%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO026-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:35:56 AM UTC 2026
% Result : Unsatisfiable 6.17s 1.56s
% Output : Refutation 7.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 9
% Syntax : Number of formulae : 195 ( 195 unt; 0 def)
% Number of atoms : 195 ( 194 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 209 ( 209 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f2,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
fof(f4,axiom,
! [X0] : multiply(X0,inverse(X0)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
fof(f5,axiom,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
fof(f6,axiom,
! [X0,X1] : add(multiply(X0,inverse(X1)),add(multiply(X0,X1),multiply(inverse(X1),X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
fof(f8,axiom,
! [X0,X1] : multiply(add(X0,inverse(X0)),multiply(add(X0,X1),add(inverse(X0),X1))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1_dual) ).
fof(f9,axiom,
! [X0,X1] : multiply(add(X0,inverse(X1)),multiply(add(X0,X1),add(inverse(X1),X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2_dual) ).
fof(f11,negated_conjecture,
multiply(add(a,b),b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add) ).
fof(f12,plain,
b != multiply(add(a,b),b),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X0,X1] : multiply(inverse(X0),add(X0,X1)) = add(n0,multiply(X1,inverse(X0))),
inference(superposition,[],[f1,f4]) ).
fof(f14,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,X0)) = add(multiply(X1,inverse(X0)),n0),
inference(superposition,[],[f1,f4]) ).
fof(f15,plain,
! [X0,X1] : add(inverse(X0),multiply(X0,X1)) = multiply(n1,add(X1,inverse(X0))),
inference(superposition,[],[f3,f2]) ).
fof(f16,plain,
! [X2,X3,X0,X1] : add(multiply(X2,X0),multiply(multiply(X1,X0),X3)) = multiply(multiply(X0,add(X1,X2)),add(X3,multiply(X2,X0))),
inference(superposition,[],[f3,f1]) ).
fof(f17,plain,
! [X0,X1] : add(inverse(X0),multiply(X1,X0)) = multiply(add(X1,inverse(X0)),n1),
inference(superposition,[],[f3,f2]) ).
fof(f19,plain,
! [X2,X3,X0,X1] : multiply(add(X2,X0),add(X3,add(X1,X0))) = add(multiply(X3,add(X2,X0)),add(X0,multiply(X1,X2))),
inference(superposition,[],[f1,f3]) ).
fof(f35,plain,
! [X0] : multiply(n1,add(inverse(X0),inverse(X0))) = add(inverse(X0),n0),
inference(superposition,[],[f15,f4]) ).
fof(f37,plain,
! [X0,X1] : multiply(n1,add(add(X1,X0),inverse(inverse(X1)))) = add(inverse(inverse(X1)),add(n0,multiply(X0,inverse(X1)))),
inference(superposition,[],[f15,f13]) ).
fof(f39,plain,
! [X0] : add(inverse(X0),multiply(X0,X0)) = multiply(n1,n1),
inference(superposition,[],[f15,f2]) ).
fof(f41,plain,
! [X0,X1] : add(n0,multiply(multiply(X1,X0),inverse(inverse(X1)))) = multiply(inverse(inverse(X1)),multiply(n1,add(X0,inverse(X1)))),
inference(superposition,[],[f13,f15]) ).
fof(f46,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),multiply(X1,add(X0,inverse(X0)))) = X1,
inference(forward_demodulation,[],[f5,f1]) ).
fof(f47,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),multiply(X1,n1)) = X1,
inference(forward_demodulation,[],[f46,f2]) ).
fof(f48,plain,
! [X1] : add(n0,multiply(X1,n1)) = X1,
inference(forward_demodulation,[],[f47,f4]) ).
fof(f49,plain,
! [X0] : add(multiply(n0,inverse(multiply(X0,n1))),n0) = multiply(inverse(multiply(X0,n1)),X0),
inference(superposition,[],[f14,f48]) ).
fof(f50,plain,
! [X0] : add(n0,multiply(multiply(X0,n1),inverse(n0))) = multiply(inverse(n0),X0),
inference(superposition,[],[f13,f48]) ).
fof(f51,plain,
! [X0,X1] : add(multiply(X0,n1),multiply(X1,n0)) = multiply(add(X1,multiply(X0,n1)),X0),
inference(superposition,[],[f3,f48]) ).
fof(f52,plain,
! [X0,X1] : add(multiply(X0,n1),multiply(n0,X1)) = multiply(X0,add(X1,multiply(X0,n1))),
inference(superposition,[],[f3,f48]) ).
fof(f53,plain,
! [X0,X1] : multiply(n1,n1) = add(inverse(add(X1,X0)),add(X0,multiply(X1,X1))),
inference(superposition,[],[f39,f3]) ).
fof(f79,plain,
! [X0,X1] : add(X1,inverse(X0)) = add(n0,add(inverse(X0),multiply(X1,X0))),
inference(superposition,[],[f48,f17]) ).
fof(f97,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),multiply(X1,add(X0,inverse(X1)))) = X0,
inference(forward_demodulation,[],[f6,f1]) ).
fof(f100,plain,
! [X0] : add(multiply(X0,inverse(inverse(X0))),add(n0,multiply(inverse(inverse(X0)),inverse(X0)))) = X0,
inference(superposition,[],[f97,f13]) ).
fof(f189,plain,
! [X0] : multiply(n1,n1) = add(inverse(X0),add(multiply(X0,n1),multiply(n0,n0))),
inference(superposition,[],[f53,f48]) ).
fof(f229,plain,
! [X0,X1] : multiply(add(X0,inverse(X0)),add(X1,multiply(X0,inverse(X0)))) = X1,
inference(forward_demodulation,[],[f8,f3]) ).
fof(f230,plain,
! [X0,X1] : multiply(add(X0,inverse(X0)),add(X1,n0)) = X1,
inference(forward_demodulation,[],[f229,f4]) ).
fof(f231,plain,
! [X1] : multiply(n1,add(X1,n0)) = X1,
inference(forward_demodulation,[],[f230,f2]) ).
fof(f234,plain,
! [X0] : add(n1,inverse(add(X0,n0))) = add(n0,add(inverse(add(X0,n0)),X0)),
inference(superposition,[],[f79,f231]) ).
fof(f236,plain,
! [X0,X1] : multiply(add(X0,n0),add(X1,n1)) = add(multiply(X1,add(X0,n0)),X0),
inference(superposition,[],[f1,f231]) ).
fof(f237,plain,
! [X0,X1] : multiply(add(X0,n0),add(n1,X1)) = add(X0,multiply(X1,add(X0,n0))),
inference(superposition,[],[f1,f231]) ).
fof(f252,plain,
! [X0,X1] : multiply(add(X0,inverse(X1)),add(X1,multiply(X0,inverse(X1)))) = X0,
inference(forward_demodulation,[],[f9,f3]) ).
fof(f257,plain,
! [X0] : multiply(add(X0,inverse(inverse(X0))),multiply(n1,add(inverse(inverse(X0)),inverse(X0)))) = X0,
inference(superposition,[],[f252,f15]) ).
fof(f264,plain,
! [X2,X0,X1] : multiply(add(X1,multiply(X0,inverse(X1))),add(add(X0,inverse(X1)),X2)) = add(X0,multiply(X2,add(X1,multiply(X0,inverse(X1))))),
inference(superposition,[],[f1,f252]) ).
fof(f293,plain,
! [X0] : multiply(X0,X0) = add(multiply(X0,n1),multiply(n0,n0)),
inference(superposition,[],[f51,f48]) ).
fof(f311,plain,
! [X0,X1] : add(multiply(X1,n1),multiply(n0,multiply(X0,n1))) = multiply(X1,multiply(n1,add(X0,X1))),
inference(superposition,[],[f52,f1]) ).
fof(f324,plain,
! [X0,X1] : add(X0,multiply(X1,X1)) = add(multiply(add(X1,X0),n1),multiply(n0,n0)),
inference(superposition,[],[f293,f3]) ).
fof(f369,plain,
! [X0] : add(X0,X0) = multiply(add(X0,n0),add(n1,n1)),
inference(superposition,[],[f236,f231]) ).
fof(f390,plain,
! [X0,X1] : multiply(X0,add(X1,X1)) = multiply(add(multiply(X1,X0),n0),add(n1,n1)),
inference(superposition,[],[f369,f1]) ).
fof(f395,plain,
! [X0] : add(n0,multiply(X0,inverse(X0))) = multiply(inverse(X0),multiply(add(X0,n0),add(n1,n1))),
inference(superposition,[],[f13,f369]) ).
fof(f416,plain,
! [X0] : add(n0,n0) = multiply(inverse(X0),multiply(add(X0,n0),add(n1,n1))),
inference(forward_demodulation,[],[f395,f4]) ).
fof(f446,plain,
! [X0] : add(n0,multiply(X0,n1)) = add(X0,multiply(n0,add(X0,n0))),
inference(superposition,[],[f3,f237]) ).
fof(f466,plain,
! [X0] : add(X0,multiply(n0,add(X0,n0))) = X0,
inference(forward_demodulation,[],[f446,f48]) ).
fof(f506,plain,
! [X0] : multiply(n0,inverse(multiply(X0,n1))) = multiply(n1,multiply(inverse(multiply(X0,n1)),X0)),
inference(superposition,[],[f231,f49]) ).
fof(f603,plain,
! [X0,X1] : add(multiply(n0,n1),multiply(multiply(X0,n1),X1)) = multiply(X0,add(X1,multiply(n0,n1))),
inference(superposition,[],[f16,f231]) ).
fof(f1160,plain,
! [X0,X1] : multiply(add(n1,n0),add(X1,add(X0,n0))) = add(multiply(X1,add(n1,n0)),X0),
inference(superposition,[],[f19,f48]) ).
fof(f1263,plain,
! [X0,X1] : add(n0,n0) = multiply(inverse(multiply(X1,X0)),multiply(X0,add(X1,X1))),
inference(superposition,[],[f416,f390]) ).
fof(f1342,plain,
! [X0] : add(n0,n0) = multiply(inverse(multiply(inverse(X0),n1)),add(inverse(X0),n0)),
inference(superposition,[],[f1263,f35]) ).
fof(f1344,plain,
add(n0,n0) = multiply(inverse(multiply(n0,n1)),n0),
inference(superposition,[],[f1263,f231]) ).
fof(f1591,plain,
multiply(n1,add(n0,n0)) = multiply(n0,inverse(multiply(n0,n1))),
inference(superposition,[],[f506,f1344]) ).
fof(f1605,plain,
n0 = multiply(n0,inverse(multiply(n0,n1))),
inference(forward_demodulation,[],[f1591,f231]) ).
fof(f3131,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),multiply(X1,add(X0,inverse(X1)))) = add(X0,multiply(multiply(X0,inverse(X1)),add(X1,multiply(X0,inverse(X1))))),
inference(superposition,[],[f3,f264]) ).
fof(f3166,plain,
! [X0,X1] : add(X0,multiply(multiply(X0,inverse(X1)),add(X1,multiply(X0,inverse(X1))))) = X0,
inference(forward_demodulation,[],[f3131,f97]) ).
fof(f3182,plain,
n0 = add(n0,multiply(n0,add(multiply(n0,n1),n0))),
inference(superposition,[],[f3166,f1605]) ).
fof(f4647,plain,
! [X0] : multiply(n1,add(n0,multiply(X0,n1))) = multiply(X0,add(n1,multiply(n0,n1))),
inference(superposition,[],[f1,f603]) ).
fof(f4694,plain,
! [X0] : multiply(n1,X0) = multiply(X0,add(n1,multiply(n0,n1))),
inference(forward_demodulation,[],[f4647,f48]) ).
fof(f4732,plain,
multiply(n1,n0) = add(multiply(n0,n1),multiply(n0,n1)),
inference(superposition,[],[f52,f4694]) ).
fof(f4740,plain,
add(multiply(add(n1,multiply(n0,n1)),n1),multiply(n0,n0)) = multiply(n1,add(n1,multiply(n0,n1))),
inference(superposition,[],[f293,f4694]) ).
fof(f4794,plain,
multiply(n1,n1) = add(multiply(add(n1,multiply(n0,n1)),n1),multiply(n0,n0)),
inference(forward_demodulation,[],[f4740,f4694]) ).
fof(f4799,plain,
multiply(n1,add(n0,n0)) = multiply(n1,n0),
inference(forward_demodulation,[],[f4732,f1]) ).
fof(f4807,plain,
multiply(n1,n1) = add(multiply(n0,n1),multiply(n1,n1)),
inference(forward_demodulation,[],[f4794,f324]) ).
fof(f4808,plain,
n0 = multiply(n1,n0),
inference(forward_demodulation,[],[f4799,f231]) ).
fof(f4812,plain,
multiply(n1,n1) = multiply(n1,add(n0,n1)),
inference(forward_demodulation,[],[f4807,f1]) ).
fof(f4817,plain,
! [X0] : add(n0,multiply(X0,n0)) = multiply(n0,add(n1,X0)),
inference(superposition,[],[f1,f4808]) ).
fof(f4823,plain,
add(n1,inverse(n0)) = add(n0,add(inverse(n0),n0)),
inference(superposition,[],[f79,f4808]) ).
fof(f4847,plain,
multiply(add(n0,n1),add(n1,n1)) = multiply(add(multiply(n1,n1),n0),add(n1,n1)),
inference(superposition,[],[f390,f4812]) ).
fof(f4851,plain,
add(multiply(n1,n1),multiply(n1,n1)) = multiply(add(n0,n1),add(n1,n1)),
inference(forward_demodulation,[],[f4847,f369]) ).
fof(f4860,plain,
add(multiply(n1,n1),multiply(n1,n1)) = add(n1,multiply(n0,n1)),
inference(forward_demodulation,[],[f4851,f3]) ).
fof(f4861,plain,
multiply(n1,add(n1,n1)) = add(n1,multiply(n0,n1)),
inference(forward_demodulation,[],[f4860,f1]) ).
fof(f5088,plain,
n1 = add(n1,add(n0,multiply(n0,n0))),
inference(superposition,[],[f466,f4817]) ).
fof(f5097,plain,
multiply(n1,n0) = add(n0,multiply(multiply(n0,n1),n0)),
inference(superposition,[],[f4694,f4817]) ).
fof(f5118,plain,
n0 = add(n0,multiply(multiply(n0,n1),n0)),
inference(forward_demodulation,[],[f5097,f4808]) ).
fof(f5171,plain,
add(multiply(n0,n1),multiply(n0,n0)) = add(multiply(multiply(n0,n1),n0),multiply(n0,n0)),
inference(superposition,[],[f324,f5118]) ).
fof(f5173,plain,
add(multiply(n0,n1),multiply(n0,n0)) = multiply(n0,add(multiply(n0,n1),n0)),
inference(forward_demodulation,[],[f5171,f1]) ).
fof(f5182,plain,
multiply(n0,n0) = multiply(n0,add(multiply(n0,n1),n0)),
inference(forward_demodulation,[],[f5173,f293]) ).
fof(f5316,plain,
n0 = add(n0,multiply(n0,n0)),
inference(superposition,[],[f3182,f5182]) ).
fof(f5360,plain,
n1 = add(n1,n0),
inference(superposition,[],[f5088,f5316]) ).
fof(f5414,plain,
multiply(n0,n1) = add(n0,multiply(n0,n0)),
inference(superposition,[],[f4817,f5360]) ).
fof(f5416,plain,
n1 = multiply(n1,n1),
inference(superposition,[],[f231,f5360]) ).
fof(f5427,plain,
add(n0,n0) = multiply(inverse(n1),multiply(n1,add(n1,n1))),
inference(superposition,[],[f416,f5360]) ).
fof(f5464,plain,
add(n0,n0) = multiply(inverse(n1),add(n1,multiply(n0,n1))),
inference(forward_demodulation,[],[f5427,f4861]) ).
fof(f5470,plain,
n0 = multiply(n0,n1),
inference(forward_demodulation,[],[f5414,f5316]) ).
fof(f5483,plain,
add(n0,n0) = multiply(n1,inverse(n1)),
inference(forward_demodulation,[],[f5464,f4694]) ).
fof(f5488,plain,
n0 = add(n0,n0),
inference(forward_demodulation,[],[f5483,f4]) ).
fof(f5489,plain,
! [X0,X1] : multiply(n1,add(X1,add(X0,n0))) = add(multiply(X1,n1),X0),
inference(forward_demodulation,[],[f1160,f5360]) ).
fof(f5509,plain,
n1 = add(n0,n1),
inference(superposition,[],[f48,f5416]) ).
fof(f5612,plain,
multiply(n0,n0) = add(n0,multiply(n0,n0)),
inference(superposition,[],[f293,f5470]) ).
fof(f5640,plain,
n0 = multiply(n0,n0),
inference(forward_demodulation,[],[f5612,f5316]) ).
fof(f5798,plain,
add(multiply(n0,n1),inverse(add(n0,n0))) = multiply(n1,add(n1,inverse(add(n0,n0)))),
inference(superposition,[],[f5489,f234]) ).
fof(f5834,plain,
multiply(n1,add(n1,inverse(n0))) = add(multiply(n0,n1),inverse(n0)),
inference(forward_demodulation,[],[f5798,f5488]) ).
fof(f5843,plain,
multiply(n1,add(n1,inverse(n0))) = add(n0,inverse(n0)),
inference(forward_demodulation,[],[f5834,f5470]) ).
fof(f5848,plain,
n1 = multiply(n1,add(n1,inverse(n0))),
inference(forward_demodulation,[],[f5843,f2]) ).
fof(f5850,plain,
n1 = add(inverse(n0),multiply(n0,n1)),
inference(forward_demodulation,[],[f5848,f15]) ).
fof(f5851,plain,
n1 = add(inverse(n0),n0),
inference(forward_demodulation,[],[f5850,f5470]) ).
fof(f5923,plain,
inverse(n0) = multiply(n1,n1),
inference(superposition,[],[f231,f5851]) ).
fof(f5976,plain,
n1 = inverse(n0),
inference(forward_demodulation,[],[f5923,f5416]) ).
fof(f6005,plain,
! [X0] : multiply(n1,X0) = add(n0,multiply(multiply(X0,n1),n1)),
inference(superposition,[],[f50,f5976]) ).
fof(f6013,plain,
add(n1,n1) = add(n0,add(n1,n0)),
inference(superposition,[],[f4823,f5976]) ).
fof(f6017,plain,
! [X0] : add(n0,multiply(X0,n1)) = multiply(n1,add(n0,X0)),
inference(superposition,[],[f13,f5976]) ).
fof(f6018,plain,
! [X0] : multiply(n1,add(X0,n0)) = add(multiply(X0,n1),n0),
inference(superposition,[],[f14,f5976]) ).
fof(f6042,plain,
! [X0] : multiply(add(X0,n1),add(n0,multiply(X0,n1))) = X0,
inference(superposition,[],[f252,f5976]) ).
fof(f6061,plain,
add(n0,n0) = multiply(inverse(multiply(n1,n1)),add(n1,n0)),
inference(superposition,[],[f1342,f5976]) ).
fof(f6070,plain,
add(n0,n0) = multiply(inverse(multiply(n1,n1)),n1),
inference(forward_demodulation,[],[f6061,f5360]) ).
fof(f6084,plain,
! [X0] : multiply(add(X0,n1),X0) = X0,
inference(forward_demodulation,[],[f6042,f48]) ).
fof(f6095,plain,
! [X0] : add(multiply(X0,n1),n0) = X0,
inference(forward_demodulation,[],[f6018,f231]) ).
fof(f6096,plain,
! [X0] : multiply(n1,add(n0,X0)) = X0,
inference(forward_demodulation,[],[f6017,f48]) ).
fof(f6097,plain,
add(n1,n1) = add(n0,n1),
inference(forward_demodulation,[],[f6013,f5360]) ).
fof(f6101,plain,
! [X0] : multiply(X0,n1) = multiply(n1,X0),
inference(forward_demodulation,[],[f6005,f48]) ).
fof(f6103,plain,
add(n0,n0) = multiply(inverse(n1),n1),
inference(forward_demodulation,[],[f6070,f5416]) ).
fof(f6114,plain,
n1 = add(n1,n1),
inference(forward_demodulation,[],[f6097,f5509]) ).
fof(f6117,plain,
n0 = multiply(inverse(n1),n1),
inference(forward_demodulation,[],[f6103,f5488]) ).
fof(f6339,plain,
add(n0,n0) = inverse(n1),
inference(superposition,[],[f48,f6117]) ).
fof(f6389,plain,
n0 = inverse(n1),
inference(forward_demodulation,[],[f6339,f5488]) ).
fof(f6728,plain,
! [X0] : add(multiply(n0,n1),multiply(n1,X0)) = multiply(add(n1,n1),add(X0,multiply(n0,n1))),
inference(superposition,[],[f603,f6084]) ).
fof(f6735,plain,
! [X0] : add(n0,multiply(n1,X0)) = multiply(add(n1,n1),add(X0,n0)),
inference(forward_demodulation,[],[f6728,f5470]) ).
fof(f6777,plain,
! [X0] : multiply(n1,add(X0,n0)) = add(n0,multiply(n1,X0)),
inference(forward_demodulation,[],[f6735,f6114]) ).
fof(f6804,plain,
! [X0] : add(n0,multiply(n1,X0)) = X0,
inference(forward_demodulation,[],[f6777,f231]) ).
fof(f7132,plain,
! [X0] : add(X0,n0) = add(multiply(n0,n1),X0),
inference(superposition,[],[f5489,f6096]) ).
fof(f7179,plain,
! [X0] : add(X0,n0) = add(n0,X0),
inference(forward_demodulation,[],[f7132,f5470]) ).
fof(f7681,plain,
! [X0] : add(X0,X0) = add(n0,multiply(add(multiply(X0,n1),n0),add(n1,n1))),
inference(superposition,[],[f6804,f390]) ).
fof(f7740,plain,
! [X0] : add(X0,X0) = add(n0,multiply(add(multiply(X0,n1),n0),n1)),
inference(forward_demodulation,[],[f7681,f6114]) ).
fof(f7768,plain,
! [X0] : add(X0,X0) = add(multiply(X0,n1),n0),
inference(forward_demodulation,[],[f7740,f48]) ).
fof(f7786,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f7768,f6095]) ).
fof(f9485,plain,
! [X0,X1] : multiply(X1,add(X0,X0)) = multiply(add(n0,multiply(X0,X1)),add(n1,n1)),
inference(superposition,[],[f390,f7179]) ).
fof(f9566,plain,
! [X0,X1] : multiply(X1,add(X0,X0)) = multiply(add(n0,multiply(X0,X1)),n1),
inference(forward_demodulation,[],[f9485,f7786]) ).
fof(f9618,plain,
! [X0,X1] : multiply(X1,add(X0,X0)) = multiply(n1,add(n0,multiply(X0,X1))),
inference(forward_demodulation,[],[f9566,f6101]) ).
fof(f9646,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,add(X0,X0)),
inference(forward_demodulation,[],[f9618,f6096]) ).
fof(f9664,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,X1),
inference(forward_demodulation,[],[f9646,f7786]) ).
fof(f10614,plain,
b != multiply(b,add(a,b)),
inference(superposition,[],[f12,f9664]) ).
fof(f10748,plain,
! [X0] : multiply(n1,n1) = add(inverse(X0),add(multiply(n1,X0),multiply(n0,n0))),
inference(superposition,[],[f189,f9664]) ).
fof(f10752,plain,
! [X0] : multiply(X0,X0) = add(multiply(n1,X0),multiply(n0,n0)),
inference(superposition,[],[f293,f9664]) ).
fof(f10982,plain,
! [X0] : multiply(X0,X0) = add(multiply(n1,X0),n0),
inference(forward_demodulation,[],[f10752,f5640]) ).
fof(f10986,plain,
! [X0] : multiply(n1,n1) = add(inverse(X0),add(multiply(n1,X0),n0)),
inference(forward_demodulation,[],[f10748,f5640]) ).
fof(f11263,plain,
! [X0] : multiply(X0,X0) = add(n0,multiply(n1,X0)),
inference(forward_demodulation,[],[f10982,f7179]) ).
fof(f11267,plain,
! [X0] : multiply(n1,n1) = add(inverse(X0),add(n0,multiply(n1,X0))),
inference(forward_demodulation,[],[f10986,f7179]) ).
fof(f11471,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f11263,f6804]) ).
fof(f11473,plain,
! [X0] : multiply(n1,n1) = add(inverse(X0),X0),
inference(forward_demodulation,[],[f11267,f6804]) ).
fof(f11617,plain,
! [X0] : n1 = add(inverse(X0),X0),
inference(forward_demodulation,[],[f11473,f5416]) ).
fof(f12239,plain,
! [X0] : inverse(inverse(X0)) = multiply(n1,add(X0,multiply(inverse(inverse(X0)),inverse(X0)))),
inference(superposition,[],[f252,f11617]) ).
fof(f12313,plain,
! [X0] : inverse(inverse(X0)) = multiply(n1,add(X0,multiply(inverse(X0),inverse(inverse(X0))))),
inference(forward_demodulation,[],[f12239,f9664]) ).
fof(f12382,plain,
! [X0] : inverse(inverse(X0)) = multiply(n1,add(X0,n0)),
inference(forward_demodulation,[],[f12313,f4]) ).
fof(f12430,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f12382,f231]) ).
fof(f12505,plain,
! [X0] : add(multiply(X0,X0),add(n0,multiply(X0,inverse(X0)))) = X0,
inference(superposition,[],[f100,f12430]) ).
fof(f12509,plain,
! [X0] : multiply(add(X0,X0),multiply(n1,add(X0,inverse(X0)))) = X0,
inference(superposition,[],[f257,f12430]) ).
fof(f12612,plain,
! [X0] : multiply(add(X0,X0),multiply(n1,n1)) = X0,
inference(forward_demodulation,[],[f12509,f2]) ).
fof(f12616,plain,
! [X0] : add(multiply(X0,X0),add(n0,n0)) = X0,
inference(forward_demodulation,[],[f12505,f4]) ).
fof(f12645,plain,
! [X0] : multiply(add(X0,X0),n1) = X0,
inference(forward_demodulation,[],[f12612,f11471]) ).
fof(f12646,plain,
! [X0] : add(multiply(X0,X0),n0) = X0,
inference(forward_demodulation,[],[f12616,f7786]) ).
fof(f12664,plain,
! [X0] : multiply(n1,add(X0,X0)) = X0,
inference(forward_demodulation,[],[f12645,f6101]) ).
fof(f12665,plain,
! [X0] : add(n0,multiply(X0,X0)) = X0,
inference(forward_demodulation,[],[f12646,f7179]) ).
fof(f12676,plain,
! [X0] : multiply(n1,X0) = X0,
inference(forward_demodulation,[],[f12664,f7786]) ).
fof(f12677,plain,
! [X0] : add(n0,X0) = X0,
inference(forward_demodulation,[],[f12665,f11471]) ).
fof(f14567,plain,
! [X0,X1] : multiply(n1,add(add(X1,X0),inverse(inverse(X1)))) = add(inverse(inverse(X1)),multiply(X0,inverse(X1))),
inference(forward_demodulation,[],[f37,f12677]) ).
fof(f14568,plain,
! [X0,X1] : multiply(n1,add(add(X1,X0),inverse(inverse(X1)))) = multiply(add(X0,inverse(inverse(X1))),n1),
inference(forward_demodulation,[],[f14567,f17]) ).
fof(f14569,plain,
! [X0,X1] : multiply(n1,add(add(X1,X0),inverse(inverse(X1)))) = multiply(n1,add(X0,inverse(inverse(X1)))),
inference(forward_demodulation,[],[f14568,f6101]) ).
fof(f14570,plain,
! [X0,X1] : multiply(n1,add(add(X1,X0),inverse(inverse(X1)))) = add(X0,inverse(inverse(X1))),
inference(forward_demodulation,[],[f14569,f12676]) ).
fof(f14571,plain,
! [X0,X1] : add(X0,X1) = multiply(n1,add(add(X1,X0),X1)),
inference(forward_demodulation,[],[f14570,f12430]) ).
fof(f14572,plain,
! [X0,X1] : add(X0,X1) = add(add(X1,X0),X1),
inference(forward_demodulation,[],[f14571,f12676]) ).
fof(f14586,plain,
! [X0] : add(n1,X0) = add(inverse(X0),X0),
inference(superposition,[],[f14572,f2]) ).
fof(f14939,plain,
! [X0] : n1 = add(n1,X0),
inference(forward_demodulation,[],[f14586,f11617]) ).
fof(f15420,plain,
! [X0] : multiply(inverse(n1),n1) = add(n0,multiply(X0,inverse(n1))),
inference(superposition,[],[f13,f14939]) ).
fof(f15587,plain,
! [X0] : multiply(X0,inverse(n1)) = multiply(inverse(n1),n1),
inference(forward_demodulation,[],[f15420,f12677]) ).
fof(f15704,plain,
! [X0] : multiply(X0,inverse(n1)) = multiply(n1,inverse(n1)),
inference(forward_demodulation,[],[f15587,f6101]) ).
fof(f15790,plain,
! [X0] : n0 = multiply(X0,inverse(n1)),
inference(forward_demodulation,[],[f15704,f4]) ).
fof(f15835,plain,
! [X0] : n0 = multiply(X0,n0),
inference(forward_demodulation,[],[f15790,f6389]) ).
fof(f16073,plain,
! [X0] : add(n0,n0) = multiply(inverse(n0),multiply(n0,add(X0,X0))),
inference(superposition,[],[f1263,f15835]) ).
fof(f16146,plain,
! [X0] : add(n0,n0) = multiply(inverse(n0),multiply(n0,X0)),
inference(forward_demodulation,[],[f16073,f7786]) ).
fof(f16193,plain,
! [X0] : add(n0,n0) = multiply(n1,multiply(n0,X0)),
inference(forward_demodulation,[],[f16146,f5976]) ).
fof(f16231,plain,
! [X0] : add(n0,n0) = multiply(n0,X0),
inference(forward_demodulation,[],[f16193,f12676]) ).
fof(f16251,plain,
! [X0] : n0 = multiply(n0,X0),
inference(forward_demodulation,[],[f16231,f7786]) ).
fof(f17193,plain,
! [X0,X1] : add(n0,multiply(multiply(X1,X0),inverse(inverse(X1)))) = multiply(inverse(inverse(X1)),add(X0,inverse(X1))),
inference(forward_demodulation,[],[f41,f12676]) ).
fof(f17194,plain,
! [X0,X1] : add(n0,multiply(multiply(X1,X0),inverse(inverse(X1)))) = add(multiply(X0,inverse(inverse(X1))),n0),
inference(forward_demodulation,[],[f17193,f14]) ).
fof(f17195,plain,
! [X0,X1] : add(n0,multiply(multiply(X1,X0),inverse(inverse(X1)))) = add(n0,multiply(X0,inverse(inverse(X1)))),
inference(forward_demodulation,[],[f17194,f7179]) ).
fof(f17196,plain,
! [X0,X1] : add(n0,multiply(multiply(X1,X0),inverse(inverse(X1)))) = multiply(X0,inverse(inverse(X1))),
inference(forward_demodulation,[],[f17195,f12677]) ).
fof(f17197,plain,
! [X0,X1] : multiply(X0,X1) = add(n0,multiply(multiply(X1,X0),X1)),
inference(forward_demodulation,[],[f17196,f12430]) ).
fof(f17198,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X1,X0),X1),
inference(forward_demodulation,[],[f17197,f12677]) ).
fof(f17199,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,multiply(X1,X0)),
inference(forward_demodulation,[],[f17198,f9664]) ).
fof(f17210,plain,
! [X0,X1] : multiply(multiply(n1,add(X1,X0)),X0) = multiply(X0,add(multiply(X0,n1),multiply(n0,multiply(X1,n1)))),
inference(superposition,[],[f17199,f311]) ).
fof(f17454,plain,
! [X0,X1] : multiply(multiply(n1,add(X1,X0)),X0) = multiply(X0,add(multiply(X0,n1),n0)),
inference(forward_demodulation,[],[f17210,f16251]) ).
fof(f17549,plain,
! [X0,X1] : multiply(X0,add(n0,multiply(X0,n1))) = multiply(multiply(n1,add(X1,X0)),X0),
inference(forward_demodulation,[],[f17454,f7179]) ).
fof(f17614,plain,
! [X0,X1] : multiply(X0,add(n0,multiply(X0,n1))) = multiply(X0,multiply(n1,add(X1,X0))),
inference(forward_demodulation,[],[f17549,f9664]) ).
fof(f17667,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(n0,multiply(X0,n1))),
inference(forward_demodulation,[],[f17614,f12676]) ).
fof(f17710,plain,
! [X0,X1] : add(multiply(X0,n1),multiply(n0,n0)) = multiply(X0,add(X1,X0)),
inference(forward_demodulation,[],[f17667,f52]) ).
fof(f17743,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X0,n1),n0),
inference(forward_demodulation,[],[f17710,f11471]) ).
fof(f17765,plain,
! [X0,X1] : add(n0,multiply(X0,n1)) = multiply(X0,add(X1,X0)),
inference(forward_demodulation,[],[f17743,f7179]) ).
fof(f17778,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(forward_demodulation,[],[f17765,f48]) ).
fof(f23630,plain,
b != b,
inference(superposition,[],[f10614,f17778]) ).
fof(f23631,plain,
$false,
inference(trivial_inequality_removal,[],[f23630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO026-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:04:45 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 6.17/1.56 % (2187295)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.17/1.56 % (2187304)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1006181370:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.17/1.56 % (2187300)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=2769178775:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.17/1.56 % (2187305)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4220984039:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.17/1.56 % (2187303)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1689760762:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.17/1.56 % (2187306)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3179832063:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.17/1.56 % (2187301)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=4167176639:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.17/1.56 % (2187302)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1059023117:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.17/1.56 % (2187304)Instruction limit reached!
% 6.17/1.56 % (2187304)------------------------------
% 6.17/1.56 % (2187304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.56 % (2187304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.56 % (2187304)CaDiCaL version: 2.1.3
% 6.17/1.56 % (2187304)Termination reason: Instruction limit
% 6.17/1.56 % (2187304)Termination phase: Saturation
% 6.17/1.56 % (2187304)Time elapsed: 0.056 s
% 6.17/1.56 % (2187304)Peak memory usage: 89 MB
% 6.17/1.56 % (2187304)Instructions burned: 182 (million)
% 6.17/1.56 % (2187303)Instruction limit reached!
% 6.17/1.56 % (2187303)------------------------------
% 6.17/1.56 % (2187303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.56 % (2187303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.56 % (2187303)CaDiCaL version: 2.1.3
% 6.17/1.56 % (2187303)Termination reason: Instruction limit
% 6.17/1.56 % (2187303)Termination phase: Saturation
% 6.17/1.56 % (2187303)Time elapsed: 0.087 s
% 6.17/1.56 % (2187303)Peak memory usage: 89 MB
% 6.17/1.56 % (2187303)Instructions burned: 136 (million)
% 6.17/1.56 % (2187314)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3121394265:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.17/1.56 % (2187305)Instruction limit reached!
% 6.17/1.56 % (2187305)------------------------------
% 6.17/1.56 % (2187305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.56 % (2187305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.56 % (2187305)CaDiCaL version: 2.1.3
% 6.17/1.56 % (2187305)Termination reason: Instruction limit
% 6.17/1.56 % (2187305)Termination phase: Saturation
% 6.17/1.56 % (2187305)Time elapsed: 0.179 s
% 6.17/1.56 % (2187305)Peak memory usage: 91 MB
% 6.17/1.56 % (2187305)Instructions burned: 257 (million)
% 6.17/1.56 % (2187315)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=649873691:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.17/1.56 % (2187317)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2016612927:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.17/1.56 % (2187317)Instruction limit reached!
% 6.17/1.56 % (2187317)------------------------------
% 6.17/1.56 % (2187317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.56 % (2187317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.56 % (2187317)CaDiCaL version: 2.1.3
% 6.17/1.56 % (2187317)Termination reason: Instruction limit
% 6.17/1.56 % (2187317)Termination phase: Saturation
% 6.17/1.56 % (2187317)Time elapsed: 0.101 s
% 6.17/1.56 % (2187317)Peak memory usage: 91 MB
% 6.17/1.56 % (2187317)Instructions burned: 216 (million)
% 6.17/1.56 % (2187306)First to succeed.
% 6.17/1.56 % (2187306)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2187295"
% 6.17/1.56 % (2187320)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=3720639241: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)
% 6.17/1.56 % (2187306)Refutation found. Thanks to Tanya!
% 6.17/1.56 % SZS status Unsatisfiable for theBenchmark
% 6.17/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 7.02/1.73 % (2187306)------------------------------
% 7.02/1.73 % (2187306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.02/1.73 % (2187306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.02/1.73 % (2187306)CaDiCaL version: 2.1.3
% 7.02/1.73 % (2187306)Termination reason: Refutation
% 7.02/1.73 % (2187306)Time elapsed: 0.476 s
% 7.02/1.73 % (2187306)Peak memory usage: 96 MB
% 7.02/1.73 % (2187306)Instructions burned: 845 (million)
% 7.02/1.73 % (2187306)------------------------------
% 7.02/1.73 % (2187306)------------------------------
% 7.02/1.73 % (2187295)Success in time 0.905 s
% 7.02/1.73 % Vampire exiting
%------------------------------------------------------------------------------