%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO031-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 15.19s 2.84s
% Output : Refutation 15.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 23
% Syntax : Number of formulae : 245 ( 212 unt; 12 def)
% Number of atoms : 309 ( 224 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 125 ( 61 ~; 57 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 497 ( 0 sgn 497 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),add(multiply(X1,X2),multiply(X2,X0))) = multiply(add(X0,X1),multiply(add(X1,X2),add(X2,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
fof(f2,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,multiply(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f3,axiom,
! [X2,X0,X1] : add(add(multiply(X0,X1),multiply(X1,X2)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(f4,axiom,
! [X0,X1] : multiply(add(X0,inverse(X0)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property3) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,add(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
fof(f7,axiom,
! [X0,X1] : add(multiply(X0,inverse(X0)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property3_dual) ).
fof(f8,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse) ).
fof(f10,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
fof(f11,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
fof(f12,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_add_property) ).
fof(f13,definition,
sF0 = add(b,c),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f14,plain,
add(b,c) = sF0,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF1 = multiply(a,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f16,plain,
multiply(a,sF0) = sF1,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF2 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f18,plain,
multiply(b,a) = sF2,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF3 = multiply(c,a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f20,plain,
multiply(c,a) = sF3,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF4 = add(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f22,plain,
add(sF2,sF3) = sF4,
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
sF1 != sF4,
inference(definition_folding,[],[f12,f22,f20,f18,f16,f14]) ).
fof(f24,plain,
! [X1] : add(n0,X1) = X1,
inference(forward_demodulation,[],[f7,f9]) ).
fof(f26,plain,
! [X1] : multiply(n1,X1) = X1,
inference(forward_demodulation,[],[f4,f8]) ).
fof(f27,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(multiply(X1,X2),X1)) = X1,
inference(forward_demodulation,[],[f3,f10]) ).
fof(f29,definition,
( spl5_1
<=> multiply(a,sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f31,plain,
( multiply(a,sF0) = sF1
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
spl5_1,
inference(avatar_split_clause,[],[f16,f29]) ).
fof(f34,definition,
( spl5_2
<=> add(sF2,sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f36,plain,
( add(sF2,sF3) = sF4
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
spl5_2,
inference(avatar_split_clause,[],[f22,f34]) ).
fof(f39,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(superposition,[],[f5,f24]) ).
fof(f44,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(superposition,[],[f2,f5]) ).
fof(f45,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(superposition,[],[f2,f26]) ).
fof(f48,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[],[f5,f2]) ).
fof(f53,plain,
! [X0] : n0 = multiply(X0,n0),
inference(superposition,[],[f24,f44]) ).
fof(f61,plain,
! [X0] : n0 = multiply(n0,X0),
inference(superposition,[],[f24,f45]) ).
fof(f66,definition,
( spl5_3
<=> sF1 = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f68,plain,
( sF1 != sF4
| spl5_3 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
~ spl5_3,
inference(avatar_split_clause,[],[f23,f66]) ).
fof(f73,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),X0),
inference(superposition,[],[f48,f45]) ).
fof(f80,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f73,f11]) ).
fof(f86,plain,
! [X2,X0,X1] : add(X0,X2) = add(X0,add(multiply(X1,X0),X2)),
inference(superposition,[],[f10,f44]) ).
fof(f87,plain,
! [X2,X0,X1] : add(X0,X2) = add(X0,add(multiply(X0,X1),X2)),
inference(superposition,[],[f10,f45]) ).
fof(f108,plain,
! [X0,X1] : add(X0,X1) = add(add(X0,X1),X0),
inference(superposition,[],[f44,f39]) ).
fof(f110,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(X1,X0)),
inference(forward_demodulation,[],[f108,f10]) ).
fof(f117,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(X0,multiply(add(X0,X1),X2)),
inference(superposition,[],[f11,f39]) ).
fof(f126,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,add(multiply(X0,X1),X2))),
inference(superposition,[],[f39,f11]) ).
fof(f137,plain,
! [X0] : add(X0,n0) = X0,
inference(superposition,[],[f2,f61]) ).
fof(f140,definition,
( spl5_4
<=> add(b,c) = sF0 ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f142,plain,
( add(b,c) = sF0
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
spl5_4,
inference(avatar_split_clause,[],[f14,f140]) ).
fof(f149,definition,
( spl5_5
<=> multiply(c,a) = sF3 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f151,plain,
( multiply(c,a) = sF3
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
spl5_5,
inference(avatar_split_clause,[],[f20,f149]) ).
fof(f158,definition,
( spl5_6
<=> multiply(b,a) = sF2 ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f160,plain,
( multiply(b,a) = sF2
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
spl5_6,
inference(avatar_split_clause,[],[f18,f158]) ).
fof(f168,plain,
! [X2,X0,X1] : add(multiply(X0,multiply(X0,X1)),add(multiply(multiply(X0,X1),X2),multiply(X2,X0))) = multiply(X0,multiply(add(multiply(X0,X1),X2),add(X2,X0))),
inference(superposition,[],[f1,f45]) ).
fof(f173,plain,
! [X2,X3,X0,X1] : add(multiply(X1,X0),add(multiply(X0,multiply(X2,multiply(X0,X3))),multiply(multiply(X2,multiply(X0,X3)),X1))) = multiply(add(X1,X0),multiply(X0,add(multiply(X2,multiply(X0,X3)),X1))),
inference(superposition,[],[f1,f2]) ).
fof(f174,plain,
! [X2,X0,X1] : add(multiply(X1,X0),add(multiply(X0,multiply(X2,X0)),multiply(multiply(X2,X0),X1))) = multiply(add(X1,X0),multiply(X0,add(multiply(X2,X0),X1))),
inference(superposition,[],[f1,f44]) ).
fof(f177,plain,
! [X0,X1] : add(multiply(X1,n0),add(multiply(n0,X0),multiply(X0,X1))) = multiply(add(X1,n0),multiply(X0,add(X0,X1))),
inference(superposition,[],[f1,f24]) ).
fof(f184,plain,
! [X0,X1] : add(multiply(X0,X1),add(multiply(X1,n0),multiply(n0,X0))) = multiply(add(X0,X1),multiply(add(X1,n0),X0)),
inference(superposition,[],[f1,f24]) ).
fof(f191,plain,
! [X2,X0,X1] : add(X0,X1) = add(add(X0,X1),add(multiply(X0,X1),add(multiply(X1,X2),multiply(X2,X0)))),
inference(superposition,[],[f45,f1]) ).
fof(f195,plain,
! [X2,X0,X1] : add(X0,X1) = add(X0,add(X1,add(multiply(X0,X1),add(multiply(X1,X2),multiply(X2,X0))))),
inference(forward_demodulation,[],[f191,f10]) ).
fof(f200,plain,
! [X0,X1] : add(multiply(X0,X1),add(multiply(X1,n0),multiply(n0,X0))) = multiply(add(X0,X1),multiply(X1,X0)),
inference(forward_demodulation,[],[f184,f137]) ).
fof(f204,plain,
! [X0,X1] : add(multiply(X1,n0),add(multiply(n0,X0),multiply(X0,X1))) = multiply(add(X1,n0),X0),
inference(forward_demodulation,[],[f177,f39]) ).
fof(f206,plain,
! [X2,X0,X1] : multiply(add(X1,X0),multiply(X0,add(multiply(X2,X0),X1))) = add(multiply(X1,X0),add(multiply(X0,multiply(X2,X0)),multiply(X2,multiply(X0,X1)))),
inference(forward_demodulation,[],[f174,f11]) ).
fof(f207,plain,
! [X2,X3,X0,X1] : multiply(add(X1,X0),multiply(X0,add(multiply(X2,multiply(X0,X3)),X1))) = add(multiply(X1,X0),add(multiply(X0,multiply(X2,multiply(X0,X3))),multiply(X2,multiply(multiply(X0,X3),X1)))),
inference(forward_demodulation,[],[f173,f11]) ).
fof(f209,plain,
! [X2,X0,X1] : multiply(X0,multiply(add(multiply(X0,X1),X2),add(X2,X0))) = add(multiply(X0,multiply(X0,X1)),add(multiply(X0,multiply(X1,X2)),multiply(X2,X0))),
inference(forward_demodulation,[],[f168,f11]) ).
fof(f212,plain,
! [X2,X0,X1] : add(X0,X1) = add(X0,add(X1,add(multiply(X1,X2),multiply(X2,X0)))),
inference(forward_demodulation,[],[f195,f86]) ).
fof(f215,plain,
! [X0,X1] : multiply(add(X0,X1),multiply(X1,X0)) = add(multiply(X0,X1),add(multiply(X1,n0),n0)),
inference(forward_demodulation,[],[f200,f61]) ).
fof(f218,plain,
! [X0,X1] : multiply(X1,X0) = add(multiply(X1,n0),add(multiply(n0,X0),multiply(X0,X1))),
inference(forward_demodulation,[],[f204,f137]) ).
fof(f219,plain,
! [X2,X0,X1] : multiply(add(X1,X0),multiply(X0,add(multiply(X2,X0),X1))) = add(multiply(X1,X0),add(multiply(X0,X2),multiply(X2,multiply(X0,X1)))),
inference(forward_demodulation,[],[f206,f80]) ).
fof(f220,plain,
! [X2,X3,X0,X1] : multiply(add(X1,X0),multiply(X0,add(multiply(X2,multiply(X0,X3)),X1))) = add(multiply(X1,X0),add(multiply(X0,multiply(X2,multiply(X0,X3))),multiply(X2,multiply(X0,multiply(X3,X1))))),
inference(forward_demodulation,[],[f207,f11]) ).
fof(f224,plain,
! [X2,X0,X1] : add(X0,X1) = add(X0,add(X1,multiply(X2,X0))),
inference(forward_demodulation,[],[f212,f87]) ).
fof(f227,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X1,n0)) = multiply(add(X0,X1),multiply(X1,X0)),
inference(forward_demodulation,[],[f215,f137]) ).
fof(f228,plain,
! [X0,X1] : multiply(X1,X0) = add(multiply(X1,n0),add(n0,multiply(X0,X1))),
inference(forward_demodulation,[],[f218,f61]) ).
fof(f232,plain,
! [X0,X1] : multiply(add(X0,X1),multiply(X1,X0)) = add(multiply(X0,X1),n0),
inference(forward_demodulation,[],[f227,f53]) ).
fof(f233,plain,
! [X0,X1] : multiply(X1,X0) = add(multiply(X1,n0),multiply(X0,X1)),
inference(forward_demodulation,[],[f228,f24]) ).
fof(f235,plain,
! [X0,X1] : multiply(X0,X1) = multiply(add(X0,X1),multiply(X1,X0)),
inference(forward_demodulation,[],[f232,f137]) ).
fof(f236,plain,
! [X0,X1] : multiply(X1,X0) = add(n0,multiply(X0,X1)),
inference(forward_demodulation,[],[f233,f53]) ).
fof(f238,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f236,f24]) ).
fof(f249,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(add(X2,multiply(X0,X1)),multiply(X0,multiply(X1,X2))),
inference(superposition,[],[f235,f11]) ).
fof(f252,plain,
! [X0] : multiply(X0,n1) = multiply(add(X0,n1),X0),
inference(superposition,[],[f235,f26]) ).
fof(f260,plain,
! [X0,X1] : multiply(X1,X0) = add(multiply(X1,X0),multiply(X0,X1)),
inference(superposition,[],[f44,f235]) ).
fof(f269,plain,
! [X0] : multiply(X0,n1) = multiply(X0,add(X0,n1)),
inference(forward_demodulation,[],[f252,f238]) ).
fof(f272,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X0,multiply(X1,X2)),add(X2,multiply(X0,X1))),
inference(forward_demodulation,[],[f249,f238]) ).
fof(f283,plain,
! [X0] : multiply(X0,n1) = X0,
inference(forward_demodulation,[],[f269,f39]) ).
fof(f286,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(X0,multiply(multiply(X1,X2),add(X2,multiply(X0,X1)))),
inference(forward_demodulation,[],[f272,f11]) ).
fof(f295,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(X0,multiply(X1,multiply(X2,add(X2,multiply(X0,X1))))),
inference(forward_demodulation,[],[f286,f11]) ).
fof(f301,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[],[f295,f39]) ).
fof(f369,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(inverse(X0),X1),multiply(X1,X0))) = multiply(n1,multiply(add(inverse(X0),X1),add(X1,X0))),
inference(superposition,[],[f1,f8]) ).
fof(f370,plain,
! [X0,X1] : add(multiply(X0,X1),add(multiply(X1,inverse(X1)),multiply(inverse(X1),X0))) = multiply(add(X0,X1),multiply(n1,add(inverse(X1),X0))),
inference(superposition,[],[f1,f8]) ).
fof(f383,plain,
! [X0,X1] : add(multiply(X0,X1),add(multiply(X1,inverse(X1)),multiply(inverse(X1),X0))) = multiply(add(X0,X1),add(inverse(X1),X0)),
inference(forward_demodulation,[],[f370,f26]) ).
fof(f384,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(inverse(X0),X1),multiply(X1,X0))) = multiply(add(inverse(X0),X1),add(X1,X0)),
inference(forward_demodulation,[],[f369,f26]) ).
fof(f386,plain,
! [X0,X1] : multiply(add(X0,X1),add(inverse(X1),X0)) = add(multiply(X0,X1),add(n0,multiply(inverse(X1),X0))),
inference(forward_demodulation,[],[f383,f9]) ).
fof(f387,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(inverse(X0),X1),multiply(X1,X0))) = multiply(add(X1,X0),add(inverse(X0),X1)),
inference(forward_demodulation,[],[f384,f238]) ).
fof(f389,plain,
! [X0,X1] : multiply(add(X0,X1),add(inverse(X1),X0)) = add(multiply(X0,X1),multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f386,f24]) ).
fof(f390,plain,
! [X0,X1] : multiply(add(X1,X0),add(inverse(X0),X1)) = add(n0,add(multiply(inverse(X0),X1),multiply(X1,X0))),
inference(forward_demodulation,[],[f387,f9]) ).
fof(f392,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),multiply(X1,X0)) = multiply(add(X1,X0),add(inverse(X0),X1)),
inference(forward_demodulation,[],[f390,f24]) ).
fof(f394,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),multiply(X1,X0)) = add(multiply(X1,X0),multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f392,f389]) ).
fof(f398,plain,
! [X0,X1] : add(inverse(X0),multiply(add(inverse(X0),X1),X0)) = add(multiply(add(inverse(X0),X1),X0),inverse(X0)),
inference(superposition,[],[f394,f39]) ).
fof(f441,plain,
! [X0,X1] : add(inverse(X0),multiply(X0,add(inverse(X0),X1))) = add(multiply(X0,add(inverse(X0),X1)),inverse(X0)),
inference(forward_demodulation,[],[f398,f238]) ).
fof(f458,plain,
! [X0,X1] : add(multiply(X0,multiply(X1,X0)),multiply(inverse(multiply(X1,X0)),X0)) = multiply(X0,add(inverse(multiply(X1,X0)),X0)),
inference(superposition,[],[f389,f44]) ).
fof(f462,plain,
! [X2,X0,X1] : add(multiply(add(X0,X1),X2),multiply(inverse(X2),add(X0,X1))) = multiply(add(X0,add(X1,X2)),add(inverse(X2),add(X0,X1))),
inference(superposition,[],[f389,f10]) ).
fof(f491,plain,
! [X0,X1] : add(multiply(X0,multiply(X1,X0)),multiply(inverse(multiply(X1,X0)),X0)) = X0,
inference(forward_demodulation,[],[f458,f48]) ).
fof(f505,plain,
! [X0,X1] : add(multiply(X0,multiply(X1,X0)),multiply(X0,inverse(multiply(X1,X0)))) = X0,
inference(forward_demodulation,[],[f491,f238]) ).
fof(f515,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(multiply(X1,X0)))) = X0,
inference(forward_demodulation,[],[f505,f80]) ).
fof(f562,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),add(X2,X0)),
inference(superposition,[],[f5,f515]) ).
fof(f572,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,add(X2,X0))),
inference(forward_demodulation,[],[f562,f11]) ).
fof(f601,plain,
! [X2,X0,X1] : add(multiply(X0,multiply(X0,X1)),add(multiply(X0,multiply(X1,X2)),multiply(X2,X0))) = multiply(X0,add(multiply(X0,X1),X2)),
inference(backward_demodulation,[],[f209,f572]) ).
fof(f741,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(X0,X1)),
inference(superposition,[],[f87,f283]) ).
fof(f742,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),X3) = add(multiply(X0,X1),add(multiply(X0,multiply(X1,X2)),X3)),
inference(superposition,[],[f87,f11]) ).
fof(f760,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(multiply(X0,X2),add(X0,X1)),
inference(superposition,[],[f5,f87]) ).
fof(f782,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(X0,multiply(X2,add(X0,X1))),
inference(forward_demodulation,[],[f760,f11]) ).
fof(f822,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = X0,
inference(superposition,[],[f741,f515]) ).
fof(f830,plain,
! [X2,X0,X1] : add(multiply(X0,add(X0,X1)),add(multiply(add(X0,X1),X2),multiply(X2,X0))) = multiply(add(X0,X1),multiply(add(add(X0,X1),X2),add(X2,X0))),
inference(superposition,[],[f1,f741]) ).
fof(f831,plain,
! [X2,X0,X1] : add(multiply(X2,X0),add(multiply(X0,add(X0,X1)),multiply(add(X0,X1),X2))) = multiply(add(X2,X0),multiply(add(X0,X1),add(add(X0,X1),X2))),
inference(superposition,[],[f1,f741]) ).
fof(f840,plain,
! [X0,X1] : add(multiply(add(inverse(X0),X1),X0),multiply(inverse(X0),add(inverse(X0),X1))) = multiply(add(add(inverse(X0),X1),X0),add(inverse(X0),X1)),
inference(superposition,[],[f389,f741]) ).
fof(f841,plain,
! [X0,X1] : add(multiply(add(inverse(X0),X1),X0),multiply(inverse(X0),add(inverse(X0),X1))) = multiply(add(inverse(X0),X1),add(add(inverse(X0),X1),X0)),
inference(forward_demodulation,[],[f840,f238]) ).
fof(f847,plain,
! [X2,X0,X1] : multiply(add(X2,X0),add(X0,X1)) = add(multiply(X2,X0),add(multiply(X0,add(X0,X1)),multiply(add(X0,X1),X2))),
inference(forward_demodulation,[],[f831,f39]) ).
fof(f848,plain,
! [X2,X0,X1] : multiply(add(X0,X1),add(X2,X0)) = add(multiply(X0,add(X0,X1)),add(multiply(add(X0,X1),X2),multiply(X2,X0))),
inference(forward_demodulation,[],[f830,f117]) ).
fof(f851,plain,
! [X0,X1] : add(multiply(X0,X1),X1) = X1,
inference(backward_demodulation,[],[f27,f822]) ).
fof(f853,plain,
! [X0,X1] : add(inverse(X0),X1) = add(multiply(add(inverse(X0),X1),X0),multiply(inverse(X0),add(inverse(X0),X1))),
inference(forward_demodulation,[],[f841,f39]) ).
fof(f856,plain,
! [X2,X0,X1] : multiply(add(X2,X0),add(X0,X1)) = add(multiply(X2,X0),add(X0,multiply(add(X0,X1),X2))),
inference(forward_demodulation,[],[f847,f39]) ).
fof(f857,plain,
! [X2,X0,X1] : multiply(add(X0,X1),add(X2,X0)) = add(X0,add(multiply(add(X0,X1),X2),multiply(X2,X0))),
inference(forward_demodulation,[],[f848,f39]) ).
fof(f860,plain,
! [X0,X1] : add(inverse(X0),X1) = add(multiply(add(inverse(X0),X1),X0),inverse(X0)),
inference(forward_demodulation,[],[f853,f39]) ).
fof(f863,plain,
! [X2,X0,X1] : multiply(add(X0,X1),add(X2,X0)) = add(X0,multiply(add(X0,X1),X2)),
inference(forward_demodulation,[],[f857,f224]) ).
fof(f866,plain,
! [X0,X1] : add(inverse(X0),X1) = add(multiply(X0,add(inverse(X0),X1)),inverse(X0)),
inference(forward_demodulation,[],[f860,f238]) ).
fof(f869,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = add(X0,multiply(add(X0,X1),inverse(X1))),
inference(backward_demodulation,[],[f389,f863]) ).
fof(f874,plain,
! [X0,X1] : add(inverse(X0),X1) = add(inverse(X0),multiply(X0,add(inverse(X0),X1))),
inference(forward_demodulation,[],[f866,f441]) ).
fof(f883,plain,
! [X0,X1] : add(X1,X0) = add(X0,add(X1,X0)),
inference(superposition,[],[f851,f48]) ).
fof(f899,plain,
! [X2,X0,X1] : add(X0,X2) = add(multiply(X1,X0),add(X0,X2)),
inference(superposition,[],[f10,f851]) ).
fof(f907,plain,
! [X2,X0,X1] : multiply(add(X2,X0),add(X0,X1)) = add(X0,multiply(add(X0,X1),X2)),
inference(backward_demodulation,[],[f856,f899]) ).
fof(f914,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[],[f883,f110]) ).
fof(f984,plain,
! [X2,X0,X1] : add(X1,X0) = add(X1,add(X0,multiply(X1,X2))),
inference(superposition,[],[f87,f914]) ).
fof(f1001,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[],[f117,f45]) ).
fof(f1006,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X1),multiply(X0,X2)),
inference(superposition,[],[f117,f515]) ).
fof(f1058,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(forward_demodulation,[],[f1006,f11]) ).
fof(f1065,plain,
! [X2,X0,X1] : multiply(X0,add(multiply(X0,X1),X2)) = add(multiply(X0,X1),add(multiply(X0,multiply(X1,X2)),multiply(X2,X0))),
inference(backward_demodulation,[],[f601,f1001]) ).
fof(f1077,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(forward_demodulation,[],[f1058,f11]) ).
fof(f1080,plain,
! [X2,X0,X1] : multiply(X0,add(multiply(X0,X1),X2)) = add(multiply(X0,X1),multiply(X2,X0)),
inference(forward_demodulation,[],[f1065,f742]) ).
fof(f1090,plain,
! [X2,X3,X0,X1] : multiply(add(X1,X0),multiply(X0,add(multiply(X2,multiply(X0,X3)),X1))) = add(multiply(X1,X0),add(multiply(X0,multiply(X2,X3)),multiply(X2,multiply(X0,multiply(X3,X1))))),
inference(backward_demodulation,[],[f220,f1077]) ).
fof(f1108,plain,
! [X2,X3,X0,X1] : add(multiply(X1,X0),add(multiply(X0,multiply(X2,X3)),multiply(X2,multiply(X0,multiply(X3,X1))))) = multiply(X0,multiply(add(multiply(X2,multiply(X0,X3)),X1),add(X1,X0))),
inference(forward_demodulation,[],[f1090,f301]) ).
fof(f1123,plain,
! [X2,X3,X0,X1] : multiply(X0,add(multiply(X2,multiply(X0,X3)),X1)) = add(multiply(X1,X0),add(multiply(X0,multiply(X2,X3)),multiply(X2,multiply(X0,multiply(X3,X1))))),
inference(forward_demodulation,[],[f1108,f572]) ).
fof(f1134,plain,
! [X2,X0,X1] : multiply(X1,add(multiply(X0,X1),X2)) = add(multiply(X0,X1),multiply(X2,X1)),
inference(superposition,[],[f1080,f238]) ).
fof(f1153,plain,
! [X2,X0,X1] : add(multiply(X1,X2),multiply(X0,X1)) = multiply(X1,add(X0,multiply(X1,X2))),
inference(superposition,[],[f1080,f914]) ).
fof(f1221,plain,
! [X2,X0,X1] : add(multiply(X1,X0),add(multiply(X0,X2),multiply(X2,multiply(X0,X1)))) = multiply(add(X1,X0),add(multiply(X2,X0),multiply(X1,X0))),
inference(backward_demodulation,[],[f219,f1134]) ).
fof(f1222,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(X0,add(multiply(X0,X1),multiply(X2,X1))),
inference(backward_demodulation,[],[f126,f1134]) ).
fof(f1247,plain,
! [X2,X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(multiply(X2,X1),X0)),
inference(forward_demodulation,[],[f1222,f1080]) ).
fof(f1260,plain,
! [X2,X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(X2,multiply(X1,X0))),
inference(forward_demodulation,[],[f1247,f11]) ).
fof(f1272,plain,
! [X2,X0,X1] : multiply(add(X1,X0),add(X0,X2)) = add(X0,multiply(X2,add(X1,X0))),
inference(superposition,[],[f1134,f48]) ).
fof(f1353,plain,
! [X2,X0,X1] : add(X0,multiply(X2,add(X1,X0))) = add(X0,multiply(add(X0,X2),X1)),
inference(forward_demodulation,[],[f1272,f907]) ).
fof(f1378,plain,
! [X2,X0,X1] : add(X0,multiply(X1,add(X2,X0))) = multiply(add(X0,X1),add(X2,X0)),
inference(backward_demodulation,[],[f863,f1353]) ).
fof(f1381,plain,
! [X2,X0,X1] : add(X0,multiply(X1,add(X2,X0))) = multiply(add(X2,X0),add(X0,X1)),
inference(backward_demodulation,[],[f907,f1353]) ).
fof(f1386,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = add(X0,multiply(X1,add(inverse(X1),X0))),
inference(backward_demodulation,[],[f869,f1353]) ).
fof(f1632,plain,
! [X2,X0,X1] : add(multiply(X1,X0),X2) = add(multiply(X1,X0),add(multiply(X0,X1),X2)),
inference(superposition,[],[f86,f235]) ).
fof(f1761,plain,
! [X2,X0,X1] : add(multiply(X1,X0),multiply(X0,X1)) = add(multiply(X1,X0),multiply(multiply(X0,X1),X2)),
inference(superposition,[],[f1632,f45]) ).
fof(f1790,plain,
! [X2,X0,X1] : add(multiply(X1,X0),multiply(X0,X1)) = add(multiply(X1,X0),multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[],[f1761,f11]) ).
fof(f1825,plain,
! [X2,X0,X1] : multiply(X1,X0) = add(multiply(X1,X0),multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[],[f1790,f260]) ).
fof(f1850,plain,
! [X2,X0,X1] : add(multiply(X1,X0),multiply(X0,X2)) = multiply(add(X1,X0),add(multiply(X2,X0),multiply(X1,X0))),
inference(backward_demodulation,[],[f1221,f1825]) ).
fof(f1901,plain,
! [X0,X1] : multiply(X1,add(inverse(X1),X0)) = multiply(multiply(X1,add(inverse(X1),X0)),add(multiply(X0,X1),multiply(inverse(X1),X0))),
inference(superposition,[],[f48,f1386]) ).
fof(f1904,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = add(X0,add(multiply(X0,X1),multiply(inverse(X1),X0))),
inference(superposition,[],[f741,f1386]) ).
fof(f1918,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = add(multiply(X0,X1),multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f1904,f224]) ).
fof(f1921,plain,
! [X0,X1] : multiply(X1,add(inverse(X1),X0)) = multiply(X1,multiply(add(inverse(X1),X0),add(multiply(X0,X1),multiply(inverse(X1),X0)))),
inference(forward_demodulation,[],[f1901,f11]) ).
fof(f1950,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = X0,
inference(forward_demodulation,[],[f1918,f45]) ).
fof(f1987,plain,
! [X0,X1] : multiply(X1,add(inverse(X1),X0)) = multiply(X1,multiply(add(inverse(X1),X0),X0)),
inference(backward_demodulation,[],[f1921,f1950]) ).
fof(f1990,plain,
! [X2,X0,X1] : add(X0,X1) = multiply(add(X0,add(X1,X2)),add(inverse(X2),add(X0,X1))),
inference(backward_demodulation,[],[f462,f1950]) ).
fof(f2011,plain,
! [X0,X1] : multiply(X1,add(inverse(X1),X0)) = multiply(X1,multiply(X0,add(inverse(X1),X0))),
inference(forward_demodulation,[],[f1987,f238]) ).
fof(f2028,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X1,add(inverse(X1),X0)),
inference(forward_demodulation,[],[f2011,f48]) ).
fof(f2042,plain,
! [X0,X1] : add(inverse(X0),X1) = add(inverse(X0),multiply(X0,X1)),
inference(backward_demodulation,[],[f874,f2028]) ).
fof(f2366,plain,
! [X2,X0,X1] : add(inverse(X0),add(multiply(X0,X1),X2)) = add(inverse(X0),add(multiply(X0,X1),multiply(X2,X0))),
inference(superposition,[],[f2042,f1080]) ).
fof(f2388,plain,
! [X2,X0,X1] : add(add(inverse(X0),X1),X2) = add(inverse(X0),add(multiply(X0,X1),X2)),
inference(superposition,[],[f10,f2042]) ).
fof(f2401,plain,
! [X2,X0,X1] : add(inverse(X0),add(X1,X2)) = add(inverse(X0),add(multiply(X0,X1),X2)),
inference(forward_demodulation,[],[f2388,f10]) ).
fof(f2419,plain,
! [X2,X0,X1] : add(inverse(X0),add(X1,X2)) = add(inverse(X0),add(multiply(X0,X1),multiply(X2,X0))),
inference(backward_demodulation,[],[f2366,f2401]) ).
fof(f2428,plain,
! [X2,X0,X1] : add(inverse(X0),add(X1,X2)) = add(inverse(X0),add(X1,multiply(X2,X0))),
inference(forward_demodulation,[],[f2419,f2401]) ).
fof(f3287,plain,
( multiply(a,b) = multiply(a,sF2)
| ~ spl5_6 ),
inference(superposition,[],[f80,f160]) ).
fof(f3347,plain,
( multiply(a,b) = multiply(sF2,a)
| ~ spl5_6 ),
inference(forward_demodulation,[],[f3287,f238]) ).
fof(f3369,plain,
( multiply(b,a) = multiply(sF2,a)
| ~ spl5_6 ),
inference(forward_demodulation,[],[f3347,f238]) ).
fof(f3385,plain,
( sF2 = multiply(sF2,a)
| ~ spl5_6 ),
inference(forward_demodulation,[],[f3369,f160]) ).
fof(f3409,definition,
( spl5_11
<=> sF2 = multiply(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f3411,plain,
( sF2 = multiply(sF2,a)
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f3409]) ).
fof(f3412,plain,
( spl5_11
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f3385,f158,f3409]) ).
fof(f4496,plain,
! [X2,X3,X0,X1] : multiply(X1,add(multiply(X0,multiply(X1,X2)),X3)) = add(multiply(X0,multiply(X1,X2)),multiply(X3,X1)),
inference(superposition,[],[f1080,f301]) ).
fof(f4585,plain,
! [X2,X3,X0,X1] : add(multiply(X1,X0),add(multiply(X0,multiply(X2,X3)),multiply(X2,multiply(X0,multiply(X3,X1))))) = add(multiply(X2,multiply(X0,X3)),multiply(X1,X0)),
inference(backward_demodulation,[],[f1123,f4496]) ).
fof(f5118,plain,
! [X2,X3,X0,X1] : add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(multiply(X1,multiply(X0,X2)),X3)) = multiply(X0,add(multiply(X3,multiply(X1,multiply(X0,X2))),multiply(X0,multiply(X1,multiply(X0,X2))))),
inference(superposition,[],[f1850,f2]) ).
fof(f5127,plain,
! [X2,X0,X1] : add(multiply(X0,add(X1,X0)),multiply(add(X1,X0),X2)) = multiply(add(X0,X1),add(multiply(X2,add(X1,X0)),multiply(X0,add(X1,X0)))),
inference(superposition,[],[f1850,f110]) ).
fof(f5195,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = multiply(add(X0,add(X1,X0)),add(multiply(X2,add(X1,X0)),X0)),
inference(superposition,[],[f1850,f48]) ).
fof(f5215,plain,
( ! [X0] : add(sF2,multiply(a,X0)) = multiply(add(sF2,a),add(multiply(X0,a),sF2))
| ~ spl5_11 ),
inference(superposition,[],[f1850,f3411]) ).
fof(f5294,plain,
( ! [X0] : add(sF2,multiply(a,X0)) = add(sF2,multiply(a,add(multiply(X0,a),sF2)))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f5215,f1378]) ).
fof(f5313,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,multiply(add(X1,X0),add(multiply(X2,add(X1,X0)),X0))),
inference(forward_demodulation,[],[f5195,f1378]) ).
fof(f5376,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = multiply(add(X0,X1),add(multiply(X2,add(X1,X0)),X0)),
inference(forward_demodulation,[],[f5127,f48]) ).
fof(f5385,plain,
! [X2,X3,X0,X1] : add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(multiply(X1,multiply(X0,X2)),X3)) = add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(multiply(X3,multiply(X1,multiply(X0,X2))),X0)),
inference(forward_demodulation,[],[f5118,f1153]) ).
fof(f5424,plain,
( ! [X0] : add(sF2,multiply(a,X0)) = add(sF2,add(multiply(X0,a),multiply(sF2,a)))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f5294,f1134]) ).
fof(f5440,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,add(multiply(X2,add(X1,X0)),multiply(X0,add(X1,X0)))),
inference(forward_demodulation,[],[f5313,f1134]) ).
fof(f5489,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,multiply(X1,add(multiply(X2,add(X1,X0)),X0))),
inference(forward_demodulation,[],[f5376,f1378]) ).
fof(f5497,plain,
! [X2,X3,X0,X1] : add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(multiply(X1,multiply(X0,X2)),X3)) = add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(X3,multiply(multiply(X1,multiply(X0,X2)),X0))),
inference(forward_demodulation,[],[f5385,f11]) ).
fof(f5528,plain,
( ! [X0] : add(sF2,multiply(X0,a)) = add(sF2,multiply(a,X0))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f5424,f984]) ).
fof(f5541,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,multiply(X2,add(X1,X0))),
inference(forward_demodulation,[],[f5440,f984]) ).
fof(f5586,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,multiply(X1,add(X0,multiply(X2,add(X1,X0))))),
inference(forward_demodulation,[],[f5489,f914]) ).
fof(f5594,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,multiply(X0,X2))) = add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(multiply(X1,multiply(X0,X2)),X3)),
inference(forward_demodulation,[],[f5497,f1260]) ).
fof(f5649,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,multiply(X0,X2))) = add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(X1,multiply(multiply(X0,X2),X3))),
inference(forward_demodulation,[],[f5594,f11]) ).
fof(f5688,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,multiply(X0,X2))) = add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(X1,multiply(X0,multiply(X2,X3)))),
inference(forward_demodulation,[],[f5649,f11]) ).
fof(f5716,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,X2)) = add(multiply(X0,multiply(X1,X2)),multiply(X1,multiply(X0,multiply(X2,X3)))),
inference(forward_demodulation,[],[f5688,f1077]) ).
fof(f5735,plain,
! [X2,X3,X0,X1] : add(multiply(X2,multiply(X0,X3)),multiply(X1,X0)) = add(multiply(X1,X0),multiply(X0,multiply(X2,X3))),
inference(backward_demodulation,[],[f4585,f5716]) ).
fof(f5889,plain,
! [X2,X3,X0,X1,X4] : add(multiply(X0,multiply(X1,add(X2,add(X0,X3)))),multiply(X4,X1)) = add(multiply(X4,X1),multiply(X1,X0)),
inference(superposition,[],[f5735,f5]) ).
fof(f5982,plain,
! [X2,X3,X0,X1] : add(multiply(X1,multiply(X0,X2)),multiply(X3,X1)) = add(multiply(X0,multiply(X1,X2)),multiply(X3,X1)),
inference(superposition,[],[f914,f5735]) ).
fof(f6658,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = multiply(add(X1,X0),add(inverse(X0),add(X1,multiply(X2,X0)))),
inference(superposition,[],[f1990,f851]) ).
fof(f6692,plain,
! [X2,X0,X1] : add(multiply(X2,add(X0,X1)),X0) = multiply(add(X0,X1),add(inverse(X1),add(multiply(X2,add(X0,X1)),X0))),
inference(superposition,[],[f1990,f851]) ).
fof(f6869,plain,
! [X2,X0,X1] : add(X0,multiply(X2,add(X0,X1))) = multiply(add(X0,X1),add(inverse(X1),add(X0,multiply(X2,add(X0,X1))))),
inference(forward_demodulation,[],[f6692,f914]) ).
fof(f6896,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = multiply(add(X1,X0),add(inverse(X0),add(X1,X2))),
inference(forward_demodulation,[],[f6658,f2428]) ).
fof(f6989,plain,
! [X2,X0,X1] : add(X0,multiply(X2,add(X0,X1))) = add(X0,multiply(multiply(X2,add(X0,X1)),X1)),
inference(backward_demodulation,[],[f6869,f6896]) ).
fof(f7056,plain,
! [X2,X0,X1] : add(X0,multiply(X2,add(X0,X1))) = add(X0,multiply(X2,multiply(add(X0,X1),X1))),
inference(forward_demodulation,[],[f6989,f11]) ).
fof(f7102,plain,
! [X2,X0,X1] : add(X0,multiply(X2,add(X0,X1))) = add(X0,multiply(X2,multiply(X1,add(X0,X1)))),
inference(forward_demodulation,[],[f7056,f238]) ).
fof(f7124,plain,
! [X2,X0,X1] : add(X0,multiply(X2,add(X0,X1))) = add(X0,multiply(X2,X1)),
inference(forward_demodulation,[],[f7102,f48]) ).
fof(f7137,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,multiply(X1,multiply(X2,add(X1,X0)))),
inference(backward_demodulation,[],[f5586,f7124]) ).
fof(f7159,plain,
! [X2,X0,X1] : add(X0,multiply(add(X1,X0),X2)) = add(X0,multiply(X1,X2)),
inference(forward_demodulation,[],[f7137,f782]) ).
fof(f7171,plain,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = add(X0,multiply(X2,add(X1,X0))),
inference(backward_demodulation,[],[f5541,f7159]) ).
fof(f7188,plain,
! [X2,X0,X1] : multiply(add(X2,X0),add(X0,X1)) = add(X0,multiply(X2,X1)),
inference(backward_demodulation,[],[f1381,f7171]) ).
fof(f7731,plain,
! [X2,X0,X1] : multiply(X1,add(X0,X2)) = multiply(X1,add(X0,multiply(X1,X2))),
inference(superposition,[],[f117,f7188]) ).
fof(f7811,plain,
! [X2,X0,X1] : multiply(X1,add(X0,X2)) = add(multiply(X1,X2),multiply(X0,X1)),
inference(forward_demodulation,[],[f7731,f1153]) ).
fof(f7947,plain,
! [X2,X3,X0,X1] : add(multiply(X0,multiply(X1,X2)),multiply(X3,X1)) = multiply(X1,add(X3,multiply(X0,X2))),
inference(backward_demodulation,[],[f5982,f7811]) ).
fof(f8053,plain,
! [X2,X3,X0,X1,X4] : add(multiply(X4,X1),multiply(X1,X0)) = multiply(X1,add(X4,multiply(X0,add(X2,add(X0,X3))))),
inference(backward_demodulation,[],[f5889,f7947]) ).
fof(f8157,plain,
! [X0,X1,X4] : add(multiply(X4,X1),multiply(X1,X0)) = multiply(X1,add(X4,X0)),
inference(forward_demodulation,[],[f8053,f5]) ).
fof(f8742,plain,
( ! [X0] : add(sF2,multiply(a,X0)) = multiply(a,add(b,X0))
| ~ spl5_6 ),
inference(superposition,[],[f8157,f160]) ).
fof(f9956,plain,
( multiply(a,sF0) = add(sF2,multiply(a,c))
| ~ spl5_4
| ~ spl5_6 ),
inference(superposition,[],[f8742,f142]) ).
fof(f10052,plain,
( multiply(a,sF0) = add(sF2,multiply(c,a))
| ~ spl5_4
| ~ spl5_6
| ~ spl5_11 ),
inference(forward_demodulation,[],[f9956,f5528]) ).
fof(f10080,plain,
( multiply(a,sF0) = add(sF2,sF3)
| ~ spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_11 ),
inference(forward_demodulation,[],[f10052,f151]) ).
fof(f10098,plain,
( multiply(a,sF0) = sF4
| ~ spl5_2
| ~ spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_11 ),
inference(forward_demodulation,[],[f10080,f36]) ).
fof(f10106,plain,
( sF1 = sF4
| ~ spl5_1
| ~ spl5_2
| ~ spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_11 ),
inference(forward_demodulation,[],[f10098,f31]) ).
fof(f10109,plain,
( $false
| ~ spl5_1
| ~ spl5_2
| spl5_3
| ~ spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f10106,f68]) ).
fof(f10110,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_3
| ~ spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f10109]) ).
cnf(s1,plain,
spl5_1,
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl5_3,
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
spl5_4,
inference(sat_conversion,[],[f143]) ).
cnf(s5,plain,
spl5_5,
inference(sat_conversion,[],[f152]) ).
cnf(s6,plain,
spl5_6,
inference(sat_conversion,[],[f161]) ).
cnf(s11,plain,
( ~ spl5_6
| spl5_11 ),
inference(sat_conversion,[],[f3412]) ).
cnf(s15,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_3
| ~ spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_11 ),
inference(sat_conversion,[],[f10110]) ).
cnf(s16,plain,
spl5_11,
inference(rat,[],[s11,s6]) ).
cnf(s22,plain,
~ spl5_1,
inference(rat,[],[s15,s16,s6,s5,s4,s3,s2]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s1,s22]) ).
fof(f10111,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO031-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n013.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.23/0.28 % CPULimit : 300
% 0.23/0.28 % WCLimit : 300
% 0.23/0.28 % DateTime : Mon Sep 28 21:04:21 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.33 Running first-order theorem proving
% 0.23/0.33 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
% 15.19/2.84 % (1580584)Detected a unit-equality problem, will run specialized UEQ schedule.
% 15.19/2.84 % (1580595)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1471861626:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 15.19/2.84 % (1580591)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3448025991:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 15.19/2.84 % (1580593)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=122656805:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 15.19/2.84 % (1580589)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=2139680040:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 15.19/2.84 % (1580594)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=27627455:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 15.19/2.84 % (1580592)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1924521770:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 15.19/2.84 % (1580590)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=2312412644:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 15.19/2.84 % (1580592)Instruction limit reached!
% 15.19/2.84 % (1580592)------------------------------
% 15.19/2.84 % (1580592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.19/2.84 % (1580592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.19/2.84 % (1580592)CaDiCaL version: 2.1.3
% 15.19/2.84 % (1580592)Termination reason: Instruction limit
% 15.19/2.84 % (1580592)Termination phase: Saturation
% 15.19/2.84 % (1580592)Time elapsed: 0.136 s
% 15.19/2.84 % (1580592)Peak memory usage: 89 MB
% 15.19/2.84 % (1580592)Instructions burned: 136 (million)
% 15.19/2.84 % (1580593)Instruction limit reached!
% 15.19/2.84 % (1580593)------------------------------
% 15.19/2.84 % (1580593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.19/2.84 % (1580593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.19/2.84 % (1580593)CaDiCaL version: 2.1.3
% 15.19/2.84 % (1580593)Termination reason: Instruction limit
% 15.19/2.84 % (1580593)Termination phase: Saturation
% 15.19/2.84 % (1580593)Time elapsed: 0.173 s
% 15.19/2.84 % (1580593)Peak memory usage: 89 MB
% 15.19/2.84 % (1580593)Instructions burned: 181 (million)
% 15.19/2.84 % (1580594)Instruction limit reached!
% 15.19/2.84 % (1580594)------------------------------
% 15.19/2.84 % (1580594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.19/2.84 % (1580594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.19/2.84 % (1580594)CaDiCaL version: 2.1.3
% 15.19/2.84 % (1580594)Termination reason: Instruction limit
% 15.19/2.84 % (1580594)Termination phase: Saturation
% 15.19/2.84 % (1580594)Time elapsed: 0.260 s
% 15.19/2.84 % (1580594)Peak memory usage: 90 MB
% 15.19/2.84 % (1580594)Instructions burned: 257 (million)
% 15.19/2.84 % (1580603)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2570776783:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 15.19/2.84 % (1580604)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3151522778:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 15.19/2.84 % (1580595)Instruction limit reached!
% 15.19/2.84 % (1580595)------------------------------
% 15.19/2.84 % (1580595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.19/2.84 % (1580595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.19/2.84 % (1580595)CaDiCaL version: 2.1.3
% 15.19/2.84 % (1580595)Termination reason: Instruction limit
% 15.19/2.84 % (1580595)Termination phase: Saturation
% 15.19/2.84 % (1580595)Time elapsed: 0.583 s
% 15.19/2.84 % (1580595)Peak memory usage: 101 MB
% 15.19/2.84 % (1580595)Instructions burned: 1188 (million)
% 15.19/2.84 % (1580605)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1543105743:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 15.19/2.84 % (1580605)Instruction limit reached!
% 15.19/2.84 % (1580605)------------------------------
% 15.19/2.84 % (1580605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.19/2.84 % (1580605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.19/2.84 % (1580605)CaDiCaL version: 2.1.3
% 15.19/2.84 % (1580605)Termination reason: Instruction limit
% 15.19/2.84 % (1580605)Termination phase: Saturation
% 15.19/2.84 % (1580605)Time elapsed: 0.190 s
% 15.19/2.84 % (1580605)Peak memory usage: 90 MB
% 15.19/2.84 % (1580605)Instructions burned: 215 (million)
% 15.19/2.84 % (1580608)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=2328589101:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 15.19/2.84 % (1580608)Instruction limit reached!
% 15.19/2.84 % (1580608)------------------------------
% 15.19/2.84 % (1580608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.19/2.84 % (1580608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.19/2.84 % (1580608)CaDiCaL version: 2.1.3
% 15.19/2.84 % (1580608)Termination reason: Instruction limit
% 15.19/2.84 % (1580608)Termination phase: Saturation
% 15.19/2.84 % (1580608)Time elapsed: 0.166 s
% 15.19/2.84 % (1580608)Peak memory usage: 93 MB
% 15.19/2.84 % (1580608)Instructions burned: 318 (million)
% 15.19/2.84 % (1580610)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=3583069630:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 15.19/2.84 % (1580612)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=546353195:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2988 on theBenchmark for (2988ds/2836Mi)
% 15.19/2.84 % (1580589)First to succeed.
% 15.19/2.84 % (1580589)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1580584"
% 15.19/2.84 % (1580589)Refutation found. Thanks to Tanya!
% 15.19/2.84 % SZS status Unsatisfiable for theBenchmark
% 15.19/2.84 % SZS output start Proof for theBenchmark
% See solution above
% 15.58/3.00 % (1580589)------------------------------
% 15.58/3.00 % (1580589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.58/3.00 % (1580589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.58/3.00 % (1580589)CaDiCaL version: 2.1.3
% 15.58/3.00 % (1580589)Termination reason: Refutation
% 15.58/3.00 % (1580589)Time elapsed: 1.570 s
% 15.58/3.00 % (1580589)Peak memory usage: 140 MB
% 15.58/3.00 % (1580589)Instructions burned: 2053 (million)
% 15.58/3.00 % (1580589)------------------------------
% 15.58/3.00 % (1580589)------------------------------
% 15.58/3.00 % (1580584)Success in time 2.111 s
% 15.58/3.00 % Vampire exiting
%------------------------------------------------------------------------------