%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO028-1 : 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 : n001.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 12.98s 2.78s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 39
% Syntax : Number of formulae : 191 ( 62 unt; 28 def)
% Number of atoms : 364 ( 128 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 327 ( 154 ~; 150 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,multiply(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f2,axiom,
! [X2,X0,X1] : add(add(multiply(X0,X1),multiply(X1,X2)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(f3,axiom,
! [X0,X1] : multiply(add(X0,X1),add(X0,inverse(X1))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,add(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
fof(f6,axiom,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
fof(f7,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f8,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f9,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(f10,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(f11,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(f12,definition,
sF0 = add(b,c),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f13,plain,
add(b,c) = sF0,
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
sF1 = multiply(a,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f15,plain,
multiply(a,sF0) = sF1,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF2 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f17,plain,
multiply(b,a) = sF2,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF3 = multiply(c,a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f19,plain,
multiply(c,a) = sF3,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF4 = add(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f21,plain,
add(sF2,sF3) = sF4,
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
sF1 != sF4,
inference(definition_folding,[],[f11,f21,f19,f17,f15,f13]) ).
fof(f24,definition,
( spl5_1
<=> sF1 = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f27,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f22,f24]) ).
fof(f29,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(multiply(X1,X2),X1)) = X1,
inference(forward_demodulation,[],[f2,f9]) ).
fof(f31,definition,
( spl5_2
<=> add(b,c) = sF0 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f33,plain,
( add(b,c) = sF0
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
spl5_2,
inference(avatar_split_clause,[],[f13,f31]) ).
fof(f35,plain,
sF1 = multiply(sF0,a),
inference(forward_demodulation,[],[f15,f8]) ).
fof(f37,definition,
( spl5_3
<=> multiply(b,a) = sF2 ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f39,plain,
( multiply(b,a) = sF2
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
spl5_3,
inference(avatar_split_clause,[],[f17,f37]) ).
fof(f42,definition,
( spl5_4
<=> multiply(c,a) = sF3 ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f44,plain,
( multiply(c,a) = sF3
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,plain,
spl5_4,
inference(avatar_split_clause,[],[f19,f42]) ).
fof(f47,definition,
( spl5_5
<=> add(sF2,sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f49,plain,
( add(sF2,sF3) = sF4
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
spl5_5,
inference(avatar_split_clause,[],[f21,f47]) ).
fof(f52,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(X1,multiply(X1,X2))) = X1,
inference(forward_demodulation,[],[f29,f7]) ).
fof(f54,definition,
( spl5_6
<=> sF1 = multiply(sF0,a) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f56,plain,
( sF1 = multiply(sF0,a)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
spl5_6,
inference(avatar_split_clause,[],[f35,f54]) ).
fof(f81,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f95,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(superposition,[],[f1,f4]) ).
fof(f152,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(superposition,[],[f81,f7]) ).
fof(f364,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(superposition,[],[f95,f8]) ).
fof(f429,definition,
( spl5_30
<=> sF4 = add(sF3,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_30])],[avatar_definition]) ).
fof(f431,plain,
( sF4 = add(sF3,sF4)
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f441,definition,
( spl5_32
<=> a = add(sF1,a) ),
introduced(definition,[new_symbols(definition,[spl5_32])],[avatar_definition]) ).
fof(f443,plain,
( a = add(sF1,a)
| ~ spl5_32 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f446,definition,
( spl5_33
<=> a = add(sF3,a) ),
introduced(definition,[new_symbols(definition,[spl5_33])],[avatar_definition]) ).
fof(f448,plain,
( a = add(sF3,a)
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f451,definition,
( spl5_34
<=> a = add(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl5_34])],[avatar_definition]) ).
fof(f453,plain,
( a = add(sF2,a)
| ~ spl5_34 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f470,plain,
( sF1 = multiply(a,add(sF1,inverse(a)))
| ~ spl5_32 ),
inference(superposition,[],[f3,f443]) ).
fof(f471,plain,
( a = multiply(a,a)
| ~ spl5_32 ),
inference(superposition,[],[f81,f443]) ).
fof(f474,definition,
( spl5_37
<=> a = multiply(a,a) ),
introduced(definition,[new_symbols(definition,[spl5_37])],[avatar_definition]) ).
fof(f476,plain,
( a = multiply(a,a)
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f477,plain,
( spl5_37
| ~ spl5_32 ),
inference(avatar_split_clause,[],[f471,f441,f474]) ).
fof(f479,definition,
( spl5_38
<=> sF1 = multiply(a,add(sF1,inverse(a))) ),
introduced(definition,[new_symbols(definition,[spl5_38])],[avatar_definition]) ).
fof(f482,plain,
( spl5_38
| ~ spl5_32 ),
inference(avatar_split_clause,[],[f470,f441,f479]) ).
fof(f518,plain,
( ! [X0] : sF3 = multiply(sF3,add(X0,sF4))
| ~ spl5_30 ),
inference(superposition,[],[f4,f431]) ).
fof(f574,definition,
( spl5_48
<=> sF1 = multiply(sF1,a) ),
introduced(definition,[new_symbols(definition,[spl5_48])],[avatar_definition]) ).
fof(f576,plain,
( sF1 = multiply(sF1,a)
| ~ spl5_48 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f628,definition,
( spl5_50
<=> sF2 = multiply(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl5_50])],[avatar_definition]) ).
fof(f630,plain,
( sF2 = multiply(sF2,a)
| ~ spl5_50 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f666,plain,
( b = add(sF2,multiply(b,inverse(a)))
| ~ spl5_3 ),
inference(superposition,[],[f6,f39]) ).
fof(f667,plain,
( c = add(sF3,multiply(c,inverse(a)))
| ~ spl5_4 ),
inference(superposition,[],[f6,f44]) ).
fof(f668,plain,
( sF0 = add(sF1,multiply(sF0,inverse(a)))
| ~ spl5_6 ),
inference(superposition,[],[f6,f56]) ).
fof(f703,definition,
( spl5_54
<=> sF0 = add(sF1,multiply(sF0,inverse(a))) ),
introduced(definition,[new_symbols(definition,[spl5_54])],[avatar_definition]) ).
fof(f705,plain,
( sF0 = add(sF1,multiply(sF0,inverse(a)))
| ~ spl5_54 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f706,plain,
( spl5_54
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f668,f54,f703]) ).
fof(f708,definition,
( spl5_55
<=> c = add(sF3,multiply(c,inverse(a))) ),
introduced(definition,[new_symbols(definition,[spl5_55])],[avatar_definition]) ).
fof(f710,plain,
( c = add(sF3,multiply(c,inverse(a)))
| ~ spl5_55 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f711,plain,
( spl5_55
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f667,f42,f708]) ).
fof(f713,definition,
( spl5_56
<=> b = add(sF2,multiply(b,inverse(a))) ),
introduced(definition,[new_symbols(definition,[spl5_56])],[avatar_definition]) ).
fof(f715,plain,
( b = add(sF2,multiply(b,inverse(a)))
| ~ spl5_56 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f716,plain,
( spl5_56
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f666,f37,f713]) ).
fof(f897,plain,
! [X0] : multiply(X0,X0) = X0,
inference(superposition,[],[f152,f1]) ).
fof(f1131,plain,
( ! [X0] : add(sF0,X0) = add(b,add(c,X0))
| ~ spl5_2 ),
inference(superposition,[],[f9,f33]) ).
fof(f1146,plain,
( ! [X0] : add(sF0,X0) = add(sF1,add(multiply(sF0,inverse(a)),X0))
| ~ spl5_54 ),
inference(superposition,[],[f9,f705]) ).
fof(f1148,plain,
( ! [X0] : add(b,X0) = add(sF2,add(multiply(b,inverse(a)),X0))
| ~ spl5_56 ),
inference(superposition,[],[f9,f715]) ).
fof(f1153,plain,
( ! [X0] : add(sF4,X0) = add(sF2,add(sF3,X0))
| ~ spl5_5 ),
inference(superposition,[],[f9,f49]) ).
fof(f1155,plain,
( ! [X0] : add(c,X0) = add(sF3,add(multiply(c,inverse(a)),X0))
| ~ spl5_55 ),
inference(superposition,[],[f9,f710]) ).
fof(f1169,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f7,f9]) ).
fof(f1194,plain,
( ! [X0] : add(sF0,X0) = add(b,add(X0,c))
| ~ spl5_2 ),
inference(superposition,[],[f1131,f7]) ).
fof(f1232,plain,
( add(sF2,a) = add(sF4,a)
| ~ spl5_5
| ~ spl5_33 ),
inference(superposition,[],[f1153,f448]) ).
fof(f1238,plain,
( ! [X0] : add(sF2,sF3) = add(sF4,multiply(X0,sF3))
| ~ spl5_5 ),
inference(superposition,[],[f1153,f95]) ).
fof(f1246,plain,
( ! [X0] : sF4 = add(sF4,multiply(X0,sF3))
| ~ spl5_5 ),
inference(forward_demodulation,[],[f1238,f49]) ).
fof(f1250,plain,
( a = add(sF4,a)
| ~ spl5_5
| ~ spl5_33
| ~ spl5_34 ),
inference(forward_demodulation,[],[f1232,f453]) ).
fof(f1256,definition,
( spl5_79
<=> a = add(sF4,a) ),
introduced(definition,[new_symbols(definition,[spl5_79])],[avatar_definition]) ).
fof(f1258,plain,
( a = add(sF4,a)
| ~ spl5_79 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f1259,plain,
( spl5_79
| ~ spl5_5
| ~ spl5_33
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f1250,f451,f446,f47,f1256]) ).
fof(f1269,plain,
( sF4 = multiply(a,add(sF4,inverse(a)))
| ~ spl5_79 ),
inference(superposition,[],[f3,f1258]) ).
fof(f1280,definition,
( spl5_82
<=> sF4 = multiply(a,add(sF4,inverse(a))) ),
introduced(definition,[new_symbols(definition,[spl5_82])],[avatar_definition]) ).
fof(f1283,plain,
( spl5_82
| ~ spl5_79 ),
inference(avatar_split_clause,[],[f1269,f1256,f1280]) ).
fof(f1472,plain,
( sF4 = add(sF4,sF3)
| ~ spl5_5 ),
inference(superposition,[],[f1246,f897]) ).
fof(f1474,plain,
( sF4 = add(sF3,sF4)
| ~ spl5_5 ),
inference(forward_demodulation,[],[f1472,f7]) ).
fof(f1481,plain,
( spl5_30
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f1474,f47,f429]) ).
fof(f1749,plain,
( ! [X0] : multiply(sF2,X0) = multiply(b,multiply(a,X0))
| ~ spl5_3 ),
inference(superposition,[],[f10,f39]) ).
fof(f1750,plain,
( ! [X0] : multiply(sF3,X0) = multiply(c,multiply(a,X0))
| ~ spl5_4 ),
inference(superposition,[],[f10,f44]) ).
fof(f1751,plain,
( ! [X0] : multiply(sF1,X0) = multiply(sF0,multiply(a,X0))
| ~ spl5_6 ),
inference(superposition,[],[f10,f56]) ).
fof(f1818,plain,
( ! [X0] : multiply(a,X0) = add(multiply(a,X0),multiply(sF2,X0))
| ~ spl5_3 ),
inference(superposition,[],[f95,f1749]) ).
fof(f1820,plain,
( ! [X0] : multiply(a,X0) = add(multiply(sF2,X0),multiply(a,X0))
| ~ spl5_3 ),
inference(forward_demodulation,[],[f1818,f7]) ).
fof(f1882,plain,
( ! [X0] : a = add(a,multiply(sF3,X0))
| ~ spl5_4 ),
inference(superposition,[],[f1,f1750]) ).
fof(f1945,plain,
( ! [X0] : a = add(a,multiply(sF1,X0))
| ~ spl5_6 ),
inference(superposition,[],[f1,f1751]) ).
fof(f1948,plain,
( ! [X0] : multiply(a,X0) = add(multiply(a,X0),multiply(sF1,X0))
| ~ spl5_6 ),
inference(superposition,[],[f95,f1751]) ).
fof(f1950,plain,
( ! [X0] : multiply(a,X0) = add(multiply(sF1,X0),multiply(a,X0))
| ~ spl5_6 ),
inference(forward_demodulation,[],[f1948,f7]) ).
fof(f1970,plain,
( a = add(a,sF1)
| ~ spl5_6
| ~ spl5_48 ),
inference(superposition,[],[f1945,f576]) ).
fof(f1979,plain,
( a = add(sF1,a)
| ~ spl5_6
| ~ spl5_48 ),
inference(forward_demodulation,[],[f1970,f7]) ).
fof(f1988,plain,
( spl5_32
| ~ spl5_6
| ~ spl5_48 ),
inference(avatar_split_clause,[],[f1979,f574,f54,f441]) ).
fof(f3475,plain,
( multiply(a,sF2) = add(sF2,multiply(a,sF2))
| ~ spl5_3 ),
inference(superposition,[],[f1820,f897]) ).
fof(f3490,plain,
( multiply(a,a) = add(sF2,multiply(a,a))
| ~ spl5_3
| ~ spl5_50 ),
inference(superposition,[],[f1820,f630]) ).
fof(f3522,plain,
( a = add(sF2,a)
| ~ spl5_3
| ~ spl5_37
| ~ spl5_50 ),
inference(forward_demodulation,[],[f3490,f476]) ).
fof(f3525,plain,
( sF2 = multiply(a,sF2)
| ~ spl5_3 ),
inference(forward_demodulation,[],[f3475,f95]) ).
fof(f3533,plain,
( spl5_34
| ~ spl5_3
| ~ spl5_37
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f3522,f628,f474,f37,f451]) ).
fof(f3534,plain,
( sF2 = multiply(sF2,a)
| ~ spl5_3 ),
inference(forward_demodulation,[],[f3525,f8]) ).
fof(f3539,plain,
( spl5_50
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f3534,f37,f628]) ).
fof(f3611,plain,
( multiply(a,sF1) = add(sF1,multiply(a,sF1))
| ~ spl5_6 ),
inference(superposition,[],[f1950,f897]) ).
fof(f3658,plain,
( sF1 = multiply(a,sF1)
| ~ spl5_6 ),
inference(forward_demodulation,[],[f3611,f95]) ).
fof(f3667,plain,
( sF1 = multiply(sF1,a)
| ~ spl5_6 ),
inference(forward_demodulation,[],[f3658,f8]) ).
fof(f3672,plain,
( spl5_48
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f3667,f54,f574]) ).
fof(f4254,plain,
( ! [X0] : add(sF1,inverse(a)) = add(sF0,add(inverse(a),multiply(inverse(a),X0)))
| ~ spl5_54 ),
inference(superposition,[],[f1146,f52]) ).
fof(f4276,plain,
( add(sF1,inverse(a)) = add(sF0,inverse(a))
| ~ spl5_54 ),
inference(forward_demodulation,[],[f4254,f364]) ).
fof(f4282,definition,
( spl5_113
<=> add(sF1,inverse(a)) = add(sF0,inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl5_113])],[avatar_definition]) ).
fof(f4285,plain,
( spl5_113
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f4276,f703,f4282]) ).
fof(f4289,plain,
( ! [X0] : add(sF2,inverse(a)) = add(b,add(inverse(a),multiply(inverse(a),X0)))
| ~ spl5_56 ),
inference(superposition,[],[f1148,f52]) ).
fof(f4318,plain,
( add(sF2,inverse(a)) = add(b,inverse(a))
| ~ spl5_56 ),
inference(forward_demodulation,[],[f4289,f364]) ).
fof(f4324,definition,
( spl5_115
<=> add(sF2,inverse(a)) = add(b,inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl5_115])],[avatar_definition]) ).
fof(f4326,plain,
( add(sF2,inverse(a)) = add(b,inverse(a))
| ~ spl5_115 ),
inference(avatar_component_clause,[],[f4324]) ).
fof(f4327,plain,
( spl5_115
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f4318,f713,f4324]) ).
fof(f4331,plain,
( ! [X0] : add(sF3,inverse(a)) = add(c,add(inverse(a),multiply(inverse(a),X0)))
| ~ spl5_55 ),
inference(superposition,[],[f1155,f52]) ).
fof(f4357,plain,
( add(sF3,inverse(a)) = add(c,inverse(a))
| ~ spl5_55 ),
inference(forward_demodulation,[],[f4331,f364]) ).
fof(f4363,definition,
( spl5_116
<=> add(sF3,inverse(a)) = add(c,inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl5_116])],[avatar_definition]) ).
fof(f4365,plain,
( add(sF3,inverse(a)) = add(c,inverse(a))
| ~ spl5_116 ),
inference(avatar_component_clause,[],[f4363]) ).
fof(f4366,plain,
( spl5_116
| ~ spl5_55 ),
inference(avatar_split_clause,[],[f4357,f708,f4363]) ).
fof(f5611,plain,
( a = add(a,sF3)
| ~ spl5_4
| ~ spl5_30 ),
inference(superposition,[],[f1882,f518]) ).
fof(f5624,plain,
( a = add(sF3,a)
| ~ spl5_4
| ~ spl5_30 ),
inference(forward_demodulation,[],[f5611,f7]) ).
fof(f5636,plain,
( spl5_33
| ~ spl5_4
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f5624,f429,f42,f446]) ).
fof(f7592,plain,
( add(sF4,inverse(a)) = add(sF2,add(c,inverse(a)))
| ~ spl5_5
| ~ spl5_116 ),
inference(superposition,[],[f1153,f4365]) ).
fof(f7609,plain,
( add(sF4,inverse(a)) = add(c,add(inverse(a),sF2))
| ~ spl5_5
| ~ spl5_116 ),
inference(forward_demodulation,[],[f7592,f1169]) ).
fof(f7627,plain,
( add(sF4,inverse(a)) = add(c,add(sF2,inverse(a)))
| ~ spl5_5
| ~ spl5_116 ),
inference(forward_demodulation,[],[f7609,f7]) ).
fof(f7628,plain,
( add(sF4,inverse(a)) = add(c,add(b,inverse(a)))
| ~ spl5_5
| ~ spl5_115
| ~ spl5_116 ),
inference(forward_demodulation,[],[f7627,f4326]) ).
fof(f7629,plain,
( add(sF4,inverse(a)) = add(b,add(inverse(a),c))
| ~ spl5_5
| ~ spl5_115
| ~ spl5_116 ),
inference(forward_demodulation,[],[f7628,f1169]) ).
fof(f7630,plain,
( add(sF4,inverse(a)) = add(sF0,inverse(a))
| ~ spl5_2
| ~ spl5_5
| ~ spl5_115
| ~ spl5_116 ),
inference(forward_demodulation,[],[f7629,f1194]) ).
fof(f7632,definition,
( spl5_154
<=> add(sF4,inverse(a)) = add(sF0,inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl5_154])],[avatar_definition]) ).
fof(f7635,plain,
( spl5_154
| ~ spl5_2
| ~ spl5_5
| ~ spl5_115
| ~ spl5_116 ),
inference(avatar_split_clause,[],[f7630,f4363,f4324,f47,f31,f7632]) ).
fof(f7636,plain,
( add(sF1,inverse(a)) != add(sF0,inverse(a))
| add(sF4,inverse(a)) != add(sF0,inverse(a))
| sF4 != multiply(a,add(sF4,inverse(a)))
| sF1 != multiply(a,add(sF1,inverse(a)))
| sF1 = sF4 ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
cnf(s1,plain,
~ spl5_1,
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
spl5_3,
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
spl5_4,
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
spl5_5,
inference(sat_conversion,[],[f50]) ).
cnf(s6,plain,
spl5_6,
inference(sat_conversion,[],[f57]) ).
cnf(s70,plain,
( ~ spl5_32
| spl5_37 ),
inference(sat_conversion,[],[f477]) ).
cnf(s71,plain,
( ~ spl5_32
| spl5_38 ),
inference(sat_conversion,[],[f482]) ).
cnf(s114,plain,
( ~ spl5_6
| spl5_54 ),
inference(sat_conversion,[],[f706]) ).
cnf(s115,plain,
( ~ spl5_4
| spl5_55 ),
inference(sat_conversion,[],[f711]) ).
cnf(s116,plain,
( ~ spl5_3
| spl5_56 ),
inference(sat_conversion,[],[f716]) ).
cnf(s237,plain,
( ~ spl5_5
| ~ spl5_33
| ~ spl5_34
| spl5_79 ),
inference(sat_conversion,[],[f1259]) ).
cnf(s240,plain,
( ~ spl5_79
| spl5_82 ),
inference(sat_conversion,[],[f1283]) ).
cnf(s294,plain,
( ~ spl5_5
| spl5_30 ),
inference(sat_conversion,[],[f1481]) ).
cnf(s358,plain,
( ~ spl5_6
| spl5_32
| ~ spl5_48 ),
inference(sat_conversion,[],[f1988]) ).
cnf(s468,plain,
( ~ spl5_3
| spl5_34
| ~ spl5_37
| ~ spl5_50 ),
inference(sat_conversion,[],[f3533]) ).
cnf(s472,plain,
( ~ spl5_3
| spl5_50 ),
inference(sat_conversion,[],[f3539]) ).
cnf(s482,plain,
( ~ spl5_6
| spl5_48 ),
inference(sat_conversion,[],[f3672]) ).
cnf(s491,plain,
( ~ spl5_54
| spl5_113 ),
inference(sat_conversion,[],[f4285]) ).
cnf(s495,plain,
( ~ spl5_56
| spl5_115 ),
inference(sat_conversion,[],[f4327]) ).
cnf(s497,plain,
( ~ spl5_55
| spl5_116 ),
inference(sat_conversion,[],[f4366]) ).
cnf(s646,plain,
( ~ spl5_4
| ~ spl5_30
| spl5_33 ),
inference(sat_conversion,[],[f5636]) ).
cnf(s877,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_115
| ~ spl5_116
| spl5_154 ),
inference(sat_conversion,[],[f7635]) ).
cnf(s878,plain,
( spl5_1
| ~ spl5_38
| ~ spl5_82
| ~ spl5_113
| ~ spl5_154 ),
inference(sat_conversion,[],[f7636]) ).
cnf(s879,plain,
spl5_48,
inference(rat,[],[s482,s6]) ).
cnf(s881,plain,
spl5_32,
inference(rat,[],[s358,s879,s6]) ).
cnf(s883,plain,
spl5_54,
inference(rat,[],[s114,s6]) ).
cnf(s887,plain,
spl5_38,
inference(rat,[],[s71,s881]) ).
cnf(s888,plain,
spl5_37,
inference(rat,[],[s70,s881]) ).
cnf(s890,plain,
spl5_113,
inference(rat,[],[s491,s883]) ).
cnf(s898,plain,
spl5_30,
inference(rat,[],[s294,s5]) ).
cnf(s914,plain,
spl5_33,
inference(rat,[],[s646,s898,s4]) ).
cnf(s920,plain,
spl5_55,
inference(rat,[],[s115,s4]) ).
cnf(s925,plain,
spl5_116,
inference(rat,[],[s497,s920]) ).
cnf(s945,plain,
spl5_50,
inference(rat,[],[s472,s3]) ).
cnf(s946,plain,
spl5_34,
inference(rat,[],[s468,s945,s888,s3]) ).
cnf(s952,plain,
spl5_56,
inference(rat,[],[s116,s3]) ).
cnf(s957,plain,
spl5_79,
inference(rat,[],[s237,s914,s5,s946]) ).
cnf(s961,plain,
spl5_115,
inference(rat,[],[s495,s952]) ).
cnf(s965,plain,
spl5_82,
inference(rat,[],[s240,s957]) ).
cnf(s980,plain,
spl5_154,
inference(rat,[],[s877,s961,s925,s5,s2]) ).
cnf(s991,plain,
spl5_1,
inference(rat,[],[s878,s965,s890,s887,s980]) ).
cnf(s1028,plain,
$false,
inference(rat,[],[s1,s991]) ).
fof(f7637,plain,
$false,
inference(avatar_sat_refutation,[],[s1028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n001.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Mon Sep 28 21:10:49 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running first-order theorem proving
% 0.10/0.27 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
% 12.98/2.78 % (752436)Detected a unit-equality problem, will run specialized UEQ schedule.
% 12.98/2.78 % (752442)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=4277011655:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 12.98/2.78 % (752448)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2263875455:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 12.98/2.78 % (752443)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=3137430821:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 12.98/2.78 % (752445)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2711606323:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 12.98/2.78 % (752446)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3231396222:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 12.98/2.78 % (752444)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2178825956:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 12.98/2.78 % (752447)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2194457727:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 12.98/2.78 % (752445)Instruction limit reached!
% 12.98/2.78 % (752445)------------------------------
% 12.98/2.78 % (752445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.98/2.78 % (752445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.98/2.78 % (752445)CaDiCaL version: 2.1.3
% 12.98/2.78 % (752445)Termination reason: Instruction limit
% 12.98/2.78 % (752445)Termination phase: Saturation
% 12.98/2.78 % (752445)Time elapsed: 0.138 s
% 12.98/2.78 % (752445)Peak memory usage: 88 MB
% 12.98/2.78 % (752445)Instructions burned: 136 (million)
% 12.98/2.78 % (752446)Instruction limit reached!
% 12.98/2.78 % (752446)------------------------------
% 12.98/2.78 % (752446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.98/2.78 % (752446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.98/2.78 % (752446)CaDiCaL version: 2.1.3
% 12.98/2.78 % (752446)Termination reason: Instruction limit
% 12.98/2.78 % (752446)Termination phase: Saturation
% 12.98/2.78 % (752446)Time elapsed: 0.180 s
% 12.98/2.78 % (752446)Peak memory usage: 89 MB
% 12.98/2.78 % (752446)Instructions burned: 182 (million)
% 12.98/2.78 % (752447)Instruction limit reached!
% 12.98/2.78 % (752447)------------------------------
% 12.98/2.78 % (752447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.98/2.78 % (752447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.98/2.78 % (752447)CaDiCaL version: 2.1.3
% 12.98/2.78 % (752447)Termination reason: Instruction limit
% 12.98/2.78 % (752447)Termination phase: Saturation
% 12.98/2.78 % (752447)Time elapsed: 0.269 s
% 12.98/2.78 % (752447)Peak memory usage: 90 MB
% 12.98/2.78 % (752447)Instructions burned: 257 (million)
% 12.98/2.78 % (752457)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3717886839:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 12.98/2.78 % (752459)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4092150727:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 12.98/2.78 % (752460)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2598934147:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 12.98/2.78 % (752460)Instruction limit reached!
% 12.98/2.78 % (752460)------------------------------
% 12.98/2.78 % (752460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.98/2.78 % (752460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.98/2.78 % (752460)CaDiCaL version: 2.1.3
% 12.98/2.78 % (752460)Termination reason: Instruction limit
% 12.98/2.78 % (752460)Termination phase: Saturation
% 12.98/2.78 % (752460)Time elapsed: 0.160 s
% 12.98/2.78 % (752460)Peak memory usage: 90 MB
% 12.98/2.78 % (752460)Instructions burned: 217 (million)
% 12.98/2.78 % (752465)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=468158705:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 12.98/2.78 % (752448)Instruction limit reached!
% 12.98/2.78 % (752448)------------------------------
% 12.98/2.78 % (752448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.98/2.78 % (752448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.98/2.78 % (752448)CaDiCaL version: 2.1.3
% 12.98/2.78 % (752448)Termination reason: Instruction limit
% 12.98/2.78 % (752448)Termination phase: Saturation
% 12.98/2.78 % (752448)Time elapsed: 1.023 s
% 12.98/2.78 % (752448)Peak memory usage: 99 MB
% 12.98/2.78 % (752448)Instructions burned: 1188 (million)
% 12.98/2.78 % (752465)First to succeed.
% 12.98/2.78 % (752465)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-752436"
% 12.98/2.78 % (752467)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=401981886:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 12.98/2.78 % (752442)Also succeeded, but the first one will report.
% 12.98/2.78 % (752465)Refutation found. Thanks to Tanya!
% 12.98/2.78 % SZS status Unsatisfiable for theBenchmark
% 12.98/2.78 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/3.04 % (752465)------------------------------
% 0.25/3.04 % (752465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/3.04 % (752465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/3.04 % (752465)CaDiCaL version: 2.1.3
% 0.25/3.04 % (752465)Termination reason: Refutation
% 0.25/3.04 % (752465)Time elapsed: 0.269 s
% 0.25/3.04 % (752465)Peak memory usage: 93 MB
% 0.25/3.04 % (752465)Instructions burned: 249 (million)
% 0.25/3.04 % (752465)------------------------------
% 0.25/3.04 % (752465)------------------------------
% 0.25/3.04 % (752436)Success in time 1.907 s
% 0.25/3.04 % Vampire exiting
%------------------------------------------------------------------------------