).
fof(f5509,plain,
addition(sF8,sF2) = multiplication(sF8,addition(one,sF2)),
inference(superposition,[],[f390,f5477]) ).
fof(f5520,plain,
sF8 = addition(sF8,sF2),
inference(forward_demodulation,[],[f5509,f5469]) ).
fof(f5530,plain,
sF2 = sF8,
inference(forward_demodulation,[],[f5520,f5433]) ).
fof(f6331,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,[],[f291,f44]) ).
fof(f6433,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(X1))),X0),
inference(forward_demodulation,[],[f6331,f36]) ).
fof(f9491,plain,
sF10 = addition(sF10,sF12),
inference(superposition,[],[f31,f3144]) ).
fof(f17508,plain,
! [X0,X1] : zero = multiplication(antidomain(zero),multiplication(X0,antidomain(antidomain(multiplication(coantidomain(X0),X1))))),
inference(superposition,[],[f774,f487]) ).
fof(f17547,plain,
! [X0,X1] : zero = multiplication(one,multiplication(X0,antidomain(antidomain(multiplication(coantidomain(X0),X1))))),
inference(forward_demodulation,[],[f17508,f2472]) ).
fof(f17585,plain,
! [X0,X1] : zero = multiplication(X0,antidomain(antidomain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[],[f17547,f37]) ).
fof(f23581,plain,
addition(sF5,multiplication(one,sF19)) = addition(multiplication(sF5,sF18),multiplication(one,sF19)),
inference(superposition,[],[f4449,f1883]) ).
fof(f23582,plain,
addition(multiplication(sF5,sF18),multiplication(one,sF19)) = addition(sF5,multiplication(sF2,sF19)),
inference(superposition,[],[f4449,f1878]) ).
fof(f23740,plain,
addition(sF5,multiplication(sF2,sF19)) = addition(multiplication(sF5,sF18),sF19),
inference(forward_demodulation,[],[f23582,f37]) ).
fof(f23741,plain,
addition(sF5,sF19) = addition(multiplication(sF5,sF18),sF19),
inference(forward_demodulation,[],[f23581,f37]) ).
fof(f23861,plain,
addition(sF5,sF19) = addition(sF5,multiplication(sF2,sF19)),
inference(forward_demodulation,[],[f23741,f23740]) ).
fof(f23949,plain,
sF20 = addition(sF5,multiplication(sF2,sF19)),
inference(forward_demodulation,[],[f23861,f1905]) ).
fof(f26008,plain,
! [X0,X1] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(X0,antidomain(antidomain(antidomain(multiplication(coantidomain(X0),X1)))))),
inference(superposition,[],[f6433,f17585]) ).
fof(f26101,plain,
! [X0,X1] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(X0,antidomain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[],[f26008,f1824]) ).
fof(f26147,plain,
! [X0,X1] : multiplication(one,X0) = multiplication(one,multiplication(X0,antidomain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[],[f26101,f2472]) ).
fof(f26165,plain,
! [X0,X1] : multiplication(one,X0) = multiplication(X0,antidomain(multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[],[f26147,f37]) ).
fof(f26170,plain,
! [X0,X1] : multiplication(X0,antidomain(multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[],[f26165,f37]) ).
fof(f26205,plain,
! [X0] : multiplication(X0,antidomain(coantidomain(X0))) = X0,
inference(superposition,[],[f26170,f4807]) ).
fof(f26338,plain,
sF10 = multiplication(sF10,antidomain(sF11)),
inference(superposition,[],[f26205,f83]) ).
fof(f26421,plain,
sF10 = multiplication(sF10,sF12),
inference(forward_demodulation,[],[f26338,f85]) ).
fof(f26484,plain,
addition(sF10,sF12) = multiplication(addition(sF10,one),sF12),
inference(superposition,[],[f159,f26421]) ).
fof(f26514,plain,
addition(sF10,sF12) = multiplication(one,sF12),
inference(forward_demodulation,[],[f26484,f2765]) ).
fof(f26528,plain,
sF12 = addition(sF10,sF12),
inference(forward_demodulation,[],[f26514,f37]) ).
fof(f26536,plain,
sF10 = sF12,
inference(forward_demodulation,[],[f26528,f9491]) ).
fof(f26546,plain,
sF17 = multiplication(sK0,sF10),
inference(superposition,[],[f1901,f26536]) ).
fof(f26560,plain,
multiplication(sF9,sF10) = multiplication(sF8,sF17),
inference(superposition,[],[f463,f26546]) ).
fof(f26604,plain,
multiplication(sF9,sF10) = multiplication(sF2,sF17),
inference(forward_demodulation,[],[f26560,f5530]) ).
fof(f26613,plain,
zero = multiplication(sF2,sF17),
inference(forward_demodulation,[],[f26604,f244]) ).
fof(f41072,plain,
zero = multiplication(antidomain(zero),multiplication(sF2,antidomain(antidomain(sF17)))),
inference(superposition,[],[f774,f26613]) ).
fof(f41083,plain,
zero = multiplication(antidomain(zero),multiplication(sF2,antidomain(sF18))),
inference(forward_demodulation,[],[f41072,f97]) ).
fof(f41109,plain,
zero = multiplication(antidomain(zero),multiplication(sF2,sF19)),
inference(forward_demodulation,[],[f41083,f99]) ).
fof(f41125,plain,
zero = multiplication(one,multiplication(sF2,sF19)),
inference(forward_demodulation,[],[f41109,f2472]) ).
fof(f41136,plain,
zero = multiplication(sF2,sF19),
inference(forward_demodulation,[],[f41125,f37]) ).
fof(f41147,plain,
sF20 = addition(sF5,zero),
inference(superposition,[],[f23949,f41136]) ).
fof(f41207,plain,
sF5 = sF20,
inference(forward_demodulation,[],[f41147,f33]) ).
fof(f41237,plain,
sF3 != sF5,
inference(superposition,[],[f102,f41207]) ).
fof(f41259,plain,
$false,
inference(forward_subsumption_resolution,[],[f41237,f1873]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE109+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n004.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 27 13:10:36 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 20.16/3.81 % (3510028)Detected formulas, will run a generic FOF schedule.
% 20.16/3.81 % (3510038)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1642032229:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 20.16/3.81 % (3510037)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=370325692:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 20.16/3.81 % (3510033)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=2253460908:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 20.16/3.81 % (3510036)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1476466326:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 20.16/3.81 % (3510035)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=2193462568:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 20.16/3.81 % (3510039)dis-21_1_sil=8000:lcm=predicate:random_seed=2666074663: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)
% 20.16/3.81 % (3510034)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=811283020:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 20.16/3.81 % (3510036)Refutation not found, incomplete strategy
% 20.16/3.81 % (3510036)------------------------------
% 20.16/3.81 % (3510036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.16/3.81 % (3510036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.16/3.81 % (3510036)CaDiCaL version: 2.1.3
% 20.16/3.81 % (3510036)Termination reason: Refutation not found, incomplete strategy
% 20.16/3.81 % (3510036)Time elapsed: 0.002 s
% 20.16/3.81 % (3510036)Peak memory usage: 88 MB
% 20.16/3.81 % (3510039)Refutation not found, incomplete strategy
% 20.16/3.81 % (3510039)------------------------------
% 20.16/3.81 % (3510039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.16/3.81 % (3510039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.16/3.81 % (3510039)CaDiCaL version: 2.1.3
% 20.16/3.81 % (3510039)Termination reason: Refutation not found, incomplete strategy
% 20.16/3.81 % (3510039)Time elapsed: 0.003 s
% 20.16/3.81 % (3510039)Peak memory usage: 88 MB
% 20.16/3.81 % (3510039)Instructions burned: 1 (million)
% 20.16/3.81 % (3510038)Instruction limit reached!
% 20.16/3.81 % (3510038)------------------------------
% 20.16/3.81 % (3510038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.16/3.81 % (3510038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.16/3.81 % (3510038)CaDiCaL version: 2.1.3
% 20.16/3.81 % (3510038)Termination reason: Instruction limit
% 20.16/3.81 % (3510038)Termination phase: Saturation
% 20.16/3.81 % (3510038)Time elapsed: 0.067 s
% 20.16/3.81 % (3510038)Peak memory usage: 89 MB
% 20.16/3.81 % (3510038)Instructions burned: 140 (million)
% 20.16/3.81 % (3510037)Instruction limit reached!
% 20.16/3.81 % (3510037)------------------------------
% 20.16/3.81 % (3510037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.16/3.81 % (3510037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.16/3.81 % (3510037)CaDiCaL version: 2.1.3
% 20.16/3.81 % (3510037)Termination reason: Instruction limit
% 20.16/3.81 % (3510037)Termination phase: Saturation
% 20.16/3.81 % (3510037)Time elapsed: 0.119 s
% 20.16/3.81 % (3510037)Peak memory usage: 89 MB
% 20.16/3.81 % (3510037)Instructions burned: 119 (million)
% 20.16/3.81 % (3510047)lrs+10_1_sil=8000:sp=occurrence:random_seed=1326727728:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 20.16/3.81 % (3510036)------------------------------
% 20.16/3.81 % (3510036)------------------------------
% 20.16/3.81 % (3510039)------------------------------
% 20.16/3.81 % (3510039)------------------------------
% 20.16/3.81 % (3510048)lrs+10_1_sil=32000:urr=on:br=off:random_seed=260854068:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 20.16/3.81 % (3510047)Instruction limit reached!
% 20.16/3.81 % (3510047)------------------------------
% 20.16/3.81 % (3510047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.16/3.81 % (3510047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510047)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510047)Termination reason: Instruction limit
% 25.22/4.57 % (3510047)Termination phase: Saturation
% 25.22/4.57 % (3510047)Time elapsed: 0.152 s
% 25.22/4.57 % (3510047)Peak memory usage: 91 MB
% 25.22/4.57 % (3510047)Instructions burned: 287 (million)
% 25.22/4.57 % (3510048)Instruction limit reached!
% 25.22/4.57 % (3510048)------------------------------
% 25.22/4.57 % (3510048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510048)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510048)Termination reason: Instruction limit
% 25.22/4.57 % (3510048)Termination phase: Saturation
% 25.22/4.57 % (3510048)Time elapsed: 0.142 s
% 25.22/4.57 % (3510048)Peak memory usage: 89 MB
% 25.22/4.57 % (3510048)Instructions burned: 158 (million)
% 25.22/4.57 % (3510052)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=1495780538:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 25.22/4.57 % (3510050)lrs+1011_1_sil=32000:sp=occurrence:random_seed=795668112:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 25.22/4.57 % (3510053)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=200622533:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 25.22/4.57 % (3510053)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510053)------------------------------
% 25.22/4.57 % (3510053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510053)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510053)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510053)Time elapsed: 0.002 s
% 25.22/4.57 % (3510053)Peak memory usage: 88 MB
% 25.22/4.57 % (3510053)Instructions burned: 2 (million)
% 25.22/4.57 % (3510054)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=333240467:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 25.22/4.57 % (3510052)Instruction limit reached!
% 25.22/4.57 % (3510052)------------------------------
% 25.22/4.57 % (3510052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510052)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510052)Termination reason: Instruction limit
% 25.22/4.57 % (3510052)Termination phase: Saturation
% 25.22/4.57 % (3510052)Time elapsed: 0.239 s
% 25.22/4.57 % (3510052)Peak memory usage: 91 MB
% 25.22/4.57 % (3510052)Instructions burned: 248 (million)
% 25.22/4.57 % (3510035)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510035)------------------------------
% 25.22/4.57 % (3510035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510035)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510035)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510035)Time elapsed: 0.971 s
% 25.22/4.57 % (3510035)Peak memory usage: 127 MB
% 25.22/4.57 % (3510035)Instructions burned: 895 (million)
% 25.22/4.57 % (3510050)Instruction limit reached!
% 25.22/4.57 % (3510050)------------------------------
% 25.22/4.57 % (3510050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510050)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510050)Termination reason: Instruction limit
% 25.22/4.57 % (3510050)Termination phase: Saturation
% 25.22/4.57 % (3510050)Time elapsed: 0.324 s
% 25.22/4.57 % (3510050)Peak memory usage: 92 MB
% 25.22/4.57 % (3510050)Instructions burned: 325 (million)
% 25.22/4.57 % (3510053)------------------------------
% 25.22/4.57 % (3510053)------------------------------
% 25.22/4.57 % (3510059)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1719565806:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 25.22/4.57 % (3510059)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510059)------------------------------
% 25.22/4.57 % (3510059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510059)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510059)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510059)Time elapsed: 0.004 s
% 25.22/4.57 % (3510059)Peak memory usage: 89 MB
% 25.22/4.57 % (3510059)Instructions burned: 2 (million)
% 25.22/4.57 % (3510060)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3319499220:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 25.22/4.57 % (3510060)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510060)------------------------------
% 25.22/4.57 % (3510060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510060)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510060)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510060)Time elapsed: 0.002 s
% 25.22/4.57 % (3510060)Peak memory usage: 88 MB
% 25.22/4.57 % (3510060)Instructions burned: 1 (million)
% 25.22/4.57 % (3510061)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3359524995:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2986 on theBenchmark for (2986ds/114Mi)
% 25.22/4.57 % (3510061)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510061)------------------------------
% 25.22/4.57 % (3510061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510061)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510061)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510061)Time elapsed: 0.003 s
% 25.22/4.57 % (3510061)Peak memory usage: 88 MB
% 25.22/4.57 % (3510061)Instructions burned: 1 (million)
% 25.22/4.57 % (3510035)------------------------------
% 25.22/4.57 % (3510035)------------------------------
% 25.22/4.57 % (3510059)------------------------------
% 25.22/4.57 % (3510059)------------------------------
% 25.22/4.57 % (3510060)------------------------------
% 25.22/4.57 % (3510060)------------------------------
% 25.22/4.57 % (3510065)lrs+10_1_sil=8000:sp=occurrence:random_seed=101571366:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2983 on theBenchmark for (2983ds/907Mi)
% 25.22/4.57 % (3510061)------------------------------
% 25.22/4.57 % (3510061)------------------------------
% 25.22/4.57 % (3510066)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4093067971:i=437:sd=1:aac=none:ss=included_2981 on theBenchmark for (2981ds/437Mi)
% 25.22/4.57 % (3510066)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510066)------------------------------
% 25.22/4.57 % (3510066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510066)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510066)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510066)Time elapsed: 0.002 s
% 25.22/4.57 % (3510066)Peak memory usage: 88 MB
% 25.22/4.57 % (3510068)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=816448873:i=5202:ss=axioms:sgt=16_2980 on theBenchmark for (2980ds/5202Mi)
% 25.22/4.57 % (3510069)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1934136892:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2979 on theBenchmark for (2979ds/134Mi)
% 25.22/4.57 % (3510069)Refutation not found, incomplete strategy
% 25.22/4.57 % (3510069)------------------------------
% 25.22/4.57 % (3510069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510069)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510069)Termination reason: Refutation not found, incomplete strategy
% 25.22/4.57 % (3510069)Time elapsed: 0.003 s
% 25.22/4.57 % (3510069)Peak memory usage: 88 MB
% 25.22/4.57 % (3510069)Instructions burned: 1 (million)
% 25.22/4.57 % (3510066)------------------------------
% 25.22/4.57 % (3510066)------------------------------
% 25.22/4.57 % (3510069)------------------------------
% 25.22/4.57 % (3510069)------------------------------
% 25.22/4.57 % (3510065)Instruction limit reached!
% 25.22/4.57 % (3510065)------------------------------
% 25.22/4.57 % (3510065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510065)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510065)Termination reason: Instruction limit
% 25.22/4.57 % (3510065)Termination phase: Saturation
% 25.22/4.57 % (3510065)Time elapsed: 0.888 s
% 25.22/4.57 % (3510065)Peak memory usage: 97 MB
% 25.22/4.57 % (3510065)Instructions burned: 907 (million)
% 25.22/4.57 % (3510073)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2284934388:st=8:i=592:sd=3:ep=RST:ss=axioms_2974 on theBenchmark for (2974ds/592Mi)
% 25.22/4.57 % (3510074)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=955801192:st=3:i=13193:sd=3:ss=axioms_2972 on theBenchmark for (2972ds/13193Mi)
% 25.22/4.57 % (3510075)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=1354385867:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2971 on theBenchmark for (2971ds/125Mi)
% 25.22/4.57 % (3510075)Instruction limit reached!
% 25.22/4.57 % (3510075)------------------------------
% 25.22/4.57 % (3510075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510075)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510075)Termination reason: Instruction limit
% 25.22/4.57 % (3510075)Termination phase: Saturation
% 25.22/4.57 % (3510075)Time elapsed: 0.142 s
% 25.22/4.57 % (3510075)Peak memory usage: 90 MB
% 25.22/4.57 % (3510075)Instructions burned: 126 (million)
% 25.22/4.57 % (3510033)First to succeed.
% 25.22/4.57 % (3510033)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3510028"
% 25.22/4.57 % (3510073)Instruction limit reached!
% 25.22/4.57 % (3510073)------------------------------
% 25.22/4.57 % (3510073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.22/4.57 % (3510073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/4.57 % (3510073)CaDiCaL version: 2.1.3
% 25.22/4.57 % (3510073)Termination reason: Instruction limit
% 25.22/4.57 % (3510073)Termination phase: Saturation
% 25.22/4.57 % (3510073)Time elapsed: 0.576 s
% 25.22/4.57 % (3510073)Peak memory usage: 95 MB
% 25.22/4.57 % (3510073)Instructions burned: 592 (million)
% 25.22/4.57 % (3510033)Refutation found. Thanks to Tanya!
% 25.22/4.57 % SZS status Theorem for theBenchmark
% 25.22/4.57 % SZS output start Proof for theBenchmark
% See solution above
% 26.05/4.76 % (3510033)------------------------------
% 26.05/4.76 % (3510033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.05/4.76 % (3510033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.05/4.76 % (3510033)CaDiCaL version: 2.1.3
% 26.05/4.76 % (3510033)Termination reason: Refutation
% 26.05/4.76 % (3510033)Time elapsed: 3.069 s
% 26.05/4.76 % (3510033)Peak memory usage: 170 MB
% 26.05/4.76 % (3510033)Instructions burned: 4975 (million)
% 26.05/4.76 % (3510033)------------------------------
% 26.05/4.76 % (3510033)------------------------------
% 26.05/4.76 % (3510028)Success in time 3.608 s
% 26.05/4.76 % Vampire exiting
%------------------------------------------------------------------------------