%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG027-9 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:11 PM UTC 2026
% Result : Unsatisfiable 43.78s 16.16s
% Output : Refutation 109.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 22
% Syntax : Number of formulae : 260 ( 260 unt; 4 def)
% Number of atoms : 260 ( 259 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 637 ( 637 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f3,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f4,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f16,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
fof(f17,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_alternative) ).
fof(f18,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
fof(f20,axiom,
! [X0,X1] : multiply(additive_inverse(X0),additive_inverse(X1)) = multiply(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses) ).
fof(f21,plain,
! [X0,X1] : multiply(X0,X1) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
fof(f23,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
fof(f25,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
associator(x,multiply(x,y),z) != multiply(associator(x,y,z),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_moufang) ).
fof(f31,definition,
sF0 = multiply(x,y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f32,plain,
multiply(x,y) = sF0,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF1 = associator(x,sF0,z),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f34,plain,
associator(x,sF0,z) = sF1,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF2 = associator(x,y,z),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f36,plain,
associator(x,y,z) = sF2,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF3 = multiply(sF2,x),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f38,plain,
multiply(sF2,x) = sF3,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
sF1 != sF3,
inference(definition_folding,[],[f30,f38,f36,f34,f32]) ).
fof(f44,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(additive_inverse(X0),multiply(X1,X2))),
inference(forward_demodulation,[],[f18,f23]) ).
fof(f49,plain,
! [X0] : associator(x,y,X0) = add(multiply(sF0,X0),multiply(additive_inverse(x),multiply(y,X0))),
inference(superposition,[],[f44,f32]) ).
fof(f53,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),multiply(additive_inverse(X0),multiply(add(X1,X2),X3))),
inference(superposition,[],[f44,f12]) ).
fof(f54,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(add(multiply(multiply(X0,X1),X2),multiply(multiply(X0,X1),X3)),multiply(additive_inverse(X0),multiply(X1,add(X2,X3)))),
inference(superposition,[],[f44,f12]) ).
fof(f55,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(multiply(X0,X1),X3),multiply(additive_inverse(X0),multiply(X1,add(X2,X3))))),
inference(forward_demodulation,[],[f54,f15]) ).
fof(f56,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),multiply(additive_inverse(X0),add(multiply(X1,X3),multiply(X2,X3)))),
inference(forward_demodulation,[],[f53,f13]) ).
fof(f58,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(multiply(X0,X1),X3),multiply(additive_inverse(X0),add(multiply(X1,X2),multiply(X1,X3))))),
inference(forward_demodulation,[],[f55,f12]) ).
fof(f59,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),add(multiply(additive_inverse(X0),multiply(X1,X3)),multiply(additive_inverse(X0),multiply(X2,X3)))),
inference(forward_demodulation,[],[f56,f12]) ).
fof(f61,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(multiply(X0,X1),X3),add(multiply(additive_inverse(X0),multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,X3))))),
inference(forward_demodulation,[],[f58,f12]) ).
fof(f62,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(add(multiply(multiply(X0,X1),X3),multiply(multiply(X0,X2),X3)),add(multiply(additive_inverse(X0),multiply(X1,X3)),multiply(additive_inverse(X0),multiply(X2,X3)))),
inference(forward_demodulation,[],[f59,f13]) ).
fof(f64,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(multiply(multiply(X0,X2),X3),add(multiply(additive_inverse(X0),multiply(X1,X3)),multiply(additive_inverse(X0),multiply(X2,X3))))),
inference(forward_demodulation,[],[f62,f15]) ).
fof(f69,plain,
! [X0,X1] : associator(X0,X1,X1) = add(multiply(X0,multiply(X1,X1)),multiply(additive_inverse(X0),multiply(X1,X1))),
inference(superposition,[],[f44,f16]) ).
fof(f71,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(multiply(X0,multiply(X1,X1)),X2),multiply(additive_inverse(multiply(X0,X1)),multiply(X1,X2))),
inference(superposition,[],[f44,f16]) ).
fof(f74,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(multiply(X0,multiply(X1,X1)),X2),multiply(multiply(additive_inverse(X0),X1),multiply(X1,X2))),
inference(forward_demodulation,[],[f71,f23]) ).
fof(f122,plain,
! [X0,X1] : associator(X0,X0,X1) = add(multiply(X0,multiply(X0,X1)),multiply(additive_inverse(X0),multiply(X0,X1))),
inference(superposition,[],[f44,f17]) ).
fof(f155,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(multiply(add(multiply(X0,X1),multiply(X2,X1)),X3),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3))),
inference(superposition,[],[f44,f13]) ).
fof(f160,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(add(multiply(multiply(X0,X1),X3),multiply(multiply(X2,X1),X3)),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3))),
inference(forward_demodulation,[],[f155,f13]) ).
fof(f166,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(multiply(multiply(X0,X1),X3),add(multiply(multiply(X2,X1),X3),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3)))),
inference(forward_demodulation,[],[f160,f15]) ).
fof(f198,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(additive_inverse(X0),multiply(X1,X2)),multiply(multiply(X0,X1),X2)),
inference(superposition,[],[f44,f14]) ).
fof(f204,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),add(multiply(additive_inverse(X0),multiply(X1,X2)),X3)) = add(associator(X0,X1,X2),X3),
inference(superposition,[],[f15,f44]) ).
fof(f211,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f224,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = add(additive_identity,X1),
inference(superposition,[],[f15,f8]) ).
fof(f227,plain,
! [X0,X1] : add(multiply(additive_inverse(X0),X1),multiply(X0,X1)) = multiply(additive_identity,X1),
inference(superposition,[],[f13,f8]) ).
fof(f230,plain,
! [X0,X1] : additive_identity = add(multiply(additive_inverse(X0),X1),multiply(X0,X1)),
inference(forward_demodulation,[],[f227,f4]) ).
fof(f231,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f224,f1]) ).
fof(f233,plain,
! [X0,X1] : additive_identity = add(multiply(X0,X1),multiply(additive_inverse(X0),X1)),
inference(forward_demodulation,[],[f230,f14]) ).
fof(f234,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X1),
inference(backward_demodulation,[],[f69,f233]) ).
fof(f235,plain,
! [X0,X1] : additive_identity = associator(X0,X0,X1),
inference(backward_demodulation,[],[f122,f233]) ).
fof(f237,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f231,f14]) ).
fof(f239,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),multiply(X1,X2)) = add(additive_inverse(multiply(multiply(X0,X1),X2)),associator(X0,X1,X2)),
inference(superposition,[],[f231,f44]) ).
fof(f246,plain,
! [X0,X1] : add(add(X1,X0),additive_inverse(X1)) = X0,
inference(superposition,[],[f14,f231]) ).
fof(f251,plain,
! [X0,X1] : add(X1,add(X0,additive_inverse(X1))) = X0,
inference(forward_demodulation,[],[f246,f15]) ).
fof(f257,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),multiply(X1,X2)) = add(associator(X0,X1,X2),additive_inverse(multiply(multiply(X0,X1),X2))),
inference(forward_demodulation,[],[f239,f14]) ).
fof(f258,plain,
! [X0,X1] : add(X1,add(additive_inverse(X1),X0)) = X0,
inference(forward_demodulation,[],[f237,f211]) ).
fof(f260,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),multiply(X1,X2)) = add(associator(X0,X1,X2),multiply(additive_inverse(multiply(X0,X1)),X2)),
inference(forward_demodulation,[],[f257,f23]) ).
fof(f261,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),multiply(X1,X2)) = add(associator(X0,X1,X2),multiply(multiply(additive_inverse(X0),X1),X2)),
inference(forward_demodulation,[],[f260,f23]) ).
fof(f296,plain,
! [X2,X0,X1] : add(multiply(X0,additive_inverse(X1)),add(multiply(X0,X1),X2)) = X2,
inference(superposition,[],[f231,f25]) ).
fof(f306,plain,
! [X0,X1] : multiply(additive_inverse(X0),multiply(X0,X1)) = add(additive_identity,multiply(multiply(additive_inverse(X0),X0),X1)),
inference(superposition,[],[f261,f235]) ).
fof(f307,plain,
! [X0,X1] : multiply(additive_inverse(X0),multiply(X0,X1)) = multiply(multiply(additive_inverse(X0),X0),X1),
inference(forward_demodulation,[],[f306,f1]) ).
fof(f310,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = add(associator(additive_inverse(X0),X1,X2),multiply(multiply(X0,X1),X2)),
inference(superposition,[],[f261,f11]) ).
fof(f313,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(multiply(multiply(additive_inverse(X0),X1),X2),multiply(X0,multiply(X1,X2))),
inference(superposition,[],[f44,f11]) ).
fof(f314,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(multiply(X0,multiply(X1,X2)),multiply(multiply(additive_inverse(X0),X1),X2)),
inference(forward_demodulation,[],[f313,f14]) ).
fof(f323,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(superposition,[],[f25,f23]) ).
fof(f326,plain,
! [X2,X0,X1] : add(multiply(additive_inverse(X0),X1),add(multiply(X0,X1),X2)) = X2,
inference(superposition,[],[f231,f23]) ).
fof(f348,plain,
! [X0,X1] : additive_identity = add(X0,add(X1,additive_inverse(add(X0,X1)))),
inference(superposition,[],[f15,f10]) ).
fof(f354,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,additive_inverse(X1)),additive_inverse(X2)),
inference(superposition,[],[f21,f25]) ).
fof(f356,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(additive_inverse(X2),multiply(additive_inverse(X0),X1)),
inference(superposition,[],[f21,f23]) ).
fof(f363,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),additive_inverse(X1)) = add(multiply(multiply(X2,additive_inverse(X0)),additive_inverse(X1)),multiply(additive_inverse(X2),multiply(X0,X1))),
inference(superposition,[],[f44,f21]) ).
fof(f364,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),additive_inverse(X1),X2) = add(multiply(multiply(X0,X1),X2),multiply(additive_inverse(additive_inverse(X0)),multiply(additive_inverse(X1),X2))),
inference(superposition,[],[f44,f21]) ).
fof(f367,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),additive_inverse(X1),X2) = add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(additive_inverse(X1),X2))),
inference(forward_demodulation,[],[f364,f11]) ).
fof(f373,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),additive_inverse(X1)) = add(multiply(multiply(X2,X0),X1),multiply(additive_inverse(X2),multiply(X0,X1))),
inference(backward_demodulation,[],[f363,f354]) ).
fof(f374,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),additive_inverse(X1)) = associator(X2,X0,X1),
inference(forward_demodulation,[],[f373,f44]) ).
fof(f379,plain,
! [X0,X1] : add(multiply(multiply(sF0,X0),X1),multiply(multiply(additive_inverse(x),multiply(y,X0)),X1)) = multiply(associator(x,y,X0),X1),
inference(superposition,[],[f13,f49]) ).
fof(f402,plain,
! [X2,X0,X1] : associator(multiply(additive_inverse(X0),X0),X1,X2) = add(multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2),multiply(additive_inverse(multiply(additive_inverse(X0),X0)),multiply(X1,X2))),
inference(superposition,[],[f44,f307]) ).
fof(f407,plain,
! [X2,X0,X1] : associator(multiply(additive_inverse(X0),X0),X1,X2) = add(multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2),multiply(multiply(additive_inverse(additive_inverse(X0)),X0),multiply(X1,X2))),
inference(forward_demodulation,[],[f402,f23]) ).
fof(f419,plain,
! [X2,X0,X1] : associator(multiply(additive_inverse(X0),X0),X1,X2) = add(multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2),multiply(multiply(additive_inverse(X0),additive_inverse(X0)),multiply(X1,X2))),
inference(forward_demodulation,[],[f407,f323]) ).
fof(f427,plain,
! [X2,X0,X1] : associator(multiply(additive_inverse(X0),X0),X1,X2) = add(multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2),multiply(additive_inverse(X0),multiply(additive_inverse(X0),multiply(X1,X2)))),
inference(forward_demodulation,[],[f419,f17]) ).
fof(f433,plain,
! [X2,X0,X1] : associator(multiply(additive_inverse(X0),X0),X1,X2) = add(multiply(additive_inverse(X0),multiply(additive_inverse(X0),multiply(X1,X2))),multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2)),
inference(forward_demodulation,[],[f427,f14]) ).
fof(f436,plain,
! [X2,X0,X1] : associator(multiply(additive_inverse(X0),X0),X1,X2) = add(multiply(X0,multiply(X0,multiply(X1,X2))),multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2)),
inference(forward_demodulation,[],[f433,f356]) ).
fof(f439,plain,
! [X2,X0,X1] : add(multiply(X0,multiply(X0,multiply(X1,X2))),multiply(multiply(additive_inverse(X0),multiply(X0,X1)),X2)) = associator(multiply(X0,additive_inverse(X0)),X1,X2),
inference(forward_demodulation,[],[f436,f323]) ).
fof(f467,plain,
! [X2,X0,X1] : associator(additive_inverse(additive_inverse(X0)),additive_inverse(additive_inverse(X1)),X2) = add(multiply(multiply(X0,X1),X2),multiply(additive_inverse(X0),multiply(additive_inverse(additive_inverse(X1)),X2))),
inference(superposition,[],[f367,f21]) ).
fof(f507,plain,
! [X2,X0,X1] : add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(additive_inverse(X1),X2))) = associator(additive_inverse(additive_inverse(X0)),additive_inverse(additive_inverse(X1)),X2),
inference(forward_demodulation,[],[f467,f356]) ).
fof(f527,plain,
! [X2,X0,X1] : add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(additive_inverse(X1),X2))) = associator(additive_inverse(additive_inverse(X0)),X1,X2),
inference(forward_demodulation,[],[f507,f11]) ).
fof(f544,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(additive_inverse(X1),X2))),
inference(forward_demodulation,[],[f527,f11]) ).
fof(f552,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(additive_inverse(X0),additive_inverse(X1),X2),
inference(backward_demodulation,[],[f367,f544]) ).
fof(f587,plain,
! [X2,X0,X1] : associator(additive_inverse(X1),X0,X2) = associator(X1,additive_inverse(X0),X2),
inference(superposition,[],[f552,f11]) ).
fof(f604,plain,
! [X2,X0,X1] : associator(X1,X2,additive_inverse(X0)) = associator(X1,additive_inverse(X2),X0),
inference(superposition,[],[f374,f11]) ).
fof(f781,plain,
! [X2,X0,X1] : add(X2,add(X0,X1)) = add(X0,add(X2,X1)),
inference(superposition,[],[f211,f14]) ).
fof(f783,plain,
! [X2,X3,X0,X1] : add(add(X0,X1),add(X3,X2)) = add(X3,add(X0,add(X1,X2))),
inference(superposition,[],[f211,f211]) ).
fof(f786,plain,
! [X2,X3,X0,X1] : add(X3,add(X0,add(X1,X2))) = add(X2,add(X3,add(X0,X1))),
inference(superposition,[],[f211,f15]) ).
fof(f873,plain,
! [X2,X3,X0,X1] : add(X3,add(X0,add(X1,X2))) = add(X0,add(X1,add(X3,X2))),
inference(forward_demodulation,[],[f783,f15]) ).
fof(f889,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(X2,multiply(additive_inverse(X0),X1))) = X2,
inference(superposition,[],[f251,f23]) ).
fof(f1140,plain,
! [X2,X3,X0,X1] : add(multiply(X0,multiply(X1,X2)),add(multiply(multiply(additive_inverse(X0),X1),X2),X3)) = add(associator(additive_inverse(X0),X1,X2),X3),
inference(superposition,[],[f15,f314]) ).
fof(f1143,plain,
! [X2,X0,X1] : multiply(multiply(additive_inverse(X0),X1),X2) = add(additive_inverse(multiply(X0,multiply(X1,X2))),associator(additive_inverse(X0),X1,X2)),
inference(superposition,[],[f231,f314]) ).
fof(f1144,plain,
! [X2,X0,X1] : multiply(multiply(additive_inverse(X0),X1),X2) = add(associator(additive_inverse(X0),X1,X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f1143,f14]) ).
fof(f1160,plain,
! [X2,X0,X1] : multiply(multiply(additive_inverse(X0),X1),X2) = add(associator(additive_inverse(X0),X1,X2),multiply(additive_inverse(X0),multiply(X1,X2))),
inference(forward_demodulation,[],[f1144,f23]) ).
fof(f1197,plain,
! [X2,X3,X0,X1] : add(associator(additive_inverse(X0),X1,X2),X3) = add(multiply(X0,multiply(X1,X2)),add(add(associator(additive_inverse(X0),X1,X2),multiply(additive_inverse(X0),multiply(X1,X2))),X3)),
inference(backward_demodulation,[],[f1140,f1160]) ).
fof(f1199,plain,
! [X2,X0,X1] : associator(multiply(X0,additive_inverse(X0)),X1,X2) = add(multiply(X0,multiply(X0,multiply(X1,X2))),add(associator(additive_inverse(X0),multiply(X0,X1),X2),multiply(additive_inverse(X0),multiply(multiply(X0,X1),X2)))),
inference(backward_demodulation,[],[f439,f1160]) ).
fof(f1204,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(multiply(X0,multiply(X1,X1)),X2),add(associator(additive_inverse(X0),X1,multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,multiply(X1,X2))))),
inference(backward_demodulation,[],[f74,f1160]) ).
fof(f1212,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(multiply(multiply(sF0,X0),X1),add(associator(additive_inverse(x),multiply(y,X0),X1),multiply(additive_inverse(x),multiply(multiply(y,X0),X1)))),
inference(backward_demodulation,[],[f379,f1160]) ).
fof(f1230,plain,
! [X2,X3,X0,X1] : add(associator(additive_inverse(X0),X1,X2),X3) = add(multiply(X0,multiply(X1,X2)),add(associator(additive_inverse(X0),X1,X2),add(multiply(additive_inverse(X0),multiply(X1,X2)),X3))),
inference(forward_demodulation,[],[f1197,f15]) ).
fof(f1555,plain,
! [X0] : multiply(x,multiply(y,X0)) = add(associator(additive_inverse(x),y,X0),multiply(sF0,X0)),
inference(superposition,[],[f310,f32]) ).
fof(f1569,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(additive_inverse(associator(additive_inverse(X0),X1,X2)),multiply(X0,multiply(X1,X2))),
inference(superposition,[],[f231,f310]) ).
fof(f1570,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(multiply(X0,multiply(X1,X2)),additive_inverse(associator(additive_inverse(X0),X1,X2))),
inference(forward_demodulation,[],[f1569,f14]) ).
fof(f1704,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(additive_inverse(X0),X1),X2),add(multiply(multiply(X0,X1),X2),X3)) = X3,
inference(superposition,[],[f326,f23]) ).
fof(f1706,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(multiply(additive_inverse(X0),X1),X2)) = X2,
inference(superposition,[],[f326,f11]) ).
fof(f1752,plain,
! [X2,X3,X0,X1] : add(X1,X0) = add(add(multiply(X2,X3),X0),add(X1,multiply(additive_inverse(X2),X3))),
inference(superposition,[],[f211,f326]) ).
fof(f1757,plain,
! [X2,X3,X0,X1] : add(X1,X0) = add(multiply(X2,X3),add(X0,add(X1,multiply(additive_inverse(X2),X3)))),
inference(forward_demodulation,[],[f1752,f15]) ).
fof(f1798,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),add(multiply(multiply(additive_inverse(X0),X1),X2),X3)) = X3,
inference(forward_demodulation,[],[f1704,f781]) ).
fof(f1819,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),add(add(associator(additive_inverse(X0),X1,X2),multiply(additive_inverse(X0),multiply(X1,X2))),X3)) = X3,
inference(forward_demodulation,[],[f1798,f1160]) ).
fof(f1829,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),add(associator(additive_inverse(X0),X1,X2),add(multiply(additive_inverse(X0),multiply(X1,X2)),X3))) = X3,
inference(forward_demodulation,[],[f1819,f15]) ).
fof(f1896,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(multiply(additive_inverse(additive_inverse(X0)),multiply(X1,X2)),associator(X0,X1,X2)),
inference(superposition,[],[f326,f198]) ).
fof(f1902,plain,
! [X2,X3,X0,X1] : add(X3,associator(X0,X1,X2)) = add(multiply(multiply(X0,X1),X2),add(X3,multiply(additive_inverse(X0),multiply(X1,X2)))),
inference(superposition,[],[f211,f198]) ).
fof(f1906,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(additive_inverse(X0),multiply(X1,X2)),associator(X0,X1,X3))),
inference(backward_demodulation,[],[f61,f1902]) ).
fof(f1907,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(multiply(additive_inverse(X0),multiply(X1,X3)),associator(X0,X2,X3))),
inference(backward_demodulation,[],[f64,f1902]) ).
fof(f1909,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(associator(X0,X1,X2),multiply(additive_inverse(additive_inverse(X0)),multiply(X1,X2))),
inference(forward_demodulation,[],[f1896,f14]) ).
fof(f1933,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(associator(X0,X1,X3),associator(X0,X2,X3)),
inference(forward_demodulation,[],[f1907,f204]) ).
fof(f1934,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(associator(X0,X1,X2),associator(X0,X1,X3)),
inference(forward_demodulation,[],[f1906,f204]) ).
fof(f1936,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(associator(X0,X1,X2),multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[],[f1909,f11]) ).
fof(f1966,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(add(associator(X0,X1,X3),multiply(X0,multiply(X1,X3))),add(multiply(multiply(X2,X1),X3),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3)))),
inference(backward_demodulation,[],[f166,f1936]) ).
fof(f1990,plain,
! [X2,X0,X1] : associator(multiply(X0,additive_inverse(X0)),X1,X2) = add(multiply(X0,multiply(X0,multiply(X1,X2))),add(associator(additive_inverse(X0),multiply(X0,X1),X2),multiply(additive_inverse(X0),add(associator(X0,X1,X2),multiply(X0,multiply(X1,X2)))))),
inference(backward_demodulation,[],[f1199,f1936]) ).
fof(f2009,plain,
! [X2,X0,X1] : add(multiply(X0,multiply(X1,X2)),additive_inverse(associator(additive_inverse(X0),X1,X2))) = add(associator(X0,X1,X2),multiply(X0,multiply(X1,X2))),
inference(backward_demodulation,[],[f1570,f1936]) ).
fof(f2014,plain,
! [X2,X3,X0,X1] : add(add(associator(X0,X1,X2),multiply(X0,multiply(X1,X2))),add(associator(additive_inverse(X0),X1,X2),add(multiply(additive_inverse(X0),multiply(X1,X2)),X3))) = X3,
inference(backward_demodulation,[],[f1829,f1936]) ).
fof(f2024,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(add(associator(X0,multiply(X1,X1),X2),multiply(X0,multiply(multiply(X1,X1),X2))),add(associator(additive_inverse(X0),X1,multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,multiply(X1,X2))))),
inference(backward_demodulation,[],[f1204,f1936]) ).
fof(f2064,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(multiply(multiply(sF0,X0),X1),add(associator(additive_inverse(x),multiply(y,X0),X1),multiply(additive_inverse(x),add(associator(y,X0,X1),multiply(y,multiply(X0,X1)))))),
inference(backward_demodulation,[],[f1212,f1936]) ).
fof(f2079,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(multiply(multiply(sF0,X0),X1),add(associator(additive_inverse(x),multiply(y,X0),X1),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1)))))),
inference(forward_demodulation,[],[f2064,f12]) ).
fof(f2111,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,multiply(multiply(X1,X1),X2)),add(associator(additive_inverse(X0),X1,multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f2024,f15]) ).
fof(f2121,plain,
! [X2,X3,X0,X1] : add(associator(X0,X1,X2),add(multiply(X0,multiply(X1,X2)),add(associator(additive_inverse(X0),X1,X2),add(multiply(additive_inverse(X0),multiply(X1,X2)),X3)))) = X3,
inference(forward_demodulation,[],[f2014,f15]) ).
fof(f2143,plain,
! [X2,X0,X1] : associator(multiply(X0,additive_inverse(X0)),X1,X2) = add(multiply(X0,multiply(X0,multiply(X1,X2))),add(associator(additive_inverse(X0),multiply(X0,X1),X2),add(multiply(additive_inverse(X0),associator(X0,X1,X2)),multiply(additive_inverse(X0),multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1990,f12]) ).
fof(f2167,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X0,multiply(X1,X3)),add(multiply(multiply(X2,X1),X3),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3))))),
inference(forward_demodulation,[],[f1966,f15]) ).
fof(f2191,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(add(associator(sF0,X0,X1),multiply(sF0,multiply(X0,X1))),add(associator(additive_inverse(x),multiply(y,X0),X1),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1)))))),
inference(forward_demodulation,[],[f2079,f1936]) ).
fof(f2217,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,add(associator(X1,X1,X2),multiply(X1,multiply(X1,X2)))),add(associator(additive_inverse(X0),X1,multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f2111,f1936]) ).
fof(f2227,plain,
! [X2,X3,X0,X1] : add(associator(X0,X1,X2),add(associator(additive_inverse(X0),X1,X2),X3)) = X3,
inference(forward_demodulation,[],[f2121,f1230]) ).
fof(f2247,plain,
! [X2,X0,X1] : associator(multiply(X0,additive_inverse(X0)),X1,X2) = add(multiply(additive_inverse(X0),associator(X0,X1,X2)),associator(additive_inverse(X0),multiply(X0,X1),X2)),
inference(forward_demodulation,[],[f2143,f1757]) ).
fof(f2266,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X0,multiply(X1,X3)),add(add(associator(X2,X1,X3),multiply(X2,multiply(X1,X3))),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3))))),
inference(forward_demodulation,[],[f2167,f1936]) ).
fof(f2285,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(sF0,X0,X1),add(multiply(sF0,multiply(X0,X1)),add(associator(additive_inverse(x),multiply(y,X0),X1),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1))))))),
inference(forward_demodulation,[],[f2191,f15]) ).
fof(f2307,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(add(multiply(X0,associator(X1,X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2)))),add(associator(additive_inverse(X0),X1,multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f2217,f12]) ).
fof(f2333,plain,
! [X2,X0,X1] : associator(multiply(X0,additive_inverse(X0)),X1,X2) = add(associator(additive_inverse(X0),multiply(X0,X1),X2),multiply(additive_inverse(X0),associator(X0,X1,X2))),
inference(forward_demodulation,[],[f2247,f14]) ).
fof(f2347,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X0,multiply(X1,X3)),add(associator(X2,X1,X3),add(multiply(X2,multiply(X1,X3)),multiply(additive_inverse(add(X0,X2)),multiply(X1,X3)))))),
inference(forward_demodulation,[],[f2266,f15]) ).
fof(f2378,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),add(multiply(X0,multiply(X1,multiply(X1,X2))),add(associator(additive_inverse(X0),X1,multiply(X1,X2)),multiply(additive_inverse(X0),multiply(X1,multiply(X1,X2))))))),
inference(forward_demodulation,[],[f2307,f15]) ).
fof(f2430,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),associator(additive_inverse(X0),X1,multiply(X1,X2)))),
inference(forward_demodulation,[],[f2378,f889]) ).
fof(f2474,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,additive_identity),associator(additive_inverse(X0),X1,multiply(X1,X2)))),
inference(forward_demodulation,[],[f2430,f235]) ).
fof(f2511,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),add(additive_identity,associator(additive_inverse(X0),X1,multiply(X1,X2)))),
inference(forward_demodulation,[],[f2474,f6]) ).
fof(f2545,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_identity,add(associator(X0,multiply(X1,X1),X2),associator(additive_inverse(X0),X1,multiply(X1,X2)))),
inference(forward_demodulation,[],[f2511,f781]) ).
fof(f2574,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),associator(additive_inverse(X0),X1,multiply(X1,X2))),
inference(forward_demodulation,[],[f2545,f1]) ).
fof(f2824,plain,
! [X2,X0,X1] : associator(X0,X1,add(X1,X2)) = add(additive_identity,associator(X0,X1,X2)),
inference(superposition,[],[f1934,f234]) ).
fof(f2833,plain,
! [X2,X0,X1] : add(associator(X0,X1,X2),additive_identity) = associator(X0,X1,add(X2,X1)),
inference(superposition,[],[f1934,f234]) ).
fof(f2862,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,X1,add(X2,X1)),
inference(forward_demodulation,[],[f2833,f2]) ).
fof(f2868,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,X1,add(X1,X2)),
inference(forward_demodulation,[],[f2824,f1]) ).
fof(f2879,plain,
! [X2,X0,X1] : associator(X0,add(X1,X2),X1) = add(additive_identity,associator(X0,X2,X1)),
inference(superposition,[],[f1933,f234]) ).
fof(f2880,plain,
! [X2,X0,X1] : add(additive_identity,associator(X0,X1,X2)) = associator(X0,add(X0,X1),X2),
inference(superposition,[],[f1933,f235]) ).
fof(f2888,plain,
! [X2,X0,X1] : add(associator(X0,X1,X2),additive_identity) = associator(X0,add(X1,X2),X2),
inference(superposition,[],[f1933,f234]) ).
fof(f2889,plain,
! [X2,X0,X1] : add(associator(X0,X1,X2),additive_identity) = associator(X0,add(X1,X0),X2),
inference(superposition,[],[f1933,f235]) ).
fof(f2905,plain,
! [X2,X3,X0,X1,X4] : add(associator(X0,X1,X3),add(associator(X0,X2,X3),X4)) = add(associator(X0,add(X1,X2),X3),X4),
inference(superposition,[],[f15,f1933]) ).
fof(f2917,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,add(X1,X0),X2),
inference(forward_demodulation,[],[f2889,f2]) ).
fof(f2918,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,add(X1,X2),X2),
inference(forward_demodulation,[],[f2888,f2]) ).
fof(f2922,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,add(X0,X1),X2),
inference(forward_demodulation,[],[f2880,f1]) ).
fof(f2923,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = associator(X0,add(X1,X2),X1),
inference(forward_demodulation,[],[f2879,f1]) ).
fof(f3175,plain,
! [X0,X1] : add(X1,additive_inverse(add(X0,X1))) = add(additive_inverse(X0),additive_identity),
inference(superposition,[],[f231,f348]) ).
fof(f3186,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(forward_demodulation,[],[f3175,f2]) ).
fof(f3276,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
inference(superposition,[],[f231,f3186]) ).
fof(f3306,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X0,multiply(X1,X3)),add(associator(X2,X1,X3),add(multiply(X2,multiply(X1,X3)),multiply(add(additive_inverse(X2),additive_inverse(X0)),multiply(X1,X3)))))),
inference(backward_demodulation,[],[f2347,f3276]) ).
fof(f3377,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X0,multiply(X1,X3)),add(associator(X2,X1,X3),add(multiply(X2,multiply(X1,X3)),add(multiply(additive_inverse(X2),multiply(X1,X3)),multiply(additive_inverse(X0),multiply(X1,X3))))))),
inference(forward_demodulation,[],[f3306,f13]) ).
fof(f3435,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X0,multiply(X1,X3)),add(associator(X2,X1,X3),multiply(additive_inverse(X0),multiply(X1,X3))))),
inference(forward_demodulation,[],[f3377,f1706]) ).
fof(f3478,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),associator(X2,X1,X3)),
inference(forward_demodulation,[],[f3435,f889]) ).
fof(f3515,plain,
! [X2,X0,X1] : associator(add(X0,X1),X0,X2) = add(additive_identity,associator(X1,X0,X2)),
inference(superposition,[],[f3478,f235]) ).
fof(f3566,plain,
! [X2,X0,X1] : associator(X1,X0,X2) = associator(add(X0,X1),X0,X2),
inference(forward_demodulation,[],[f3515,f1]) ).
fof(f5895,plain,
! [X0,X1] : additive_identity = associator(X0,X1,add(X1,X0)),
inference(superposition,[],[f234,f2917]) ).
fof(f5913,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X0),
inference(forward_demodulation,[],[f5895,f2868]) ).
fof(f5963,plain,
! [X2,X0,X1] : associator(add(X0,X1),X2,X1) = add(associator(X0,X2,X1),additive_identity),
inference(superposition,[],[f3478,f5913]) ).
fof(f5967,plain,
! [X2,X0,X1] : add(associator(X0,X1,X2),additive_identity) = associator(X0,X1,add(X2,X0)),
inference(superposition,[],[f1934,f5913]) ).
fof(f5987,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,X1,add(X2,X0)),
inference(forward_demodulation,[],[f5967,f2]) ).
fof(f5991,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = associator(add(X0,X1),X2,X1),
inference(forward_demodulation,[],[f5963,f2]) ).
fof(f6024,plain,
! [X2,X3,X0,X1] : associator(X0,X3,add(multiply(X1,X2),X0)) = associator(multiply(X1,additive_inverse(X2)),X3,add(multiply(X1,X2),X0)),
inference(superposition,[],[f5991,f296]) ).
fof(f6094,plain,
! [X2,X3,X0,X1] : associator(multiply(X1,additive_inverse(X2)),X3,add(multiply(X1,X2),X0)) = associator(X0,X3,multiply(X1,X2)),
inference(forward_demodulation,[],[f6024,f5987]) ).
fof(f6718,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = associator(X0,additive_inverse(add(X2,X1)),X2),
inference(superposition,[],[f587,f2923]) ).
fof(f6719,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = associator(X0,add(X2,X1),additive_inverse(X2)),
inference(forward_demodulation,[],[f6718,f604]) ).
fof(f7314,plain,
! [X2,X0,X1] : associator(X1,add(X2,X0),X0) = associator(X1,add(X2,X0),additive_inverse(X2)),
inference(superposition,[],[f2862,f231]) ).
fof(f7397,plain,
! [X2,X0,X1] : associator(X1,X2,X0) = associator(X1,add(X2,X0),additive_inverse(X2)),
inference(forward_demodulation,[],[f7314,f2918]) ).
fof(f7424,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = associator(X0,X2,X1),
inference(backward_demodulation,[],[f6719,f7397]) ).
fof(f7440,plain,
! [X2,X0,X1] : add(associator(X0,X1,X2),multiply(X0,multiply(X1,X2))) = add(multiply(X0,multiply(X1,X2)),additive_inverse(associator(X0,X2,X1))),
inference(backward_demodulation,[],[f2009,f7424]) ).
fof(f7452,plain,
! [X2,X3,X0,X1] : add(associator(X0,X1,X2),add(associator(X0,X2,X1),X3)) = X3,
inference(backward_demodulation,[],[f2227,f7424]) ).
fof(f7498,plain,
! [X2,X0,X1] : associator(multiply(X0,additive_inverse(X0)),X1,X2) = add(associator(X0,X2,multiply(X0,X1)),multiply(additive_inverse(X0),associator(X0,X1,X2))),
inference(backward_demodulation,[],[f2333,f7424]) ).
fof(f7500,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,X2,additive_inverse(X1)),
inference(backward_demodulation,[],[f552,f7424]) ).
fof(f7511,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(associator(X0,multiply(X1,X1),X2),associator(X0,multiply(X1,X2),X1)),
inference(backward_demodulation,[],[f2574,f7424]) ).
fof(f7520,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(sF0,X0,X1),add(multiply(sF0,multiply(X0,X1)),add(associator(x,X1,multiply(y,X0)),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1))))))),
inference(backward_demodulation,[],[f2285,f7424]) ).
fof(f7523,plain,
! [X0] : multiply(x,multiply(y,X0)) = add(associator(x,X0,y),multiply(sF0,X0)),
inference(backward_demodulation,[],[f1555,f7424]) ).
fof(f7530,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(x,X1,multiply(y,X0)),add(associator(sF0,X0,X1),add(multiply(sF0,multiply(X0,X1)),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1))))))),
inference(forward_demodulation,[],[f7520,f873]) ).
fof(f7772,plain,
! [X0] : multiply(sF0,X0) = add(additive_inverse(associator(x,X0,y)),multiply(x,multiply(y,X0))),
inference(superposition,[],[f231,f7523]) ).
fof(f7791,plain,
! [X0] : multiply(sF0,X0) = add(multiply(x,multiply(y,X0)),additive_inverse(associator(x,X0,y))),
inference(forward_demodulation,[],[f7772,f14]) ).
fof(f7811,plain,
! [X0] : multiply(sF0,X0) = add(associator(x,y,X0),multiply(x,multiply(y,X0))),
inference(forward_demodulation,[],[f7791,f7440]) ).
fof(f7865,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(x,X1,multiply(y,X0)),add(associator(sF0,X0,X1),add(add(associator(x,y,multiply(X0,X1)),multiply(x,multiply(y,multiply(X0,X1)))),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1))))))),
inference(backward_demodulation,[],[f7530,f7811]) ).
fof(f7892,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(x,X1,multiply(y,X0)),add(associator(sF0,X0,X1),add(associator(x,y,multiply(X0,X1)),add(multiply(x,multiply(y,multiply(X0,X1))),add(multiply(additive_inverse(x),associator(y,X0,X1)),multiply(additive_inverse(x),multiply(y,multiply(X0,X1)))))))),
inference(forward_demodulation,[],[f7865,f15]) ).
fof(f7938,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(x,X1,multiply(y,X0)),add(associator(sF0,X0,X1),add(associator(x,y,multiply(X0,X1)),multiply(additive_inverse(x),associator(y,X0,X1))))),
inference(forward_demodulation,[],[f7892,f889]) ).
fof(f8057,plain,
! [X2,X3,X0,X1] : associator(multiply(X0,additive_inverse(X1)),X2,X3) = associator(multiply(X0,X1),X3,X2),
inference(superposition,[],[f7424,f25]) ).
fof(f8141,plain,
! [X2,X0,X1] : add(associator(X0,X2,multiply(X0,X1)),multiply(additive_inverse(X0),associator(X0,X1,X2))) = associator(multiply(X0,X0),X2,X1),
inference(backward_demodulation,[],[f7498,f8057]) ).
fof(f8166,plain,
! [X2,X3,X0,X1] : associator(X0,X3,multiply(X1,X2)) = associator(multiply(X1,X2),add(multiply(X1,X2),X0),X3),
inference(backward_demodulation,[],[f6094,f8057]) ).
fof(f8260,plain,
! [X2,X3,X0,X1] : associator(multiply(X1,X2),X0,X3) = associator(X0,X3,multiply(X1,X2)),
inference(forward_demodulation,[],[f8166,f2922]) ).
fof(f8711,plain,
! [X2,X3,X0,X1] : add(associator(X0,multiply(X1,X1),X2),add(associator(X0,multiply(X1,X2),X1),X3)) = add(X3,associator(multiply(X0,X1),X1,X2)),
inference(superposition,[],[f211,f7511]) ).
fof(f8738,plain,
! [X2,X3,X0,X1] : add(associator(X0,multiply(X1,X1),X2),add(associator(X0,multiply(X1,X2),X1),X3)) = add(X3,associator(X1,X2,multiply(X0,X1))),
inference(forward_demodulation,[],[f8711,f8260]) ).
fof(f10146,plain,
! [X2,X0,X1] : associator(add(additive_inverse(X1),X0),X2,X1) = associator(add(additive_inverse(X1),X0),X2,X0),
inference(superposition,[],[f5987,f258]) ).
fof(f10165,plain,
! [X2,X0,X1] : associator(additive_inverse(X1),X2,X0) = associator(add(additive_inverse(X1),X0),X2,X1),
inference(forward_demodulation,[],[f10146,f5991]) ).
fof(f10187,plain,
! [X2,X0,X1] : associator(X1,X0,X2) = associator(add(additive_inverse(X1),X0),X2,X1),
inference(forward_demodulation,[],[f10165,f7424]) ).
fof(f10207,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = associator(X1,add(X1,X0),X2),
inference(superposition,[],[f10187,f231]) ).
fof(f10267,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = associator(add(additive_inverse(additive_inverse(X0)),X1),X0,X2),
inference(superposition,[],[f7500,f10187]) ).
fof(f10295,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = associator(add(X0,X1),X0,X2),
inference(forward_demodulation,[],[f10267,f11]) ).
fof(f10351,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = associator(add(X0,X1),X0,X2),
inference(forward_demodulation,[],[f10295,f7424]) ).
fof(f10492,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X2,X0,X1),
inference(superposition,[],[f3566,f10351]) ).
fof(f16040,plain,
! [X2,X3,X0,X1] : add(associator(X1,X0,X2),add(associator(X0,X1,X2),X3)) = X3,
inference(superposition,[],[f7452,f10492]) ).
fof(f16095,plain,
! [X2,X0,X1] : additive_inverse(associator(X0,X1,X2)) = associator(X0,X2,X1),
inference(superposition,[],[f251,f7452]) ).
fof(f20153,plain,
additive_inverse(sF2) = associator(x,z,y),
inference(superposition,[],[f16095,f36]) ).
fof(f20175,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = multiply(associator(X0,X2,X1),additive_inverse(X3)),
inference(superposition,[],[f323,f16095]) ).
fof(f20176,plain,
! [X2,X3,X0,X1] : multiply(X3,associator(X0,X1,X2)) = multiply(additive_inverse(X3),associator(X0,X2,X1)),
inference(superposition,[],[f323,f16095]) ).
fof(f20240,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X2,X1) = add(associator(X0,X2,multiply(X0,X1)),multiply(X0,associator(X0,X2,X1))),
inference(backward_demodulation,[],[f8141,f20176]) ).
fof(f20262,plain,
! [X0,X1] : multiply(associator(x,y,X0),X1) = add(associator(x,X1,multiply(y,X0)),add(associator(sF0,X0,X1),add(associator(x,y,multiply(X0,X1)),multiply(x,associator(y,X1,X0))))),
inference(backward_demodulation,[],[f7938,f20176]) ).
fof(f20773,plain,
! [X0] : multiply(sF2,X0) = multiply(associator(x,z,y),additive_inverse(X0)),
inference(superposition,[],[f21,f20153]) ).
fof(f20900,plain,
! [X0] : multiply(sF2,X0) = multiply(associator(x,y,z),X0),
inference(forward_demodulation,[],[f20773,f20175]) ).
fof(f20926,plain,
! [X0] : multiply(sF2,X0) = add(associator(x,X0,multiply(y,z)),add(associator(sF0,z,X0),add(associator(x,y,multiply(z,X0)),multiply(x,associator(y,X0,z))))),
inference(forward_demodulation,[],[f20900,f20262]) ).
fof(f20947,plain,
! [X0] : multiply(sF2,X0) = add(multiply(x,associator(y,X0,z)),add(associator(x,X0,multiply(y,z)),add(associator(sF0,z,X0),associator(x,y,multiply(z,X0))))),
inference(forward_demodulation,[],[f20926,f786]) ).
fof(f20961,plain,
! [X0] : multiply(sF2,X0) = add(associator(sF0,z,X0),add(multiply(x,associator(y,X0,z)),add(associator(x,X0,multiply(y,z)),associator(x,y,multiply(z,X0))))),
inference(forward_demodulation,[],[f20947,f873]) ).
fof(f20972,plain,
! [X0] : multiply(sF2,X0) = add(associator(z,X0,sF0),add(multiply(x,associator(y,X0,z)),add(associator(x,X0,multiply(y,z)),associator(x,y,multiply(z,X0))))),
inference(forward_demodulation,[],[f20961,f10492]) ).
fof(f21027,plain,
sF3 = add(associator(z,x,sF0),add(multiply(x,associator(y,x,z)),add(associator(x,x,multiply(y,z)),associator(x,y,multiply(z,x))))),
inference(backward_demodulation,[],[f38,f20972]) ).
fof(f21067,plain,
sF3 = add(associator(z,x,sF0),add(multiply(x,associator(y,x,z)),add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),associator(x,x,multiply(y,z)))))),
inference(forward_demodulation,[],[f21027,f8738]) ).
fof(f21109,plain,
sF3 = add(associator(z,multiply(x,x),y),add(associator(z,x,sF0),add(multiply(x,associator(y,x,z)),add(associator(z,multiply(x,y),x),associator(x,x,multiply(y,z)))))),
inference(forward_demodulation,[],[f21067,f873]) ).
fof(f21150,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(multiply(x,associator(y,x,z)),add(associator(z,multiply(x,y),x),associator(x,x,multiply(y,z)))))),
inference(forward_demodulation,[],[f21109,f781]) ).
fof(f21188,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,y),x),add(associator(z,multiply(x,x),y),add(multiply(x,associator(y,x,z)),associator(x,x,multiply(y,z)))))),
inference(forward_demodulation,[],[f21150,f873]) ).
fof(f21222,plain,
sF3 = add(associator(z,multiply(x,x),y),add(associator(z,x,sF0),add(associator(z,multiply(x,y),x),add(multiply(x,associator(y,x,z)),associator(x,x,multiply(y,z)))))),
inference(forward_demodulation,[],[f21188,f873]) ).
fof(f21255,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),add(multiply(x,associator(y,x,z)),associator(x,x,multiply(y,z)))))),
inference(forward_demodulation,[],[f21222,f781]) ).
fof(f21285,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),add(multiply(x,associator(y,x,z)),additive_identity)))),
inference(forward_demodulation,[],[f21255,f235]) ).
fof(f21312,plain,
sF3 = add(associator(z,x,sF0),add(additive_identity,add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),multiply(x,associator(y,x,z)))))),
inference(forward_demodulation,[],[f21285,f786]) ).
fof(f21339,plain,
sF3 = add(additive_identity,add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),multiply(x,associator(y,x,z)))))),
inference(forward_demodulation,[],[f21312,f781]) ).
fof(f21367,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),multiply(x,associator(y,x,z))))),
inference(forward_demodulation,[],[f21339,f1]) ).
fof(f21445,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(z,multiply(x,y),x),multiply(x,associator(x,z,y))))),
inference(forward_demodulation,[],[f21367,f10492]) ).
fof(f21513,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(x,add(x,z),multiply(x,y)),multiply(x,associator(x,z,y))))),
inference(forward_demodulation,[],[f21445,f10207]) ).
fof(f21581,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(x,x,multiply(x,y)),add(associator(x,z,multiply(x,y)),multiply(x,associator(x,z,y)))))),
inference(forward_demodulation,[],[f21513,f2905]) ).
fof(f21649,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(x,x,multiply(x,y)),associator(multiply(x,x),z,y)))),
inference(forward_demodulation,[],[f21581,f20240]) ).
fof(f21717,plain,
sF3 = add(associator(multiply(x,x),z,y),add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),associator(x,x,multiply(x,y))))),
inference(forward_demodulation,[],[f21649,f786]) ).
fof(f21785,plain,
sF3 = add(associator(z,x,sF0),add(associator(multiply(x,x),z,y),add(associator(z,multiply(x,x),y),associator(x,x,multiply(x,y))))),
inference(forward_demodulation,[],[f21717,f781]) ).
fof(f21850,plain,
sF3 = add(associator(z,multiply(x,x),y),add(associator(z,x,sF0),add(associator(multiply(x,x),z,y),associator(x,x,multiply(x,y))))),
inference(forward_demodulation,[],[f21785,f873]) ).
fof(f21914,plain,
sF3 = add(associator(z,x,sF0),add(associator(z,multiply(x,x),y),add(associator(multiply(x,x),z,y),associator(x,x,multiply(x,y))))),
inference(forward_demodulation,[],[f21850,f781]) ).
fof(f21978,plain,
sF3 = add(associator(z,x,sF0),associator(x,x,multiply(x,y))),
inference(forward_demodulation,[],[f21914,f16040]) ).
fof(f22040,plain,
sF3 = add(associator(z,x,sF0),additive_identity),
inference(forward_demodulation,[],[f21978,f235]) ).
fof(f22101,plain,
sF3 = associator(z,x,sF0),
inference(forward_demodulation,[],[f22040,f2]) ).
fof(f22162,plain,
associator(x,sF0,z) = sF3,
inference(forward_demodulation,[],[f22101,f10492]) ).
fof(f22220,plain,
sF1 = sF3,
inference(forward_demodulation,[],[f22162,f34]) ).
fof(f22278,plain,
$false,
inference(forward_subsumption_resolution,[],[f22220,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG027-9 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.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 22:59:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 86.79/13.07 % (3428540)Detected a unit-equality problem, will run specialized UEQ schedule.
% 86.79/13.07 % (3428546)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=125526867:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 86.79/13.07 % (3428551)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3108757824:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 86.79/13.07 % (3428547)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3701238977:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 86.79/13.07 % (3428545)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2352752983:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 86.79/13.07 % (3428549)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3495335243:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 86.79/13.07 % (3428548)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1852931493:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 86.79/13.07 % (3428550)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=40673219:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 86.79/13.07 % (3428549)Refutation not found, incomplete strategy
% 86.79/13.07 % (3428549)------------------------------
% 86.79/13.07 % (3428549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 86.79/13.07 % (3428549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.79/13.07 % (3428549)CaDiCaL version: 2.1.3
% 86.79/13.07 % (3428549)Termination reason: Refutation not found, incomplete strategy
% 86.79/13.07 % (3428549)Time elapsed: 0.002 s
% 86.79/13.07 % (3428549)Peak memory usage: 88 MB
% 86.79/13.07 % (3428549)Instructions burned: 2 (million)
% 86.79/13.07 % (3428548)Instruction limit reached!
% 86.79/13.07 % (3428548)------------------------------
% 86.79/13.07 % (3428548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 86.79/13.07 % (3428548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.79/13.07 % (3428548)CaDiCaL version: 2.1.3
% 86.79/13.07 % (3428548)Termination reason: Instruction limit
% 86.79/13.07 % (3428548)Termination phase: Saturation
% 86.79/13.07 % (3428548)Time elapsed: 0.067 s
% 86.79/13.07 % (3428548)Peak memory usage: 88 MB
% 86.79/13.07 % (3428548)Instructions burned: 139 (million)
% 86.79/13.07 % (3428550)Instruction limit reached!
% 86.79/13.07 % (3428550)------------------------------
% 86.79/13.07 % (3428550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 86.79/13.07 % (3428550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.79/13.07 % (3428550)CaDiCaL version: 2.1.3
% 86.79/13.07 % (3428550)Termination reason: Instruction limit
% 86.79/13.07 % (3428550)Termination phase: Saturation
% 86.79/13.07 % (3428550)Time elapsed: 0.156 s
% 86.79/13.07 % (3428550)Peak memory usage: 90 MB
% 86.79/13.07 % (3428550)Instructions burned: 258 (million)
% 86.79/13.07 % (3428549)------------------------------
% 86.79/13.07 % (3428549)------------------------------
% 86.79/13.07 % (3428559)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2833850925:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 86.79/13.07 % (3428560)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3508687928:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 86.79/13.07 % (3428562)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=684882190:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 86.79/13.07 % (3428562)Instruction limit reached!
% 86.79/13.07 % (3428562)------------------------------
% 86.79/13.07 % (3428562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 86.79/13.07 % (3428562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.79/13.07 % (3428562)CaDiCaL version: 2.1.3
% 86.79/13.07 % (3428562)Termination reason: Instruction limit
% 43.78/16.16 % (3428562)Termination phase: Saturation
% 43.78/16.16 % (3428562)Time elapsed: 0.109 s
% 43.78/16.16 % (3428562)Peak memory usage: 89 MB
% 43.78/16.16 % (3428562)Instructions burned: 216 (million)
% 43.78/16.16 % (3428551)Instruction limit reached!
% 43.78/16.16 % (3428551)------------------------------
% 43.78/16.16 % (3428551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428551)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428551)Termination reason: Instruction limit
% 43.78/16.16 % (3428551)Termination phase: Saturation
% 43.78/16.16 % (3428551)Time elapsed: 0.628 s
% 43.78/16.16 % (3428551)Peak memory usage: 98 MB
% 43.78/16.16 % (3428551)Instructions burned: 1188 (million)
% 43.78/16.16 % (3428565)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=4249863830:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 43.78/16.16 % (3428566)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2287093841:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 43.78/16.16 % (3428565)Instruction limit reached!
% 43.78/16.16 % (3428565)------------------------------
% 43.78/16.16 % (3428565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428565)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428565)Termination reason: Instruction limit
% 43.78/16.16 % (3428565)Termination phase: Saturation
% 43.78/16.16 % (3428565)Time elapsed: 0.183 s
% 43.78/16.16 % (3428565)Peak memory usage: 92 MB
% 43.78/16.16 % (3428565)Instructions burned: 318 (million)
% 43.78/16.16 % (3428569)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=4123467906:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2989 on theBenchmark for (2989ds/2836Mi)
% 43.78/16.16 % (3428559)Instruction limit reached!
% 43.78/16.16 % (3428559)------------------------------
% 43.78/16.16 % (3428559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428559)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428559)Termination reason: Instruction limit
% 43.78/16.16 % (3428559)Termination phase: Saturation
% 43.78/16.16 % (3428559)Time elapsed: 1.301 s
% 43.78/16.16 % (3428559)Peak memory usage: 141 MB
% 43.78/16.16 % (3428559)Instructions burned: 2051 (million)
% 43.78/16.16 % (3428571)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=4093071973:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2982 on theBenchmark for (2982ds/14534Mi)
% 43.78/16.16 % (3428569)Instruction limit reached!
% 43.78/16.16 % (3428569)------------------------------
% 43.78/16.16 % (3428569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428569)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428569)Termination reason: Instruction limit
% 43.78/16.16 % (3428569)Termination phase: Saturation
% 43.78/16.16 % (3428569)Time elapsed: 1.762 s
% 43.78/16.16 % (3428569)Peak memory usage: 123 MB
% 43.78/16.16 % (3428569)Instructions burned: 2840 (million)
% 43.78/16.16 % (3428573)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=290555701:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2970 on theBenchmark for (2970ds/11832Mi)
% 43.78/16.16 % (3428560)Instruction limit reached!
% 43.78/16.16 % (3428560)------------------------------
% 43.78/16.16 % (3428560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428560)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428560)Termination reason: Instruction limit
% 43.78/16.16 % (3428560)Termination phase: Saturation
% 43.78/16.16 % (3428560)Time elapsed: 2.947 s
% 43.78/16.16 % (3428560)Peak memory usage: 166 MB
% 43.78/16.16 % (3428560)Instructions burned: 4948 (million)
% 43.78/16.16 % (3428575)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=1320209595:i=2279:fgj=on:bd=all_2965 on theBenchmark for (2965ds/2279Mi)
% 43.78/16.16 % (3428575)Instruction limit reached!
% 43.78/16.16 % (3428575)------------------------------
% 43.78/16.16 % (3428575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428575)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428575)Termination reason: Instruction limit
% 43.78/16.16 % (3428575)Termination phase: Saturation
% 43.78/16.16 % (3428575)Time elapsed: 1.364 s
% 43.78/16.16 % (3428575)Peak memory usage: 139 MB
% 43.78/16.16 % (3428575)Instructions burned: 2280 (million)
% 43.78/16.16 % (3428577)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:drc=off:fde=none:sp=reverse_arity:urr=ec_only:gs=on:s2agt=16:random_seed=1590316297:st=3:i=6225:bd=all:gtg=exists_all:ss=included:er=filter:sgt=10_2950 on theBenchmark for (2950ds/6225Mi)
% 43.78/16.16 % (3428566)Instruction limit reached!
% 43.78/16.16 % (3428566)------------------------------
% 43.78/16.16 % (3428566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428566)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428566)Termination reason: Instruction limit
% 43.78/16.16 % (3428566)Termination phase: Saturation
% 43.78/16.16 % (3428566)Time elapsed: 7.188 s
% 43.78/16.16 % (3428566)Peak memory usage: 245 MB
% 43.78/16.16 % (3428566)Instructions burned: 12131 (million)
% 43.78/16.16 % (3428579)lrs-1010_1_sil=32000:tgt=ground:etr=on:sp=const_frequency:spb=goal_then_units:rnwc=on:lwlo=on:random_seed=1283947479:lrd=on:i=21755:kws=frequency:fgj=on:bd=preordered:nm=4:ins=20:av=off_2918 on theBenchmark for (2918ds/21755Mi)
% 43.78/16.16 % (3428577)Instruction limit reached!
% 43.78/16.16 % (3428577)------------------------------
% 43.78/16.16 % (3428577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428577)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428577)Termination reason: Instruction limit
% 43.78/16.16 % (3428577)Termination phase: Saturation
% 43.78/16.16 % (3428577)Time elapsed: 3.547 s
% 43.78/16.16 % (3428577)Peak memory usage: 160 MB
% 43.78/16.16 % (3428577)Instructions burned: 6226 (million)
% 43.78/16.16 % (3428581)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:drc=off:flr=on:random_seed=3614031664:s2pl=no:i=16427:s2at=1.5:bd=all:fsr=off_2912 on theBenchmark for (2912ds/16427Mi)
% 43.78/16.16 % (3428573)Instruction limit reached!
% 43.78/16.16 % (3428573)------------------------------
% 43.78/16.16 % (3428573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428573)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428573)Termination reason: Instruction limit
% 43.78/16.16 % (3428573)Termination phase: Saturation
% 43.78/16.16 % (3428573)Time elapsed: 7.341 s
% 43.78/16.16 % (3428573)Peak memory usage: 231 MB
% 43.78/16.16 % (3428573)Instructions burned: 11833 (million)
% 43.78/16.16 % (3428583)lrs+1011_1_to=lpo:ncem=casc2026/models/loop7.pt:sil=32000:npcc=on:drc=off:fde=none:sp=const_frequency:spb=goal:fd=preordered:random_seed=3906751131:i=9356:fgj=on:bd=preordered:av=off_2895 on theBenchmark for (2895ds/9356Mi)
% 43.78/16.16 % (3428571)Instruction limit reached!
% 43.78/16.16 % (3428571)------------------------------
% 43.78/16.16 % (3428571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428571)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428571)Termination reason: Instruction limit
% 43.78/16.16 % (3428571)Termination phase: Saturation
% 43.78/16.16 % (3428571)Time elapsed: 8.917 s
% 43.78/16.16 % (3428571)Peak memory usage: 257 MB
% 43.78/16.16 % (3428571)Instructions burned: 14535 (million)
% 43.78/16.16 % (3428585)dis+10_6_sil=8000:tgt=ground:prc=on:drc=ordering:spb=non_intro:fd=preordered:foolp=on:slsqc=1:slsq=on:random_seed=1599204550:i=2070:kws=inv_precedence:slsql=off:bd=all_2891 on theBenchmark for (2891ds/2070Mi)
% 43.78/16.16 % (3428585)Instruction limit reached!
% 43.78/16.16 % (3428585)------------------------------
% 43.78/16.16 % (3428585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 43.78/16.16 % (3428585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.78/16.16 % (3428585)CaDiCaL version: 2.1.3
% 43.78/16.16 % (3428585)Termination reason: Instruction limit
% 43.78/16.16 % (3428585)Termination phase: Saturation
% 43.78/16.16 % (3428585)Time elapsed: 1.227 s
% 43.78/16.16 % (3428585)Peak memory usage: 126 MB
% 43.78/16.16 % (3428585)Instructions burned: 2071 (million)
% 43.78/16.16 % (3428587)lrs+1002_1_to=lpo:ncem=casc2026/models/loop4.pt:sil=8000:tgt=ground:npcc=on:fde=unused:sp=const_min:urr=ec_only:s2agt=32:random_seed=1154577634:st=3:i=6461:fgj=on:bd=preordered:av=off:ss=axioms_2877 on theBenchmark for (2877ds/6461Mi)
% 43.78/16.16 % (3428587)First to succeed.
% 43.78/16.16 % (3428587)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3428540"
% 43.78/16.16 % (3428587)Refutation found. Thanks to Tanya!
% 43.78/16.16 % SZS status Unsatisfiable for theBenchmark
% 43.78/16.16 % SZS output start Proof for theBenchmark
% See solution above
% 109.06/16.36 % (3428587)------------------------------
% 109.06/16.36 % (3428587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 109.06/16.36 % (3428587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 109.06/16.36 % (3428587)CaDiCaL version: 2.1.3
% 109.06/16.36 % (3428587)Termination reason: Refutation
% 109.06/16.36 % (3428587)Time elapsed: 2.616 s
% 109.06/16.36 % (3428587)Peak memory usage: 154 MB
% 109.06/16.36 % (3428587)Instructions burned: 4381 (million)
% 109.06/16.36 % (3428587)------------------------------
% 109.06/16.36 % (3428587)------------------------------
% 109.06/16.36 % (3428540)Success in time 15.305 s
% 109.06/16.36 % Vampire exiting
%------------------------------------------------------------------------------