%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG005-1 : 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 : n017.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 09:07:31 AM UTC 2026
% Result : Unsatisfiable 8.02s 1.78s
% Output : Refutation 9.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 14
% Syntax : Number of formulae : 303 ( 303 unt; 9 def)
% Number of atoms : 303 ( 297 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 221 ( 221 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X0,difference(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
fof(f3,axiom,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3) ).
fof(f4,axiom,
! [X0,X1] : multiply(X0,X1) = difference(X0,difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f5,plain,
! [X0,X1] : difference(X0,difference(X0,X1)) = multiply(X0,X1),
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
fof(f7,plain,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(definition_unfolding,[],[f6,f5,f5,f5,f5]) ).
fof(f8,definition,
~ sP0(difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f9,plain,
sP0(difference(a,difference(a,difference(b,difference(b,c))))),
inference(inequality_splitting,[],[f7,f8]) ).
fof(f10,definition,
sF1 = difference(a,b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
difference(a,b) = sF1,
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
sF2 = difference(a,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
difference(a,sF1) = sF2,
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
sF3 = difference(sF2,c),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
difference(sF2,c) = sF3,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF4 = difference(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f17,plain,
difference(sF2,sF3) = sF4,
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
~ sP0(sF4),
inference(definition_folding,[],[f8,f17,f15,f13,f11,f13,f11]) ).
fof(f19,definition,
sF5 = difference(b,c),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f20,plain,
difference(b,c) = sF5,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF6 = difference(b,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f22,plain,
difference(b,sF5) = sF6,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF7 = difference(a,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
difference(a,sF6) = sF7,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF8 = difference(a,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f26,plain,
difference(a,sF7) = sF8,
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
sP0(sF8),
inference(definition_folding,[],[f9,f26,f24,f22,f20]) ).
fof(f28,plain,
difference(a,difference(a,b)) = sF2,
inference(forward_demodulation,[],[f13,f11]) ).
fof(f29,plain,
difference(b,difference(b,c)) = sF6,
inference(forward_demodulation,[],[f22,f20]) ).
fof(f30,plain,
sF2 = difference(b,difference(b,a)),
inference(forward_demodulation,[],[f28,f2]) ).
fof(f31,plain,
sF6 = difference(c,difference(c,b)),
inference(forward_demodulation,[],[f29,f2]) ).
fof(f32,plain,
c = difference(c,sF3),
inference(superposition,[],[f1,f15]) ).
fof(f33,plain,
sF3 = difference(sF3,sF4),
inference(superposition,[],[f1,f17]) ).
fof(f34,plain,
sF6 = difference(sF6,sF7),
inference(superposition,[],[f1,f24]) ).
fof(f35,plain,
sF7 = difference(sF7,sF8),
inference(superposition,[],[f1,f26]) ).
fof(f36,plain,
! [X0,X1] : difference(X1,X0) = difference(difference(X1,X0),X0),
inference(superposition,[],[f1,f1]) ).
fof(f37,plain,
sF3 = difference(sF3,c),
inference(superposition,[],[f1,f32]) ).
fof(f38,plain,
sF4 = difference(sF4,sF3),
inference(superposition,[],[f1,f33]) ).
fof(f39,plain,
sF7 = difference(sF7,sF6),
inference(superposition,[],[f1,f34]) ).
fof(f40,plain,
sF8 = difference(sF8,sF7),
inference(superposition,[],[f1,f35]) ).
fof(f45,plain,
difference(b,a) = difference(difference(b,a),sF2),
inference(superposition,[],[f1,f30]) ).
fof(f46,plain,
difference(c,b) = difference(difference(c,b),sF6),
inference(superposition,[],[f1,f31]) ).
fof(f51,plain,
sF2 = difference(sF2,difference(b,a)),
inference(superposition,[],[f36,f30]) ).
fof(f53,plain,
sF6 = difference(sF6,difference(c,b)),
inference(superposition,[],[f36,f31]) ).
fof(f81,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X0))) = difference(difference(X1,X0),difference(X1,X0)),
inference(superposition,[],[f2,f36]) ).
fof(f82,plain,
difference(sF6,difference(sF6,difference(c,b))) = difference(difference(c,b),difference(c,b)),
inference(superposition,[],[f2,f46]) ).
fof(f83,plain,
difference(sF2,sF3) = difference(c,difference(c,sF2)),
inference(superposition,[],[f2,f15]) ).
fof(f84,plain,
difference(sF3,difference(sF3,sF2)) = difference(sF2,sF4),
inference(superposition,[],[f2,f17]) ).
fof(f85,plain,
difference(difference(b,a),difference(difference(b,a),sF2)) = difference(sF2,sF2),
inference(superposition,[],[f2,f51]) ).
fof(f86,plain,
difference(sF4,difference(sF4,sF3)) = difference(sF3,sF3),
inference(superposition,[],[f2,f33]) ).
fof(f87,plain,
difference(c,difference(c,sF3)) = difference(sF3,sF3),
inference(superposition,[],[f2,f37]) ).
fof(f88,plain,
difference(sF7,difference(sF7,sF6)) = difference(sF6,sF6),
inference(superposition,[],[f2,f34]) ).
fof(f89,plain,
difference(sF8,difference(sF8,sF7)) = difference(sF7,sF7),
inference(superposition,[],[f2,f35]) ).
fof(f93,plain,
! [X0,X1] : difference(X1,X0) = difference(difference(X1,X0),difference(X0,difference(X0,X1))),
inference(superposition,[],[f1,f2]) ).
fof(f94,plain,
difference(sF7,sF7) = difference(sF8,sF8),
inference(forward_demodulation,[],[f89,f40]) ).
fof(f95,plain,
difference(sF6,sF6) = difference(sF7,sF7),
inference(forward_demodulation,[],[f88,f39]) ).
fof(f96,plain,
difference(sF3,sF3) = difference(c,c),
inference(forward_demodulation,[],[f87,f32]) ).
fof(f97,plain,
difference(sF3,sF3) = difference(sF4,sF4),
inference(forward_demodulation,[],[f86,f38]) ).
fof(f98,plain,
difference(sF2,sF2) = difference(difference(b,a),difference(b,a)),
inference(forward_demodulation,[],[f85,f45]) ).
fof(f99,plain,
sF4 = difference(c,difference(c,sF2)),
inference(forward_demodulation,[],[f83,f17]) ).
fof(f100,plain,
difference(sF6,difference(sF6,difference(c,b))) = difference(difference(c,c),b),
inference(forward_demodulation,[],[f82,f3]) ).
fof(f101,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X0))) = difference(difference(X1,X1),X0),
inference(forward_demodulation,[],[f81,f3]) ).
fof(f110,plain,
difference(sF6,sF6) = difference(sF8,sF8),
inference(forward_demodulation,[],[f95,f94]) ).
fof(f111,plain,
difference(c,c) = difference(sF4,sF4),
inference(forward_demodulation,[],[f97,f96]) ).
fof(f112,plain,
difference(sF2,sF2) = difference(difference(b,b),a),
inference(forward_demodulation,[],[f98,f3]) ).
fof(f113,plain,
difference(sF6,sF6) = difference(difference(c,c),b),
inference(forward_demodulation,[],[f100,f53]) ).
fof(f114,plain,
! [X0,X1] : difference(X0,X0) = difference(difference(X1,X1),X0),
inference(forward_demodulation,[],[f101,f1]) ).
fof(f120,plain,
difference(sF8,sF8) = difference(difference(c,c),b),
inference(backward_demodulation,[],[f110,f113]) ).
fof(f122,plain,
difference(sF8,sF8) = difference(b,b),
inference(forward_demodulation,[],[f120,f114]) ).
fof(f124,plain,
difference(sF7,sF7) = difference(b,b),
inference(backward_demodulation,[],[f94,f122]) ).
fof(f126,plain,
difference(c,sF2) = difference(difference(c,sF2),sF4),
inference(superposition,[],[f1,f99]) ).
fof(f130,plain,
sF8 = difference(sF8,difference(b,b)),
inference(superposition,[],[f1,f122]) ).
fof(f155,plain,
! [X2,X0,X1] : difference(difference(X0,X2),difference(X1,X0)) = difference(X0,difference(X2,difference(X1,X0))),
inference(superposition,[],[f3,f1]) ).
fof(f158,plain,
! [X2,X0,X1] : difference(difference(difference(X1,X0),X2),X0) = difference(difference(X1,X0),difference(X2,X0)),
inference(superposition,[],[f3,f36]) ).
fof(f163,plain,
! [X0] : difference(difference(a,X0),sF7) = difference(sF8,difference(X0,sF7)),
inference(superposition,[],[f3,f26]) ).
fof(f165,plain,
! [X0] : difference(difference(c,X0),sF3) = difference(c,difference(X0,sF3)),
inference(superposition,[],[f3,f32]) ).
fof(f166,plain,
! [X0] : difference(difference(c,X0),difference(c,b)) = difference(sF6,difference(X0,difference(c,b))),
inference(superposition,[],[f3,f31]) ).
fof(f168,plain,
! [X0] : difference(difference(sF2,X0),c) = difference(sF3,difference(X0,c)),
inference(superposition,[],[f3,f15]) ).
fof(f169,plain,
! [X0] : difference(difference(sF2,X0),sF3) = difference(sF4,difference(X0,sF3)),
inference(superposition,[],[f3,f17]) ).
fof(f174,plain,
! [X0] : difference(sF4,difference(X0,sF3)) = difference(difference(sF4,X0),sF3),
inference(superposition,[],[f3,f38]) ).
fof(f175,plain,
! [X0] : difference(difference(sF4,X0),sF4) = difference(difference(c,c),difference(X0,sF4)),
inference(superposition,[],[f3,f111]) ).
fof(f178,plain,
! [X0] : difference(difference(sF6,X0),sF7) = difference(sF6,difference(X0,sF7)),
inference(superposition,[],[f3,f34]) ).
fof(f184,plain,
! [X0] : difference(sF8,difference(X0,sF7)) = difference(difference(sF8,X0),sF7),
inference(superposition,[],[f3,f40]) ).
fof(f186,plain,
! [X0] : difference(difference(sF8,X0),difference(b,b)) = difference(sF8,difference(X0,difference(b,b))),
inference(superposition,[],[f3,f130]) ).
fof(f194,plain,
! [X0] : difference(difference(X0,a),sF6) = difference(difference(X0,sF6),sF7),
inference(superposition,[],[f3,f24]) ).
fof(f196,plain,
! [X0] : difference(difference(X0,difference(b,a)),sF2) = difference(difference(X0,b),difference(b,a)),
inference(superposition,[],[f3,f30]) ).
fof(f219,plain,
! [X2,X0,X1] : difference(difference(X2,X0),difference(difference(X2,X0),difference(X1,X0))) = difference(difference(X1,X0),difference(difference(X1,X2),X0)),
inference(superposition,[],[f2,f3]) ).
fof(f224,plain,
! [X2,X0,X1] : difference(difference(X2,X0),difference(difference(X2,X0),difference(X1,X0))) = difference(difference(X1,difference(X1,X2)),X0),
inference(forward_demodulation,[],[f219,f3]) ).
fof(f243,plain,
! [X0] : difference(difference(a,X0),sF7) = difference(difference(sF8,X0),sF7),
inference(backward_demodulation,[],[f184,f163]) ).
fof(f245,plain,
! [X2,X0,X1] : difference(difference(difference(X1,X0),X2),X0) = difference(difference(X1,X2),X0),
inference(forward_demodulation,[],[f158,f3]) ).
fof(f247,plain,
! [X2,X0,X1] : difference(difference(X1,difference(X1,X2)),X0) = difference(difference(X2,X0),difference(difference(X2,X1),X0)),
inference(forward_demodulation,[],[f224,f3]) ).
fof(f252,plain,
! [X2,X0,X1] : difference(difference(X1,difference(X1,X2)),X0) = difference(difference(X2,difference(X2,X1)),X0),
inference(forward_demodulation,[],[f247,f3]) ).
fof(f275,plain,
! [X0] : difference(difference(X0,sF6),sF6) = difference(difference(X0,sF6),difference(difference(c,c),b)),
inference(superposition,[],[f3,f113]) ).
fof(f277,plain,
difference(difference(c,c),b) = difference(difference(difference(c,c),b),sF6),
inference(superposition,[],[f36,f113]) ).
fof(f280,plain,
difference(b,b) = difference(difference(b,b),sF6),
inference(forward_demodulation,[],[f277,f114]) ).
fof(f282,plain,
! [X0] : difference(difference(X0,sF6),sF6) = difference(difference(X0,sF6),difference(b,b)),
inference(forward_demodulation,[],[f275,f114]) ).
fof(f283,plain,
difference(sF6,sF6) = difference(b,b),
inference(forward_demodulation,[],[f280,f114]) ).
fof(f284,plain,
! [X0] : difference(X0,sF6) = difference(difference(X0,sF6),difference(b,b)),
inference(forward_demodulation,[],[f282,f36]) ).
fof(f294,plain,
! [X2,X0,X1] : difference(difference(X0,X0),X1) = difference(difference(X2,X2),X1),
inference(superposition,[],[f114,f114]) ).
fof(f300,plain,
! [X2,X0,X1] : difference(X2,X2) = difference(difference(difference(X1,X1),X0),X2),
inference(superposition,[],[f114,f3]) ).
fof(f311,plain,
! [X2,X0,X1] : difference(difference(X0,X0),X1) = difference(difference(X2,X2),difference(X0,X1)),
inference(superposition,[],[f3,f114]) ).
fof(f313,plain,
! [X0] : difference(c,c) = difference(difference(X0,X0),sF4),
inference(superposition,[],[f111,f114]) ).
fof(f314,plain,
! [X0] : difference(b,b) = difference(difference(X0,X0),sF6),
inference(superposition,[],[f283,f114]) ).
fof(f316,plain,
! [X2,X0,X1] : difference(difference(X2,X0),difference(X0,X0)) = difference(difference(X2,difference(X1,X1)),X0),
inference(superposition,[],[f3,f114]) ).
fof(f323,plain,
! [X2,X0,X1] : difference(difference(X2,X0),X0) = difference(difference(X2,difference(X1,X1)),X0),
inference(forward_demodulation,[],[f316,f3]) ).
fof(f328,plain,
! [X2,X0,X1] : difference(X2,X0) = difference(difference(X2,difference(X1,X1)),X0),
inference(forward_demodulation,[],[f323,f36]) ).
fof(f345,plain,
! [X0] : difference(difference(sF2,X0),sF2) = difference(difference(difference(b,b),a),difference(X0,sF2)),
inference(superposition,[],[f3,f112]) ).
fof(f347,plain,
sF2 = difference(sF2,difference(difference(b,b),a)),
inference(superposition,[],[f1,f112]) ).
fof(f349,plain,
! [X0] : difference(difference(b,b),a) = difference(difference(X0,X0),sF2),
inference(superposition,[],[f114,f112]) ).
fof(f350,plain,
! [X0] : difference(difference(X0,X0),sF2) = difference(a,a),
inference(forward_demodulation,[],[f349,f114]) ).
fof(f351,plain,
sF2 = difference(sF2,difference(a,a)),
inference(forward_demodulation,[],[f347,f114]) ).
fof(f353,plain,
! [X0] : difference(difference(sF2,X0),sF2) = difference(difference(a,a),difference(X0,sF2)),
inference(forward_demodulation,[],[f345,f114]) ).
fof(f360,plain,
difference(sF2,sF2) = difference(difference(a,a),difference(difference(a,a),sF2)),
inference(superposition,[],[f2,f351]) ).
fof(f363,plain,
difference(sF2,sF2) = difference(difference(a,a),difference(a,a)),
inference(forward_demodulation,[],[f360,f350]) ).
fof(f366,plain,
difference(sF2,sF2) = difference(difference(a,a),a),
inference(forward_demodulation,[],[f363,f3]) ).
fof(f368,plain,
difference(sF2,sF2) = difference(a,a),
inference(forward_demodulation,[],[f366,f36]) ).
fof(f385,plain,
! [X0,X1] : difference(difference(difference(X0,X0),X1),sF4) = difference(difference(c,c),difference(X1,sF4)),
inference(superposition,[],[f3,f313]) ).
fof(f392,plain,
! [X1] : difference(sF4,sF4) = difference(difference(c,c),difference(X1,sF4)),
inference(forward_demodulation,[],[f385,f300]) ).
fof(f396,plain,
! [X1] : difference(c,c) = difference(difference(c,c),difference(X1,sF4)),
inference(forward_demodulation,[],[f392,f111]) ).
fof(f397,plain,
! [X0] : difference(c,c) = difference(difference(sF4,X0),sF4),
inference(backward_demodulation,[],[f175,f396]) ).
fof(f452,plain,
! [X0,X1] : difference(difference(difference(X0,X0),X1),sF6) = difference(difference(b,b),difference(X1,sF6)),
inference(superposition,[],[f3,f314]) ).
fof(f459,plain,
! [X1] : difference(sF6,sF6) = difference(difference(b,b),difference(X1,sF6)),
inference(forward_demodulation,[],[f452,f300]) ).
fof(f463,plain,
! [X1] : difference(b,b) = difference(difference(b,b),difference(X1,sF6)),
inference(forward_demodulation,[],[f459,f283]) ).
fof(f495,plain,
! [X0,X1] : difference(difference(difference(X0,X0),X1),sF2) = difference(difference(a,a),difference(X1,sF2)),
inference(superposition,[],[f3,f350]) ).
fof(f502,plain,
! [X1] : difference(sF2,sF2) = difference(difference(a,a),difference(X1,sF2)),
inference(forward_demodulation,[],[f495,f300]) ).
fof(f506,plain,
! [X1] : difference(a,a) = difference(difference(a,a),difference(X1,sF2)),
inference(forward_demodulation,[],[f502,f368]) ).
fof(f507,plain,
! [X0] : difference(difference(sF2,X0),sF2) = difference(a,a),
inference(backward_demodulation,[],[f353,f506]) ).
fof(f532,plain,
difference(sF3,sF2) = difference(a,a),
inference(superposition,[],[f507,f15]) ).
fof(f554,plain,
difference(sF2,sF4) = difference(sF3,difference(a,a)),
inference(backward_demodulation,[],[f84,f532]) ).
fof(f575,plain,
! [X0] : difference(difference(X0,sF2),sF4) = difference(difference(X0,sF4),difference(sF3,difference(a,a))),
inference(superposition,[],[f3,f554]) ).
fof(f576,plain,
! [X0] : difference(difference(sF2,X0),sF4) = difference(difference(sF3,difference(a,a)),difference(X0,sF4)),
inference(superposition,[],[f3,f554]) ).
fof(f579,plain,
difference(sF3,difference(a,a)) = difference(difference(sF3,difference(a,a)),sF4),
inference(superposition,[],[f36,f554]) ).
fof(f581,plain,
difference(sF3,sF4) = difference(sF3,difference(a,a)),
inference(forward_demodulation,[],[f579,f328]) ).
fof(f584,plain,
! [X0] : difference(sF3,difference(X0,sF4)) = difference(difference(sF2,X0),sF4),
inference(forward_demodulation,[],[f576,f328]) ).
fof(f585,plain,
sF3 = difference(sF3,difference(a,a)),
inference(forward_demodulation,[],[f581,f33]) ).
fof(f587,plain,
! [X0] : difference(difference(X0,sF4),sF3) = difference(difference(X0,sF2),sF4),
inference(backward_demodulation,[],[f575,f585]) ).
fof(f592,plain,
difference(c,sF2) = difference(difference(c,sF4),sF3),
inference(backward_demodulation,[],[f126,f587]) ).
fof(f594,plain,
difference(c,sF2) = difference(c,difference(sF4,sF3)),
inference(forward_demodulation,[],[f592,f165]) ).
fof(f596,plain,
difference(c,sF2) = difference(c,sF4),
inference(forward_demodulation,[],[f594,f38]) ).
fof(f597,plain,
sF4 = difference(c,difference(c,sF4)),
inference(backward_demodulation,[],[f99,f596]) ).
fof(f812,plain,
difference(difference(a,sF6),sF7) = difference(sF8,sF6),
inference(superposition,[],[f163,f34]) ).
fof(f825,plain,
difference(difference(a,a),sF6) = difference(sF8,sF6),
inference(forward_demodulation,[],[f812,f194]) ).
fof(f831,plain,
difference(sF6,sF6) = difference(sF8,sF6),
inference(forward_demodulation,[],[f825,f114]) ).
fof(f835,plain,
difference(b,b) = difference(sF8,sF6),
inference(forward_demodulation,[],[f831,f283]) ).
fof(f837,plain,
! [X0] : difference(difference(X0,sF6),difference(b,b)) = difference(difference(X0,sF8),sF6),
inference(superposition,[],[f3,f835]) ).
fof(f838,plain,
! [X0] : difference(difference(b,b),difference(X0,sF6)) = difference(difference(sF8,X0),sF6),
inference(superposition,[],[f3,f835]) ).
fof(f841,plain,
! [X0] : difference(b,b) = difference(difference(sF8,X0),sF6),
inference(forward_demodulation,[],[f838,f463]) ).
fof(f842,plain,
! [X0] : difference(X0,sF6) = difference(difference(X0,sF8),sF6),
inference(forward_demodulation,[],[f837,f284]) ).
fof(f857,plain,
! [X0] : difference(difference(sF8,X0),difference(b,b)) = difference(sF6,difference(sF6,difference(sF8,X0))),
inference(superposition,[],[f2,f841]) ).
fof(f860,plain,
! [X0] : difference(sF8,difference(X0,difference(b,b))) = difference(sF6,difference(sF6,difference(sF8,X0))),
inference(forward_demodulation,[],[f857,f186]) ).
fof(f887,plain,
difference(sF3,difference(sF3,c)) = difference(sF4,c),
inference(superposition,[],[f168,f17]) ).
fof(f903,plain,
difference(c,difference(c,sF3)) = difference(sF4,c),
inference(forward_demodulation,[],[f887,f2]) ).
fof(f910,plain,
difference(c,c) = difference(sF4,c),
inference(forward_demodulation,[],[f903,f32]) ).
fof(f916,plain,
! [X0] : difference(difference(X0,sF4),c) = difference(difference(X0,c),difference(c,c)),
inference(superposition,[],[f3,f910]) ).
fof(f917,plain,
! [X0] : difference(difference(sF4,X0),c) = difference(difference(c,c),difference(X0,c)),
inference(superposition,[],[f3,f910]) ).
fof(f924,plain,
! [X0] : difference(difference(sF4,X0),c) = difference(difference(c,X0),c),
inference(forward_demodulation,[],[f917,f3]) ).
fof(f925,plain,
! [X0] : difference(difference(X0,sF4),c) = difference(difference(X0,c),c),
inference(forward_demodulation,[],[f916,f3]) ).
fof(f926,plain,
! [X0] : difference(X0,c) = difference(difference(X0,sF4),c),
inference(forward_demodulation,[],[f925,f36]) ).
fof(f951,plain,
! [X0] : difference(difference(c,c),c) = difference(difference(sF4,X0),c),
inference(superposition,[],[f926,f397]) ).
fof(f966,plain,
! [X0] : difference(c,c) = difference(difference(sF4,X0),c),
inference(forward_demodulation,[],[f951,f36]) ).
fof(f968,plain,
! [X0] : difference(c,c) = difference(difference(c,X0),c),
inference(backward_demodulation,[],[f924,f966]) ).
fof(f970,plain,
difference(c,c) = difference(sF6,c),
inference(superposition,[],[f968,f31]) ).
fof(f992,plain,
! [X0] : difference(difference(X0,c),difference(c,c)) = difference(difference(X0,sF6),c),
inference(superposition,[],[f3,f970]) ).
fof(f999,plain,
! [X0] : difference(difference(X0,c),c) = difference(difference(X0,sF6),c),
inference(forward_demodulation,[],[f992,f3]) ).
fof(f1001,plain,
! [X0] : difference(X0,c) = difference(difference(X0,sF6),c),
inference(forward_demodulation,[],[f999,f36]) ).
fof(f1049,plain,
! [X0] : difference(difference(X0,sF6),c) = difference(difference(X0,sF8),c),
inference(superposition,[],[f1001,f842]) ).
fof(f1051,plain,
! [X0] : difference(difference(b,b),c) = difference(difference(sF8,X0),c),
inference(superposition,[],[f1001,f841]) ).
fof(f1054,plain,
difference(difference(b,b),c) = difference(sF8,c),
inference(superposition,[],[f1001,f835]) ).
fof(f1069,plain,
difference(c,c) = difference(sF8,c),
inference(forward_demodulation,[],[f1054,f114]) ).
fof(f1071,plain,
! [X0] : difference(c,c) = difference(difference(sF8,X0),c),
inference(forward_demodulation,[],[f1051,f114]) ).
fof(f1073,plain,
! [X0] : difference(X0,c) = difference(difference(X0,sF8),c),
inference(forward_demodulation,[],[f1049,f1001]) ).
fof(f1093,plain,
difference(c,difference(c,sF8)) = difference(sF8,difference(c,c)),
inference(superposition,[],[f2,f1069]) ).
fof(f1115,plain,
! [X0] : difference(c,difference(c,difference(sF8,X0))) = difference(difference(sF8,X0),difference(c,c)),
inference(superposition,[],[f2,f1071]) ).
fof(f1462,plain,
! [X0] : difference(sF3,difference(sF3,difference(c,X0))) = difference(difference(c,X0),difference(c,difference(X0,sF3))),
inference(superposition,[],[f2,f165]) ).
fof(f1593,plain,
! [X0] : difference(sF7,difference(sF7,difference(sF6,X0))) = difference(difference(sF6,X0),difference(sF6,difference(X0,sF7))),
inference(superposition,[],[f2,f178]) ).
fof(f2308,plain,
! [X0,X1] : difference(difference(X1,difference(sF8,X0)),sF7) = difference(difference(X1,sF7),difference(difference(a,X0),sF7)),
inference(superposition,[],[f3,f243]) ).
fof(f2311,plain,
! [X0] : difference(sF7,difference(sF7,difference(sF8,X0))) = difference(difference(sF8,X0),difference(difference(a,X0),sF7)),
inference(superposition,[],[f2,f243]) ).
fof(f2315,plain,
! [X0,X1] : difference(difference(X1,difference(sF8,X0)),sF7) = difference(difference(X1,difference(a,X0)),sF7),
inference(forward_demodulation,[],[f2308,f3]) ).
fof(f2492,plain,
! [X2,X0,X1] : difference(difference(X0,X2),X0) = difference(difference(X1,X1),difference(X2,X0)),
inference(superposition,[],[f3,f294]) ).
fof(f2673,plain,
! [X0] : difference(c,c) = difference(difference(c,c),difference(c,difference(c,difference(c,X0)))),
inference(superposition,[],[f93,f968]) ).
fof(f2754,plain,
difference(c,c) = difference(difference(c,c),difference(c,difference(c,sF6))),
inference(superposition,[],[f93,f970]) ).
fof(f3020,plain,
difference(c,c) = difference(difference(c,c),difference(c,sF6)),
inference(forward_demodulation,[],[f2754,f311]) ).
fof(f3075,plain,
! [X0] : difference(c,c) = difference(difference(c,c),difference(c,difference(c,X0))),
inference(forward_demodulation,[],[f2673,f311]) ).
fof(f3115,plain,
difference(c,c) = difference(difference(c,c),sF6),
inference(forward_demodulation,[],[f3020,f311]) ).
fof(f3150,plain,
! [X0] : difference(c,c) = difference(difference(c,c),difference(c,X0)),
inference(forward_demodulation,[],[f3075,f311]) ).
fof(f3178,plain,
difference(c,c) = difference(b,b),
inference(forward_demodulation,[],[f3115,f314]) ).
fof(f3202,plain,
! [X0] : difference(c,c) = difference(difference(c,c),X0),
inference(forward_demodulation,[],[f3150,f311]) ).
fof(f3215,plain,
difference(sF7,sF7) = difference(c,c),
inference(backward_demodulation,[],[f124,f3178]) ).
fof(f3216,plain,
sF8 = difference(sF8,difference(c,c)),
inference(backward_demodulation,[],[f130,f3178]) ).
fof(f3219,plain,
! [X0] : difference(difference(sF8,X0),difference(c,c)) = difference(sF8,difference(X0,difference(c,c))),
inference(backward_demodulation,[],[f186,f3178]) ).
fof(f3233,plain,
! [X0] : difference(sF6,difference(sF6,difference(sF8,X0))) = difference(sF8,difference(X0,difference(c,c))),
inference(backward_demodulation,[],[f860,f3178]) ).
fof(f3292,plain,
! [X0] : difference(c,difference(c,difference(sF8,X0))) = difference(sF8,difference(X0,difference(c,c))),
inference(forward_demodulation,[],[f3219,f1115]) ).
fof(f3293,plain,
sF8 = difference(c,difference(c,sF8)),
inference(backward_demodulation,[],[f1093,f3216]) ).
fof(f3307,plain,
! [X0] : difference(sF6,difference(sF6,difference(sF8,X0))) = difference(c,difference(c,difference(sF8,X0))),
inference(backward_demodulation,[],[f3233,f3292]) ).
fof(f3594,plain,
! [X0,X1] : difference(c,c) = difference(difference(X0,X0),X1),
inference(superposition,[],[f294,f3202]) ).
fof(f3595,plain,
! [X0] : difference(X0,X0) = difference(c,c),
inference(superposition,[],[f114,f3202]) ).
fof(f3598,plain,
! [X0] : difference(X0,difference(c,c)) = X0,
inference(superposition,[],[f1,f3202]) ).
fof(f3634,plain,
! [X0] : difference(sF8,X0) = difference(c,difference(c,difference(sF8,X0))),
inference(backward_demodulation,[],[f1115,f3598]) ).
fof(f3659,plain,
! [X2,X0] : difference(c,c) = difference(difference(X0,X2),X0),
inference(backward_demodulation,[],[f2492,f3594]) ).
fof(f3662,plain,
! [X0] : difference(sF8,X0) = difference(sF6,difference(sF6,difference(sF8,X0))),
inference(backward_demodulation,[],[f3307,f3634]) ).
fof(f3718,plain,
! [X0,X1] : difference(X1,difference(X0,X0)) = X1,
inference(superposition,[],[f3598,f3595]) ).
fof(f3982,plain,
difference(sF7,a) = difference(c,c),
inference(superposition,[],[f3659,f24]) ).
fof(f4045,plain,
! [X0,X1] : difference(X1,difference(X1,difference(X1,X0))) = difference(difference(X1,X0),difference(c,c)),
inference(superposition,[],[f2,f3659]) ).
fof(f4047,plain,
! [X2,X0,X1] : difference(difference(X2,difference(X1,X0)),X1) = difference(difference(X2,X1),difference(c,c)),
inference(superposition,[],[f3,f3659]) ).
fof(f4053,plain,
! [X2,X0,X1] : difference(X2,X1) = difference(difference(X2,difference(X1,X0)),X1),
inference(forward_demodulation,[],[f4047,f3718]) ).
fof(f4055,plain,
! [X0,X1] : difference(X1,X0) = difference(X1,difference(X1,difference(X1,X0))),
inference(forward_demodulation,[],[f4045,f3718]) ).
fof(f4083,plain,
difference(a,difference(a,sF7)) = difference(sF7,difference(c,c)),
inference(superposition,[],[f2,f3982]) ).
fof(f4092,plain,
sF7 = difference(a,difference(a,sF7)),
inference(forward_demodulation,[],[f4083,f3718]) ).
fof(f4096,plain,
sF7 = difference(a,sF8),
inference(forward_demodulation,[],[f4092,f26]) ).
fof(f4328,plain,
! [X2,X0,X1] : difference(X2,X1) = difference(difference(X2,X1),difference(X1,difference(X0,difference(X2,X1)))),
inference(superposition,[],[f1,f155]) ).
fof(f6858,plain,
difference(difference(c,b),difference(c,b)) = difference(sF6,b),
inference(superposition,[],[f166,f1]) ).
fof(f6898,plain,
difference(difference(c,c),b) = difference(sF6,b),
inference(forward_demodulation,[],[f6858,f3]) ).
fof(f6908,plain,
difference(b,b) = difference(sF6,b),
inference(forward_demodulation,[],[f6898,f114]) ).
fof(f6911,plain,
difference(c,c) = difference(sF6,b),
inference(forward_demodulation,[],[f6908,f3178]) ).
fof(f6918,plain,
! [X0] : difference(difference(X0,b),difference(c,c)) = difference(difference(X0,sF6),b),
inference(superposition,[],[f3,f6911]) ).
fof(f6928,plain,
! [X0] : difference(X0,b) = difference(difference(X0,sF6),b),
inference(forward_demodulation,[],[f6918,f3718]) ).
fof(f6959,plain,
difference(a,b) = difference(sF7,b),
inference(superposition,[],[f6928,f24]) ).
fof(f6997,plain,
difference(b,difference(b,sF7)) = difference(sF7,difference(a,b)),
inference(superposition,[],[f2,f6959]) ).
fof(f7005,plain,
difference(c,c) = difference(difference(a,b),sF7),
inference(superposition,[],[f3659,f6959]) ).
fof(f7200,plain,
difference(sF8,difference(c,c)) = difference(difference(a,difference(a,b)),sF7),
inference(superposition,[],[f163,f7005]) ).
fof(f7219,plain,
difference(sF8,difference(c,c)) = difference(difference(b,difference(b,a)),sF7),
inference(forward_demodulation,[],[f7200,f252]) ).
fof(f7225,plain,
difference(sF8,difference(c,c)) = difference(sF2,sF7),
inference(forward_demodulation,[],[f7219,f30]) ).
fof(f7229,plain,
sF8 = difference(sF2,sF7),
inference(forward_demodulation,[],[f7225,f3718]) ).
fof(f7232,plain,
difference(sF8,sF4) = difference(sF3,difference(sF7,sF4)),
inference(superposition,[],[f584,f7229]) ).
fof(f7233,plain,
difference(sF8,sF3) = difference(sF4,difference(sF7,sF3)),
inference(superposition,[],[f169,f7229]) ).
fof(f7242,plain,
difference(sF2,sF8) = difference(sF7,difference(sF7,sF2)),
inference(superposition,[],[f2,f7229]) ).
fof(f7250,plain,
difference(c,c) = difference(sF8,sF2),
inference(superposition,[],[f3659,f7229]) ).
fof(f7281,plain,
! [X0] : difference(difference(X0,sF2),difference(c,c)) = difference(difference(X0,sF8),sF2),
inference(superposition,[],[f3,f7250]) ).
fof(f7291,plain,
! [X0] : difference(X0,sF2) = difference(difference(X0,sF8),sF2),
inference(forward_demodulation,[],[f7281,f3718]) ).
fof(f7380,plain,
difference(a,sF2) = difference(sF7,sF2),
inference(superposition,[],[f7291,f4096]) ).
fof(f7414,plain,
difference(sF2,sF8) = difference(sF7,difference(a,sF2)),
inference(backward_demodulation,[],[f7242,f7380]) ).
fof(f9356,plain,
difference(sF3,sF7) = difference(difference(sF8,sF4),sF7),
inference(superposition,[],[f4053,f7232]) ).
fof(f9360,plain,
difference(sF4,sF7) = difference(difference(sF8,sF3),sF7),
inference(superposition,[],[f4053,f7233]) ).
fof(f9437,plain,
! [X2,X0,X1] : difference(c,c) = difference(difference(X0,X2),difference(X0,difference(X2,X1))),
inference(superposition,[],[f3659,f4053]) ).
fof(f9538,plain,
! [X0] : difference(c,c) = difference(sF3,difference(sF3,difference(c,X0))),
inference(backward_demodulation,[],[f1462,f9437]) ).
fof(f9542,plain,
! [X0] : difference(c,c) = difference(sF7,difference(sF7,difference(sF6,X0))),
inference(backward_demodulation,[],[f1593,f9437]) ).
fof(f9580,plain,
difference(sF4,sF7) = difference(difference(a,sF3),sF7),
inference(forward_demodulation,[],[f9360,f243]) ).
fof(f9584,plain,
difference(sF3,sF7) = difference(difference(a,sF4),sF7),
inference(forward_demodulation,[],[f9356,f243]) ).
fof(f9672,plain,
! [X0] : difference(difference(X0,difference(a,sF3)),sF7) = difference(difference(X0,sF7),difference(sF4,sF7)),
inference(superposition,[],[f3,f9580]) ).
fof(f9680,plain,
! [X0] : difference(difference(X0,difference(a,sF3)),sF7) = difference(difference(X0,sF4),sF7),
inference(forward_demodulation,[],[f9672,f3]) ).
fof(f9732,plain,
difference(c,c) = difference(sF3,difference(sF3,sF8)),
inference(superposition,[],[f9538,f3293]) ).
fof(f9785,plain,
difference(c,c) = difference(sF8,difference(sF8,sF3)),
inference(forward_demodulation,[],[f9732,f2]) ).
fof(f9824,plain,
difference(difference(c,c),sF7) = difference(difference(a,difference(sF8,sF3)),sF7),
inference(superposition,[],[f243,f9785]) ).
fof(f9851,plain,
difference(difference(c,c),sF7) = difference(difference(a,difference(a,sF3)),sF7),
inference(forward_demodulation,[],[f9824,f2315]) ).
fof(f9853,plain,
difference(difference(c,c),sF7) = difference(difference(a,sF4),sF7),
inference(forward_demodulation,[],[f9851,f9680]) ).
fof(f9854,plain,
difference(sF7,sF7) = difference(difference(a,sF4),sF7),
inference(forward_demodulation,[],[f9853,f114]) ).
fof(f9855,plain,
difference(c,c) = difference(difference(a,sF4),sF7),
inference(forward_demodulation,[],[f9854,f3215]) ).
fof(f9856,plain,
difference(c,c) = difference(sF3,sF7),
inference(backward_demodulation,[],[f9584,f9855]) ).
fof(f9879,plain,
difference(sF3,difference(c,c)) = difference(sF7,difference(sF7,sF3)),
inference(superposition,[],[f2,f9856]) ).
fof(f9881,plain,
! [X0] : difference(difference(X0,sF7),difference(c,c)) = difference(difference(X0,sF3),sF7),
inference(superposition,[],[f3,f9856]) ).
fof(f9892,plain,
! [X0] : difference(X0,sF7) = difference(difference(X0,sF3),sF7),
inference(forward_demodulation,[],[f9881,f3718]) ).
fof(f9894,plain,
sF3 = difference(sF7,difference(sF7,sF3)),
inference(forward_demodulation,[],[f9879,f3718]) ).
fof(f9903,plain,
difference(a,sF7) = difference(sF4,sF7),
inference(backward_demodulation,[],[f9580,f9892]) ).
fof(f9911,plain,
sF8 = difference(sF4,sF7),
inference(forward_demodulation,[],[f9903,f26]) ).
fof(f9959,plain,
! [X0] : difference(sF4,difference(sF7,difference(X0,sF4))) = difference(sF8,difference(X0,sF4)),
inference(superposition,[],[f155,f9911]) ).
fof(f10689,plain,
! [X0] : difference(c,c) = difference(sF7,difference(sF7,difference(sF8,X0))),
inference(superposition,[],[f9542,f3662]) ).
fof(f10746,plain,
! [X0] : difference(c,c) = difference(difference(sF8,X0),difference(difference(a,X0),sF7)),
inference(backward_demodulation,[],[f2311,f10689]) ).
fof(f11583,plain,
! [X2,X0,X1] : difference(X1,difference(X0,difference(X2,X1))) = difference(difference(X1,X0),difference(difference(X1,X0),difference(X1,difference(X0,difference(X2,X1))))),
inference(superposition,[],[f4055,f155]) ).
fof(f11641,plain,
! [X0] : difference(sF4,difference(X0,sF3)) = difference(difference(sF4,X0),difference(difference(sF4,X0),difference(sF4,difference(X0,sF3)))),
inference(superposition,[],[f4055,f174]) ).
fof(f11668,plain,
! [X0] : difference(sF6,difference(X0,sF7)) = difference(difference(sF6,X0),difference(difference(sF6,X0),difference(sF6,difference(X0,sF7)))),
inference(superposition,[],[f4055,f178]) ).
fof(f11669,plain,
! [X0] : difference(difference(a,X0),sF7) = difference(difference(sF8,X0),difference(difference(sF8,X0),difference(difference(a,X0),sF7))),
inference(superposition,[],[f4055,f243]) ).
fof(f11983,plain,
! [X0] : difference(difference(a,X0),sF7) = difference(difference(sF8,X0),difference(c,c)),
inference(forward_demodulation,[],[f11669,f10746]) ).
fof(f11984,plain,
! [X0] : difference(sF6,difference(X0,sF7)) = difference(difference(sF6,X0),difference(c,c)),
inference(forward_demodulation,[],[f11668,f9437]) ).
fof(f12003,plain,
! [X0] : difference(sF4,difference(X0,sF3)) = difference(difference(sF4,X0),difference(c,c)),
inference(forward_demodulation,[],[f11641,f9437]) ).
fof(f12054,plain,
! [X2,X0,X1] : difference(difference(X1,X0),difference(c,c)) = difference(X1,difference(X0,difference(X2,X1))),
inference(forward_demodulation,[],[f11583,f9437]) ).
fof(f12169,plain,
! [X0] : difference(difference(a,X0),sF7) = difference(sF8,X0),
inference(forward_demodulation,[],[f11983,f3718]) ).
fof(f12170,plain,
! [X0] : difference(sF6,X0) = difference(sF6,difference(X0,sF7)),
inference(forward_demodulation,[],[f11984,f3718]) ).
fof(f12184,plain,
! [X0] : difference(sF4,difference(X0,sF3)) = difference(sF4,X0),
inference(forward_demodulation,[],[f12003,f3718]) ).
fof(f12211,plain,
! [X2,X0,X1] : difference(X1,X0) = difference(X1,difference(X0,difference(X2,X1))),
inference(forward_demodulation,[],[f12054,f3718]) ).
fof(f12230,plain,
! [X0] : difference(sF8,difference(X0,sF7)) = difference(sF8,X0),
inference(backward_demodulation,[],[f163,f12169]) ).
fof(f12324,plain,
! [X0] : difference(difference(sF2,X0),sF3) = difference(sF4,X0),
inference(backward_demodulation,[],[f169,f12184]) ).
fof(f12393,plain,
! [X2,X0,X1] : difference(X0,X2) = difference(difference(X0,X2),difference(X1,X0)),
inference(backward_demodulation,[],[f155,f12211]) ).
fof(f12396,plain,
! [X2,X0,X1] : difference(X2,X1) = difference(difference(X2,X1),difference(X1,X0)),
inference(backward_demodulation,[],[f4328,f12211]) ).
fof(f12554,plain,
! [X0] : difference(sF4,sF7) = difference(sF8,difference(X0,sF4)),
inference(backward_demodulation,[],[f9959,f12211]) ).
fof(f12697,plain,
! [X0] : sF8 = difference(sF8,difference(X0,sF4)),
inference(forward_demodulation,[],[f12554,f9911]) ).
fof(f12790,plain,
! [X0] : difference(difference(X0,difference(b,a)),sF2) = difference(X0,b),
inference(backward_demodulation,[],[f196,f12396]) ).
fof(f14715,plain,
! [X0] : sF4 = difference(sF4,difference(X0,c)),
inference(superposition,[],[f12393,f597]) ).
fof(f14789,plain,
! [X0] : sF3 = difference(sF3,difference(X0,sF7)),
inference(superposition,[],[f12393,f9894]) ).
fof(f14820,plain,
! [X2,X0,X1] : difference(difference(X1,difference(X1,X0)),X2) = difference(difference(difference(X1,difference(X1,X0)),X2),difference(X1,X0)),
inference(superposition,[],[f12393,f4055]) ).
fof(f15104,plain,
! [X2,X0,X1] : difference(difference(X1,X2),difference(X1,X0)) = difference(difference(X1,difference(X1,X0)),X2),
inference(forward_demodulation,[],[f14820,f245]) ).
fof(f15587,plain,
! [X0,X1] : difference(difference(X1,sF3),difference(X0,sF7)) = difference(difference(X1,difference(X0,sF7)),sF3),
inference(superposition,[],[f3,f14789]) ).
fof(f16835,plain,
! [X0] : difference(sF8,difference(sF8,X0)) = difference(sF8,difference(a,X0)),
inference(superposition,[],[f12230,f12169]) ).
fof(f16890,plain,
difference(a,b) = difference(a,sF2),
inference(superposition,[],[f12790,f1]) ).
fof(f16944,plain,
difference(sF2,sF8) = difference(sF7,difference(a,b)),
inference(backward_demodulation,[],[f7414,f16890]) ).
fof(f16957,plain,
difference(sF2,sF8) = difference(b,difference(b,sF7)),
inference(forward_demodulation,[],[f16944,f6997]) ).
fof(f18886,plain,
difference(sF4,sF8) = difference(difference(b,difference(b,sF7)),sF3),
inference(superposition,[],[f12324,f16957]) ).
fof(f18888,plain,
difference(sF2,c) = difference(difference(b,difference(b,sF7)),c),
inference(superposition,[],[f1073,f16957]) ).
fof(f18913,plain,
difference(sF2,c) = difference(difference(b,c),difference(b,sF7)),
inference(forward_demodulation,[],[f18888,f15104]) ).
fof(f18915,plain,
difference(sF4,sF8) = difference(difference(b,sF3),difference(b,sF7)),
inference(forward_demodulation,[],[f18886,f15104]) ).
fof(f18925,plain,
sF3 = difference(difference(b,c),difference(b,sF7)),
inference(forward_demodulation,[],[f18913,f15]) ).
fof(f22373,plain,
! [X0] : difference(difference(X0,difference(b,c)),difference(b,sF7)) = difference(difference(X0,difference(b,sF7)),sF3),
inference(superposition,[],[f3,f18925]) ).
fof(f22387,plain,
! [X0] : difference(difference(X0,difference(b,c)),difference(b,sF7)) = difference(difference(X0,sF3),difference(b,sF7)),
inference(forward_demodulation,[],[f22373,f15587]) ).
fof(f22391,plain,
difference(sF4,sF8) = difference(difference(b,difference(b,c)),difference(b,sF7)),
inference(backward_demodulation,[],[f18915,f22387]) ).
fof(f22394,plain,
difference(sF4,sF8) = difference(difference(c,difference(c,b)),difference(b,sF7)),
inference(forward_demodulation,[],[f22391,f252]) ).
fof(f22395,plain,
difference(sF4,sF8) = difference(sF6,difference(b,sF7)),
inference(forward_demodulation,[],[f22394,f31]) ).
fof(f22396,plain,
difference(sF4,sF8) = difference(sF6,b),
inference(forward_demodulation,[],[f22395,f12170]) ).
fof(f22397,plain,
difference(c,c) = difference(sF4,sF8),
inference(forward_demodulation,[],[f22396,f6911]) ).
fof(f22428,plain,
difference(sF4,difference(c,c)) = difference(sF8,difference(sF8,sF4)),
inference(superposition,[],[f2,f22397]) ).
fof(f22448,plain,
difference(sF4,difference(c,c)) = difference(sF8,difference(a,sF4)),
inference(forward_demodulation,[],[f22428,f16835]) ).
fof(f22458,plain,
sF8 = difference(sF4,difference(c,c)),
inference(forward_demodulation,[],[f22448,f12697]) ).
fof(f22644,plain,
sF4 = sF8,
inference(forward_demodulation,[],[f22458,f14715]) ).
fof(f22828,plain,
~ sP0(sF8),
inference(backward_demodulation,[],[f18,f22644]) ).
fof(f22904,plain,
$false,
inference(forward_subsumption_resolution,[],[f22828,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 19:12:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 8.02/1.78 % (3912343)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.02/1.78 % (3912354)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3734349035:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.02/1.78 % (3912348)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=2659774988:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.02/1.78 % (3912352)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2048692820:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.02/1.78 % (3912353)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3375942822:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.02/1.78 % (3912349)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=1710408351:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.02/1.78 % (3912351)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=277678334:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.02/1.78 % (3912350)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1768820649:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.02/1.78 % (3912351)Instruction limit reached!
% 8.02/1.78 % (3912351)------------------------------
% 8.02/1.78 % (3912351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/1.78 % (3912351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.78 % (3912351)CaDiCaL version: 2.1.3
% 8.02/1.78 % (3912351)Termination reason: Instruction limit
% 8.02/1.78 % (3912351)Termination phase: Saturation
% 8.02/1.78 % (3912351)Time elapsed: 0.080 s
% 8.02/1.78 % (3912351)Peak memory usage: 88 MB
% 8.02/1.78 % (3912351)Instructions burned: 136 (million)
% 8.02/1.78 % (3912352)Instruction limit reached!
% 8.02/1.78 % (3912352)------------------------------
% 8.02/1.78 % (3912352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/1.78 % (3912352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.78 % (3912352)CaDiCaL version: 2.1.3
% 8.02/1.78 % (3912352)Termination reason: Instruction limit
% 8.02/1.78 % (3912352)Termination phase: Saturation
% 8.02/1.78 % (3912352)Time elapsed: 0.099 s
% 8.02/1.78 % (3912352)Peak memory usage: 89 MB
% 8.02/1.78 % (3912352)Instructions burned: 183 (million)
% 8.02/1.78 % (3912353)Instruction limit reached!
% 8.02/1.78 % (3912353)------------------------------
% 8.02/1.78 % (3912353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/1.78 % (3912353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.78 % (3912353)CaDiCaL version: 2.1.3
% 8.02/1.78 % (3912353)Termination reason: Instruction limit
% 8.02/1.78 % (3912353)Termination phase: Saturation
% 8.02/1.78 % (3912353)Time elapsed: 0.158 s
% 8.02/1.78 % (3912353)Peak memory usage: 90 MB
% 8.02/1.78 % (3912353)Instructions burned: 257 (million)
% 8.02/1.78 % (3912362)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3200738470:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 8.02/1.78 % (3912363)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2257850850:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 8.02/1.78 % (3912354)Instruction limit reached!
% 8.02/1.78 % (3912354)------------------------------
% 8.02/1.78 % (3912354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/1.78 % (3912354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.78 % (3912354)CaDiCaL version: 2.1.3
% 8.02/1.78 % (3912354)Termination reason: Instruction limit
% 8.02/1.78 % (3912354)Termination phase: Saturation
% 8.02/1.78 % (3912354)Time elapsed: 0.336 s
% 8.02/1.78 % (3912354)Peak memory usage: 97 MB
% 8.02/1.78 % (3912354)Instructions burned: 1187 (million)
% 8.02/1.78 % (3912364)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2982601786:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 8.02/1.78 % (3912367)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=1666176465:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 8.02/1.78 % (3912364)Instruction limit reached!
% 8.02/1.78 % (3912364)------------------------------
% 8.02/1.78 % (3912364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/1.78 % (3912364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.78 % (3912364)CaDiCaL version: 2.1.3
% 8.02/1.78 % (3912364)Termination reason: Instruction limit
% 8.02/1.78 % (3912364)Termination phase: Saturation
% 8.02/1.78 % (3912364)Time elapsed: 0.105 s
% 8.02/1.78 % (3912364)Peak memory usage: 90 MB
% 8.02/1.78 % (3912364)Instructions burned: 215 (million)
% 8.02/1.78 % (3912367)Instruction limit reached!
% 8.02/1.78 % (3912367)------------------------------
% 8.02/1.78 % (3912367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/1.78 % (3912367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.78 % (3912367)CaDiCaL version: 2.1.3
% 8.02/1.78 % (3912367)Termination reason: Instruction limit
% 8.02/1.78 % (3912367)Termination phase: Saturation
% 8.02/1.78 % (3912367)Time elapsed: 0.111 s
% 8.02/1.78 % (3912367)Peak memory usage: 93 MB
% 8.02/1.78 % (3912367)Instructions burned: 317 (million)
% 8.02/1.78 % (3912370)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=3094661085:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 8.02/1.78 % (3912371)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3015548155:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2993 on theBenchmark for (2993ds/2836Mi)
% 8.02/1.78 % (3912371)First to succeed.
% 8.02/1.78 % (3912371)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3912343"
% 8.02/1.78 % (3912371)Refutation found. Thanks to Tanya!
% 8.02/1.78 % SZS status Unsatisfiable for theBenchmark
% 8.02/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 9.97/1.97 % (3912371)------------------------------
% 9.97/1.97 % (3912371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.97/1.97 % (3912371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.97/1.97 % (3912371)CaDiCaL version: 2.1.3
% 9.97/1.97 % (3912371)Termination reason: Refutation
% 9.97/1.97 % (3912371)Time elapsed: 0.387 s
% 9.97/1.97 % (3912371)Peak memory usage: 106 MB
% 9.97/1.97 % (3912371)Instructions burned: 1103 (million)
% 9.97/1.97 % (3912371)------------------------------
% 9.97/1.97 % (3912371)------------------------------
% 9.97/1.97 % (3912343)Success in time 1.356 s
% 9.97/1.97 % Vampire exiting
%------------------------------------------------------------------------------