%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE084-10 : TPTP v9.3.1. Released v7.5.0.
% 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 11:40:17 AM UTC 2026
% Result : Unsatisfiable 5.75s 1.94s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 41
% Syntax : Number of formulae : 184 ( 82 unt; 28 def)
% Number of atoms : 377 ( 129 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 370 ( 177 ~; 173 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f5,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f7,axiom,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f8,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f9,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f10,axiom,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f11,axiom,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f14,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f15,plain,
! [X0] : zero = multiplication(zero,X0),
inference(reorient_equations,[],[f14]) ).
fof(f19,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f20,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f22,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f24,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(reorient_equations,[],[f23]) ).
fof(f25,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f26,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(reorient_equations,[],[f25]) ).
fof(f35,negated_conjecture,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f36,plain,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))),
inference(definition_unfolding,[],[f35,f26,f26,f26]) ).
fof(f37,definition,
sF0 = multiplication(sK2_goals_X0,sK1_goals_X1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f38,plain,
multiplication(sK2_goals_X0,sK1_goals_X1) = sF0,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF1 = antidomain(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f40,plain,
antidomain(sF0) = sF1,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF2 = antidomain(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f42,plain,
antidomain(sF1) = sF2,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF3 = antidomain(sK1_goals_X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f44,plain,
antidomain(sK1_goals_X1) = sF3,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF4 = antidomain(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f46,plain,
antidomain(sF3) = sF4,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF5 = multiplication(sK2_goals_X0,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f48,plain,
multiplication(sK2_goals_X0,sF4) = sF5,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF6 = antidomain(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f50,plain,
antidomain(sF5) = sF6,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF7 = antidomain(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f52,plain,
antidomain(sF6) = sF7,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
sF2 != sF7,
inference(definition_folding,[],[f36,f52,f50,f48,f46,f44,f42,f40,f38]) ).
fof(f55,definition,
( spl8_1
<=> multiplication(sK2_goals_X0,sK1_goals_X1) = sF0 ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f57,plain,
( multiplication(sK2_goals_X0,sK1_goals_X1) = sF0
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
spl8_1,
inference(avatar_split_clause,[],[f38,f55]) ).
fof(f60,definition,
( spl8_2
<=> sF2 = sF7 ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f62,plain,
( sF2 != sF7
| spl8_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f53,f60]) ).
fof(f65,definition,
( spl8_3
<=> antidomain(sF6) = sF7 ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f67,plain,
( antidomain(sF6) = sF7
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
spl8_3,
inference(avatar_split_clause,[],[f52,f65]) ).
fof(f70,definition,
( spl8_4
<=> antidomain(sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f72,plain,
( antidomain(sF1) = sF2
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
spl8_4,
inference(avatar_split_clause,[],[f42,f70]) ).
fof(f75,definition,
( spl8_5
<=> multiplication(sK2_goals_X0,sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
fof(f77,plain,
( multiplication(sK2_goals_X0,sF4) = sF5
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
spl8_5,
inference(avatar_split_clause,[],[f48,f75]) ).
fof(f152,definition,
( spl8_6
<=> antidomain(sK1_goals_X1) = sF3 ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
fof(f154,plain,
( antidomain(sK1_goals_X1) = sF3
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
spl8_6,
inference(avatar_split_clause,[],[f44,f152]) ).
fof(f160,definition,
( spl8_7
<=> antidomain(sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f162,plain,
( antidomain(sF0) = sF1
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
spl8_7,
inference(avatar_split_clause,[],[f40,f160]) ).
fof(f164,plain,
( one = addition(antidomain(sF1),sF1)
| ~ spl8_7 ),
inference(superposition,[],[f24,f162]) ).
fof(f165,plain,
( one = addition(sF1,antidomain(sF1))
| ~ spl8_7 ),
inference(forward_demodulation,[],[f164,f3]) ).
fof(f166,plain,
( one = addition(sF1,sF2)
| ~ spl8_4
| ~ spl8_7 ),
inference(forward_demodulation,[],[f165,f72]) ).
fof(f168,definition,
( spl8_8
<=> antidomain(sF5) = sF6 ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f170,plain,
( antidomain(sF5) = sF6
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
spl8_8,
inference(avatar_split_clause,[],[f50,f168]) ).
fof(f172,plain,
( one = addition(antidomain(sF6),sF6)
| ~ spl8_8 ),
inference(superposition,[],[f24,f170]) ).
fof(f173,plain,
( one = addition(sF6,antidomain(sF6))
| ~ spl8_8 ),
inference(forward_demodulation,[],[f172,f3]) ).
fof(f174,plain,
( one = addition(sF6,sF7)
| ~ spl8_3
| ~ spl8_8 ),
inference(forward_demodulation,[],[f173,f67]) ).
fof(f176,definition,
( spl8_9
<=> antidomain(sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f178,plain,
( antidomain(sF3) = sF4
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,plain,
spl8_9,
inference(avatar_split_clause,[],[f46,f176]) ).
fof(f217,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f3,f5]) ).
fof(f271,plain,
( zero = multiplication(sF7,sF6)
| ~ spl8_3 ),
inference(superposition,[],[f20,f67]) ).
fof(f274,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f10,f20]) ).
fof(f277,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,antidomain(X1)),X1),
inference(superposition,[],[f11,f20]) ).
fof(f279,plain,
zero = antidomain(one),
inference(superposition,[],[f8,f20]) ).
fof(f281,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f277,f5]) ).
fof(f284,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[],[f274,f5]) ).
fof(f298,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f281,f24]) ).
fof(f317,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f298,f9]) ).
fof(f326,plain,
( sK1_goals_X1 = multiplication(antidomain(sF3),sK1_goals_X1)
| ~ spl8_6 ),
inference(superposition,[],[f317,f154]) ).
fof(f339,plain,
one = antidomain(antidomain(one)),
inference(superposition,[],[f8,f317]) ).
fof(f340,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f339,f279]) ).
fof(f348,plain,
( sK1_goals_X1 = multiplication(sF4,sK1_goals_X1)
| ~ spl8_6
| ~ spl8_9 ),
inference(forward_demodulation,[],[f326,f178]) ).
fof(f434,definition,
( spl8_11
<=> one = antidomain(zero) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
fof(f436,plain,
( one = antidomain(zero)
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f437,plain,
spl8_11,
inference(avatar_split_clause,[],[f340,f434]) ).
fof(f614,plain,
( antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1)))) = addition(antidomain(sF0),antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1)))))
| ~ spl8_1 ),
inference(superposition,[],[f22,f57]) ).
fof(f631,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f281,f22]) ).
fof(f637,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f631,f20]) ).
fof(f652,plain,
( antidomain(multiplication(sK2_goals_X0,antidomain(sF3))) = addition(antidomain(sF0),antidomain(multiplication(sK2_goals_X0,antidomain(sF3))))
| ~ spl8_1
| ~ spl8_6 ),
inference(forward_demodulation,[],[f614,f154]) ).
fof(f669,plain,
( antidomain(multiplication(sK2_goals_X0,sF4)) = addition(antidomain(sF0),antidomain(multiplication(sK2_goals_X0,sF4)))
| ~ spl8_1
| ~ spl8_6
| ~ spl8_9 ),
inference(forward_demodulation,[],[f652,f178]) ).
fof(f679,plain,
( antidomain(sF5) = addition(antidomain(sF0),antidomain(sF5))
| ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_9 ),
inference(forward_demodulation,[],[f669,f77]) ).
fof(f684,plain,
( sF6 = addition(antidomain(sF0),sF6)
| ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_8
| ~ spl8_9 ),
inference(forward_demodulation,[],[f679,f170]) ).
fof(f686,plain,
( sF6 = addition(sF6,antidomain(sF0))
| ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_8
| ~ spl8_9 ),
inference(forward_demodulation,[],[f684,f3]) ).
fof(f687,plain,
( sF6 = addition(sF6,sF1)
| ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_9 ),
inference(forward_demodulation,[],[f686,f162]) ).
fof(f688,plain,
( sF6 = addition(sF1,sF6)
| ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_9 ),
inference(forward_demodulation,[],[f687,f3]) ).
fof(f867,definition,
( spl8_15
<=> sK1_goals_X1 = multiplication(sF4,sK1_goals_X1) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
fof(f869,plain,
( sK1_goals_X1 = multiplication(sF4,sK1_goals_X1)
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f870,plain,
( spl8_15
| ~ spl8_6
| ~ spl8_9 ),
inference(avatar_split_clause,[],[f348,f176,f152,f867]) ).
fof(f899,plain,
! [X0,X1] : multiplication(zero,X1) = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(superposition,[],[f7,f20]) ).
fof(f906,plain,
( ! [X0] : multiplication(sK2_goals_X0,multiplication(sF4,X0)) = multiplication(sF5,X0)
| ~ spl8_5 ),
inference(superposition,[],[f7,f77]) ).
fof(f945,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(forward_demodulation,[],[f899,f15]) ).
fof(f991,plain,
( multiplication(sK2_goals_X0,sK1_goals_X1) = multiplication(sF5,sK1_goals_X1)
| ~ spl8_5
| ~ spl8_15 ),
inference(superposition,[],[f906,f869]) ).
fof(f1013,plain,
( sF0 = multiplication(sF5,sK1_goals_X1)
| ~ spl8_1
| ~ spl8_5
| ~ spl8_15 ),
inference(forward_demodulation,[],[f991,f57]) ).
fof(f1204,definition,
( spl8_17
<=> zero = multiplication(sF7,sF6) ),
introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition]) ).
fof(f1206,plain,
( zero = multiplication(sF7,sF6)
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1207,plain,
( spl8_17
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f271,f65,f1204]) ).
fof(f1252,definition,
( spl8_19
<=> sF6 = addition(sF1,sF6) ),
introduced(definition,[new_symbols(definition,[spl8_19])],[avatar_definition]) ).
fof(f1254,plain,
( sF6 = addition(sF1,sF6)
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f1255,plain,
( spl8_19
| ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_9 ),
inference(avatar_split_clause,[],[f688,f176,f168,f160,f152,f75,f55,f1252]) ).
fof(f1257,plain,
( multiplication(antidomain(sF6),sF6) = multiplication(antidomain(sF6),sF1)
| ~ spl8_19 ),
inference(superposition,[],[f284,f1254]) ).
fof(f1263,plain,
( multiplication(sF7,sF6) = multiplication(sF7,sF1)
| ~ spl8_3
| ~ spl8_19 ),
inference(forward_demodulation,[],[f1257,f67]) ).
fof(f1264,plain,
( zero = multiplication(sF7,sF1)
| ~ spl8_3
| ~ spl8_17
| ~ spl8_19 ),
inference(forward_demodulation,[],[f1263,f1206]) ).
fof(f1266,definition,
( spl8_20
<=> zero = multiplication(sF7,sF1) ),
introduced(definition,[new_symbols(definition,[spl8_20])],[avatar_definition]) ).
fof(f1268,plain,
( zero = multiplication(sF7,sF1)
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1269,plain,
( spl8_20
| ~ spl8_3
| ~ spl8_17
| ~ spl8_19 ),
inference(avatar_split_clause,[],[f1264,f1252,f1204,f65,f1266]) ).
fof(f1271,plain,
( ! [X0] : addition(zero,multiplication(sF7,X0)) = multiplication(sF7,addition(sF1,X0))
| ~ spl8_20 ),
inference(superposition,[],[f10,f1268]) ).
fof(f1284,plain,
( ! [X0] : multiplication(sF7,X0) = multiplication(sF7,addition(sF1,X0))
| ~ spl8_20 ),
inference(forward_demodulation,[],[f1271,f217]) ).
fof(f2083,definition,
( spl8_29
<=> one = addition(sF1,sF2) ),
introduced(definition,[new_symbols(definition,[spl8_29])],[avatar_definition]) ).
fof(f2085,plain,
( one = addition(sF1,sF2)
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f2083]) ).
fof(f2086,plain,
( spl8_29
| ~ spl8_4
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f166,f160,f70,f2083]) ).
fof(f2105,definition,
( spl8_31
<=> one = addition(sF6,sF7) ),
introduced(definition,[new_symbols(definition,[spl8_31])],[avatar_definition]) ).
fof(f2107,plain,
( one = addition(sF6,sF7)
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f2105]) ).
fof(f2108,plain,
( spl8_31
| ~ spl8_3
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f174,f168,f65,f2105]) ).
fof(f2122,definition,
( spl8_32
<=> sF0 = multiplication(sF5,sK1_goals_X1) ),
introduced(definition,[new_symbols(definition,[spl8_32])],[avatar_definition]) ).
fof(f2124,plain,
( sF0 = multiplication(sF5,sK1_goals_X1)
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f2125,plain,
( spl8_32
| ~ spl8_1
| ~ spl8_5
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f1013,f867,f75,f55,f2122]) ).
fof(f2136,plain,
( zero = multiplication(antidomain(sF5),sF0)
| ~ spl8_32 ),
inference(superposition,[],[f945,f2124]) ).
fof(f2137,plain,
( zero = multiplication(sF6,sF0)
| ~ spl8_8
| ~ spl8_32 ),
inference(forward_demodulation,[],[f2136,f170]) ).
fof(f2313,definition,
( spl8_34
<=> zero = multiplication(sF6,sF0) ),
introduced(definition,[new_symbols(definition,[spl8_34])],[avatar_definition]) ).
fof(f2315,plain,
( zero = multiplication(sF6,sF0)
| ~ spl8_34 ),
inference(avatar_component_clause,[],[f2313]) ).
fof(f2316,plain,
( spl8_34
| ~ spl8_8
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f2137,f2122,f168,f2313]) ).
fof(f5960,plain,
( multiplication(sF7,one) = multiplication(sF7,sF2)
| ~ spl8_20
| ~ spl8_29 ),
inference(superposition,[],[f1284,f2085]) ).
fof(f6003,plain,
( sF7 = multiplication(sF7,sF2)
| ~ spl8_20
| ~ spl8_29 ),
inference(forward_demodulation,[],[f5960,f8]) ).
fof(f6013,definition,
( spl8_48
<=> sF7 = multiplication(sF7,sF2) ),
introduced(definition,[new_symbols(definition,[spl8_48])],[avatar_definition]) ).
fof(f6015,plain,
( sF7 = multiplication(sF7,sF2)
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f6013]) ).
fof(f6016,plain,
( spl8_48
| ~ spl8_20
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f6003,f2083,f1266,f6013]) ).
fof(f7031,plain,
( zero = multiplication(antidomain(zero),multiplication(sF6,antidomain(antidomain(sF0))))
| ~ spl8_34 ),
inference(superposition,[],[f637,f2315]) ).
fof(f7041,plain,
( zero = multiplication(antidomain(zero),multiplication(sF6,antidomain(sF1)))
| ~ spl8_7
| ~ spl8_34 ),
inference(forward_demodulation,[],[f7031,f162]) ).
fof(f7057,plain,
( zero = multiplication(antidomain(zero),multiplication(sF6,sF2))
| ~ spl8_4
| ~ spl8_7
| ~ spl8_34 ),
inference(forward_demodulation,[],[f7041,f72]) ).
fof(f7067,plain,
( zero = multiplication(one,multiplication(sF6,sF2))
| ~ spl8_4
| ~ spl8_7
| ~ spl8_11
| ~ spl8_34 ),
inference(forward_demodulation,[],[f7057,f436]) ).
fof(f7074,plain,
( zero = multiplication(sF6,sF2)
| ~ spl8_4
| ~ spl8_7
| ~ spl8_11
| ~ spl8_34 ),
inference(forward_demodulation,[],[f7067,f9]) ).
fof(f7079,definition,
( spl8_55
<=> zero = multiplication(sF6,sF2) ),
introduced(definition,[new_symbols(definition,[spl8_55])],[avatar_definition]) ).
fof(f7081,plain,
( zero = multiplication(sF6,sF2)
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f7079]) ).
fof(f7082,plain,
( spl8_55
| ~ spl8_4
| ~ spl8_7
| ~ spl8_11
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f7074,f2313,f434,f160,f70,f7079]) ).
fof(f7089,plain,
( ! [X0] : addition(zero,multiplication(X0,sF2)) = multiplication(addition(sF6,X0),sF2)
| ~ spl8_55 ),
inference(superposition,[],[f11,f7081]) ).
fof(f7113,plain,
( ! [X0] : multiplication(X0,sF2) = multiplication(addition(sF6,X0),sF2)
| ~ spl8_55 ),
inference(forward_demodulation,[],[f7089,f217]) ).
fof(f8574,plain,
( multiplication(one,sF2) = multiplication(sF7,sF2)
| ~ spl8_31
| ~ spl8_55 ),
inference(superposition,[],[f7113,f2107]) ).
fof(f8628,plain,
( sF7 = multiplication(one,sF2)
| ~ spl8_31
| ~ spl8_48
| ~ spl8_55 ),
inference(forward_demodulation,[],[f8574,f6015]) ).
fof(f8640,plain,
( sF2 = sF7
| ~ spl8_31
| ~ spl8_48
| ~ spl8_55 ),
inference(forward_demodulation,[],[f8628,f9]) ).
fof(f8646,plain,
( $false
| spl8_2
| ~ spl8_31
| ~ spl8_48
| ~ spl8_55 ),
inference(forward_subsumption_resolution,[],[f8640,f62]) ).
fof(f8647,plain,
( spl8_2
| ~ spl8_31
| ~ spl8_48
| ~ spl8_55 ),
inference(avatar_contradiction_clause,[],[f8646]) ).
cnf(s1,plain,
spl8_1,
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
~ spl8_2,
inference(sat_conversion,[],[f63]) ).
cnf(s3,plain,
spl8_3,
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
spl8_4,
inference(sat_conversion,[],[f73]) ).
cnf(s5,plain,
spl8_5,
inference(sat_conversion,[],[f78]) ).
cnf(s6,plain,
spl8_6,
inference(sat_conversion,[],[f155]) ).
cnf(s7,plain,
spl8_7,
inference(sat_conversion,[],[f163]) ).
cnf(s8,plain,
spl8_8,
inference(sat_conversion,[],[f171]) ).
cnf(s9,plain,
spl8_9,
inference(sat_conversion,[],[f179]) ).
cnf(s11,plain,
spl8_11,
inference(sat_conversion,[],[f437]) ).
cnf(s15,plain,
( ~ spl8_6
| ~ spl8_9
| spl8_15 ),
inference(sat_conversion,[],[f870]) ).
cnf(s17,plain,
( ~ spl8_3
| spl8_17 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s19,plain,
( ~ spl8_1
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_9
| spl8_19 ),
inference(sat_conversion,[],[f1255]) ).
cnf(s20,plain,
( ~ spl8_3
| ~ spl8_17
| ~ spl8_19
| spl8_20 ),
inference(sat_conversion,[],[f1269]) ).
cnf(s29,plain,
( ~ spl8_4
| ~ spl8_7
| spl8_29 ),
inference(sat_conversion,[],[f2086]) ).
cnf(s31,plain,
( ~ spl8_3
| ~ spl8_8
| spl8_31 ),
inference(sat_conversion,[],[f2108]) ).
cnf(s32,plain,
( ~ spl8_1
| ~ spl8_5
| ~ spl8_15
| spl8_32 ),
inference(sat_conversion,[],[f2125]) ).
cnf(s34,plain,
( ~ spl8_8
| ~ spl8_32
| spl8_34 ),
inference(sat_conversion,[],[f2316]) ).
cnf(s48,plain,
( ~ spl8_20
| ~ spl8_29
| spl8_48 ),
inference(sat_conversion,[],[f6016]) ).
cnf(s55,plain,
( ~ spl8_4
| ~ spl8_7
| ~ spl8_11
| ~ spl8_34
| spl8_55 ),
inference(sat_conversion,[],[f7082]) ).
cnf(s59,plain,
( spl8_2
| ~ spl8_31
| ~ spl8_48
| ~ spl8_55 ),
inference(sat_conversion,[],[f8647]) ).
cnf(s68,plain,
spl8_15,
inference(rat,[],[s15,s9,s6]) ).
cnf(s78,plain,
spl8_29,
inference(rat,[],[s29,s7,s4]) ).
cnf(s87,plain,
spl8_31,
inference(rat,[],[s31,s8,s3]) ).
cnf(s91,plain,
spl8_17,
inference(rat,[],[s17,s3]) ).
cnf(s94,plain,
spl8_32,
inference(rat,[],[s32,s5,s68,s1]) ).
cnf(s95,plain,
spl8_19,
inference(rat,[],[s19,s5,s9,s8,s7,s6,s1]) ).
cnf(s97,plain,
spl8_34,
inference(rat,[],[s34,s8,s94]) ).
cnf(s99,plain,
spl8_20,
inference(rat,[],[s20,s91,s3,s95]) ).
cnf(s102,plain,
spl8_55,
inference(rat,[],[s55,s4,s7,s11,s97]) ).
cnf(s103,plain,
spl8_48,
inference(rat,[],[s48,s78,s99]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s59,s2,s87,s102,s103]) ).
fof(f8649,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE084-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n013.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 13:08:37 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 5.75/1.94 % (214407)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.75/1.94 % (214542)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=46037402:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.75/1.94 % (214549)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2290088604:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.75/1.94 % (214543)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=1544875721:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.75/1.94 % (214546)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2576501742:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.75/1.94 % (214548)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2947782619:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.75/1.94 % (214544)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1272291649:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.75/1.94 % (214545)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=147042739:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.75/1.94 % (214545)Instruction limit reached!
% 5.75/1.94 % (214545)------------------------------
% 5.75/1.94 % (214545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.75/1.94 % (214545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.75/1.94 % (214545)CaDiCaL version: 2.1.3
% 5.75/1.94 % (214545)Termination reason: Instruction limit
% 5.75/1.94 % (214545)Termination phase: Saturation
% 5.75/1.94 % (214545)Time elapsed: 0.085 s
% 5.75/1.94 % (214545)Peak memory usage: 89 MB
% 5.75/1.94 % (214545)Instructions burned: 137 (million)
% 5.75/1.94 % (214546)Instruction limit reached!
% 5.75/1.94 % (214546)------------------------------
% 5.75/1.94 % (214546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.75/1.94 % (214546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.75/1.94 % (214546)CaDiCaL version: 2.1.3
% 5.75/1.94 % (214546)Termination reason: Instruction limit
% 5.75/1.94 % (214546)Termination phase: Saturation
% 5.75/1.94 % (214546)Time elapsed: 0.107 s
% 5.75/1.94 % (214546)Peak memory usage: 90 MB
% 5.75/1.94 % (214546)Instructions burned: 182 (million)
% 5.75/1.94 % (214548)Instruction limit reached!
% 5.75/1.94 % (214548)------------------------------
% 5.75/1.94 % (214548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.75/1.94 % (214548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.75/1.94 % (214548)CaDiCaL version: 2.1.3
% 5.75/1.94 % (214548)Termination reason: Instruction limit
% 5.75/1.94 % (214548)Termination phase: Saturation
% 5.75/1.94 % (214548)Time elapsed: 0.166 s
% 5.75/1.94 % (214548)Peak memory usage: 91 MB
% 5.75/1.94 % (214548)Instructions burned: 258 (million)
% 5.75/1.94 % (214560)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2161412806:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.75/1.94 % (214561)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=408573076:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.75/1.94 % (214562)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2335417169:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.75/1.94 % (214562)Instruction limit reached!
% 5.75/1.94 % (214562)------------------------------
% 5.75/1.94 % (214562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.75/1.94 % (214562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.75/1.94 % (214562)CaDiCaL version: 2.1.3
% 5.75/1.94 % (214562)Termination reason: Instruction limit
% 5.75/1.94 % (214562)Termination phase: Saturation
% 5.75/1.94 % (214562)Time elapsed: 0.114 s
% 5.75/1.94 % (214562)Peak memory usage: 91 MB
% 5.75/1.94 % (214562)Instructions burned: 216 (million)
% 5.75/1.94 % (214566)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=2378652812:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 5.75/1.94 % (214549)Instruction limit reached!
% 5.75/1.94 % (214549)------------------------------
% 5.75/1.94 % (214549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.75/1.94 % (214549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.75/1.94 % (214549)CaDiCaL version: 2.1.3
% 5.75/1.94 % (214549)Termination reason: Instruction limit
% 5.75/1.94 % (214549)Termination phase: Saturation
% 5.75/1.94 % (214549)Time elapsed: 0.634 s
% 5.75/1.94 % (214549)Peak memory usage: 99 MB
% 5.75/1.94 % (214549)Instructions burned: 1189 (million)
% 5.75/1.94 % (214566)Instruction limit reached!
% 5.75/1.94 % (214566)------------------------------
% 5.75/1.94 % (214566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.75/1.94 % (214566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.75/1.94 % (214566)CaDiCaL version: 2.1.3
% 5.75/1.94 % (214566)Termination reason: Instruction limit
% 5.75/1.94 % (214566)Termination phase: Saturation
% 5.75/1.94 % (214566)Time elapsed: 0.183 s
% 5.75/1.94 % (214566)Peak memory usage: 92 MB
% 5.75/1.94 % (214566)Instructions burned: 317 (million)
% 5.75/1.94 % (214542)First to succeed.
% 5.75/1.94 % (214542)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-214407"
% 5.75/1.94 % (214568)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=1218487310:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 5.75/1.94 % (214543)Also succeeded, but the first one will report.
% 5.75/1.94 % (214544)Also succeeded, but the first one will report.
% 5.75/1.94 % (214569)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1685640800:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 5.75/1.94 % (214542)Refutation found. Thanks to Tanya!
% 5.75/1.94 % SZS status Unsatisfiable for theBenchmark
% 5.75/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/2.14 % (214542)------------------------------
% 0.20/2.14 % (214542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/2.14 % (214542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/2.14 % (214542)CaDiCaL version: 2.1.3
% 0.20/2.14 % (214542)Termination reason: Refutation
% 0.20/2.14 % (214542)Time elapsed: 0.801 s
% 0.20/2.14 % (214542)Peak memory usage: 143 MB
% 0.20/2.14 % (214542)Instructions burned: 2219 (million)
% 0.20/2.14 % (214542)------------------------------
% 0.20/2.14 % (214542)------------------------------
% 0.20/2.14 % (214407)Success in time 1.064 s
% 0.20/2.14 % Vampire exiting
%------------------------------------------------------------------------------