%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 10:17:12 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.67s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 33
% Syntax : Number of formulae : 187 ( 18 unt; 14 def)
% Number of atoms : 474 ( 177 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 537 ( 250 ~; 273 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f10]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = multiply(sk_c2,sk_c3)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c3 = inverse(sk_c2)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f44,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| multiply(X1,X2) != sk_c6
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| multiply(X1,X2) != sk_c6
| inverse(X1) != X2
| sk_c6 != multiply(X2,sk_c7)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,plain,
! [X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != multiply(X1,inverse(X1))
| sk_c6 != multiply(inverse(X1),sk_c7)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(equality_resolution,[],[f45]) ).
fof(f48,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f49,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f52,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_3
<=> ! [X1] :
( sk_c6 != multiply(X1,inverse(X1))
| sk_c6 != multiply(inverse(X1),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f55,plain,
( ! [X1] :
( sk_c6 != multiply(X1,inverse(X1))
| sk_c6 != multiply(inverse(X1),sk_c7) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f46,f48,f54,f51,f48]) ).
fof(f58,definition,
( spl0_4
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f67,definition,
( spl0_6
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f69,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f41,f62,f67]) ).
fof(f72,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f74,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f39,f62,f72]) ).
fof(f77,definition,
( spl0_8
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f79,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f37,f62,f77]) ).
fof(f82,definition,
( spl0_9
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f84,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f35,f82,f58]) ).
fof(f86,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f33,f82,f67]) ).
fof(f87,plain,
( spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f31,f82,f72]) ).
fof(f88,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f29,f82,f77]) ).
fof(f90,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = multiply(sk_c2,sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f27,f90,f58]) ).
fof(f94,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f25,f90,f67]) ).
fof(f95,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f23,f90,f72]) ).
fof(f96,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f21,f90,f77]) ).
fof(f98,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f19,f98,f58]) ).
fof(f102,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f17,f98,f67]) ).
fof(f106,definition,
( spl0_12
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f108,plain,
( inverse(sk_c1) = sk_c7
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f11,f106,f58]) ).
fof(f110,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f9,f106,f67]) ).
fof(f113,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f52,f79]) ).
fof(f114,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f113]) ).
fof(f115,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f114,f74]) ).
fof(f116,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f115]) ).
fof(f129,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f69]) ).
fof(f130,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f84]) ).
fof(f131,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_12 ),
inference(superposition,[],[f3,f108]) ).
fof(f132,plain,
( identity != sk_c6
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f52,f3]) ).
fof(f134,definition,
( spl0_15
<=> sk_c7 = inverse(inverse(sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f136,plain,
( sk_c7 != inverse(inverse(sk_c7))
| spl0_15 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f138,definition,
( spl0_16
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f139,plain,
( identity = sk_c6
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f140,plain,
( identity != sk_c6
| spl0_16 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f132,f51,f138,f134]) ).
fof(f144,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f148,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c3,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f92]) ).
fof(f151,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f144,f1]) ).
fof(f154,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f129]) ).
fof(f155,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f154,f1]) ).
fof(f156,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,multiply(sk_c2,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f130]) ).
fof(f157,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c2,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f156,f1]) ).
fof(f160,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f155,f60]) ).
fof(f166,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f52,f160]) ).
fof(f168,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f166]) ).
fof(f181,plain,
( sk_c3 = multiply(sk_c3,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f157,f92]) ).
fof(f191,plain,
( multiply(sk_c2,sk_c3) = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f148,f181]) ).
fof(f193,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f191,f92]) ).
fof(f259,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f151,f3]) ).
fof(f260,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f151,f151]) ).
fof(f264,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_12 ),
inference(superposition,[],[f151,f131]) ).
fof(f265,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f151,f160]) ).
fof(f266,plain,
( sk_c5 = multiply(inverse(sk_c7),identity)
| ~ spl0_6 ),
inference(superposition,[],[f151,f129]) ).
fof(f269,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f151,f193]) ).
fof(f288,plain,
( identity = sk_c6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f269,f3]) ).
fof(f292,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f259,f260]) ).
fof(f295,plain,
( $false
| ~ spl0_9
| ~ spl0_10
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f288,f140]) ).
fof(f296,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f313,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f266,f139]) ).
fof(f318,plain,
( sk_c7 = sk_c5
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f313,f265]) ).
fof(f325,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f69,f318]) ).
fof(f326,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f325,f168]) ).
fof(f327,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f337,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f264,f292]) ).
fof(f364,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| sk_c6 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f55,f84]) ).
fof(f365,plain,
( identity != sk_c6
| sk_c6 != multiply(sk_c7,inverse(sk_c7))
| ~ spl0_3 ),
inference(superposition,[],[f55,f3]) ).
fof(f366,plain,
( sk_c6 != multiply(sk_c7,inverse(sk_c7))
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f365,f139]) ).
fof(f367,plain,
( sk_c6 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f364,f64]) ).
fof(f371,plain,
( sk_c6 != multiply(sk_c7,sk_c1)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f366,f337]) ).
fof(f378,plain,
( identity != sk_c6
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f371,f131]) ).
fof(f383,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f378,f139]) ).
fof(f384,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f383]) ).
fof(f385,plain,
( inverse(sk_c1) != sk_c7
| ~ spl0_12
| spl0_15 ),
inference(superposition,[],[f136,f337]) ).
fof(f390,plain,
( $false
| ~ spl0_12
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f385,f108]) ).
fof(f391,plain,
( ~ spl0_12
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f397,plain,
( sk_c7 != sk_c7
| inverse(sk_c1) != sk_c7
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f49,f100]) ).
fof(f400,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f49,f60]) ).
fof(f402,plain,
( sk_c7 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f400]) ).
fof(f403,plain,
( inverse(sk_c1) != sk_c7
| ~ spl0_1
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f397]) ).
fof(f405,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f403,f108]) ).
fof(f406,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f420,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f402,f69]) ).
fof(f421,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f435,plain,
( ~ spl0_10
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f367,f82,f62,f54,f90]) ).
fof(f470,plain,
( multiply(sk_c4,sk_c7) != sk_c6
| sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f55,f74]) ).
fof(f489,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f470,f79]) ).
fof(f502,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f489,f160]) ).
fof(f503,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f502]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(rat,[],[s1]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f75]) ).
cnf(s6,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f85]) ).
cnf(s8,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f86]) ).
cnf(s9,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f87]) ).
cnf(s10,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f88]) ).
cnf(s11,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f93]) ).
cnf(s12,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f94]) ).
cnf(s13,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f95]) ).
cnf(s14,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s15,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s16,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s19,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s20,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s23,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s25,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f141]) ).
cnf(s31,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f296]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(sat_conversion,[],[f327]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(sat_conversion,[],[f384]) ).
cnf(s41,plain,
( ~ spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f391]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f406]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f421]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f435]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f503]) ).
cnf(s53,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s31,s40,s7,s11,s19]) ).
cnf(s54,plain,
( spl0_5
| ~ spl0_3 ),
inference(rat,[],[s52,s4,s5,s6,s53]) ).
cnf(s55,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s52,s12,s13,s14,s53]) ).
cnf(s56,plain,
~ spl0_3,
inference(rat,[],[s52,s8,s9,s10,s47,s55,s54,s53]) ).
cnf(s57,plain,
( ~ spl0_16
| ~ spl0_4
| ~ spl0_2 ),
inference(rat,[],[s20,s41,s33,s25]) ).
cnf(s58,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s23,s13,s14]) ).
cnf(s59,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s23,s9,s10]) ).
cnf(s60,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s19,s41,s57,s25]) ).
cnf(s61,plain,
~ spl0_2,
inference(rat,[],[s60,s31,s59,s58]) ).
cnf(s62,plain,
spl0_1,
inference(rat,[],[s2,s56,s61]) ).
cnf(s63,plain,
spl0_6,
inference(rat,[],[s42,s16,s20,s62]) ).
cnf(s64,plain,
~ spl0_4,
inference(rat,[],[s44,s62,s63]) ).
cnf(s65,plain,
spl0_12,
inference(rat,[],[s19,s64]) ).
cnf(s66,plain,
spl0_11,
inference(rat,[],[s15,s64]) ).
cnf(s71,plain,
$false,
inference(rat,[],[s42,s62,s65,s66]) ).
fof(f507,plain,
$false,
inference(avatar_sat_refutation,[],[s71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.22 % Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.25 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.58 % Computer : n001.cluster.edu
% 0.13/0.58 % Model : x86_64 x86_64
% 0.13/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.58 % Memory : 8046.5625MB
% 0.13/0.58 % OS : Linux 6.8.0-71-generic
% 0.13/0.58 % CPULimit : 300
% 0.13/0.58 % WCLimit : 300
% 0.13/0.58 % DateTime : Sun Sep 27 09:43:46 UTC 2026
% 0.13/0.59 % CPUTime :
% 0.13/0.59 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.62 Running first-order model finding
% 0.13/0.62 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.67 % (3305530)Will run a generic schedule for satisfiability detection.
% 0.16/0.67 % (3305535)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=688991110_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.67 % TRYING [1]
% 0.16/0.67 % TRYING [2]
% 0.16/0.67 % TRYING [3]
% 0.16/0.67 % TRYING [4]
% 0.16/0.67 % (3305536)% WARNING: option uhcvi not known.
% 0.16/0.67 % (3305536)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4267992060:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.67 % (3305537)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2404368502:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.67 % (3305538)dis+10_1_sil=32000:sp=arity:random_seed=1022884546:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.67 % (3305539)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=107640307:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.67 % (3305540)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1218178039:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.67 % TRYING [5]
% 0.16/0.67 % (3305541)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3937088542:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.67 % (3305539) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3305530-3305539"...
% 0.16/0.67 % TRYING [6]
% 0.16/0.67 % (3305538) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3305530-3305538"...
% 0.16/0.67 % (3305539)...printing done.
% 0.16/0.67 % (3305539)Refutation found. Thanks to Tanya!
% 0.16/0.67 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.68 % (3305539)------------------------------
% 0.16/0.68 % (3305539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.68 % (3305539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.68 % (3305539)CaDiCaL version: 2.1.3
% 0.16/0.68 % (3305539)Termination reason: Refutation
% 0.16/0.68 % (3305539)Time elapsed: 0.012 s
% 0.16/0.68 % (3305539)Peak memory usage: 12 MB
% 0.16/0.68 % (3305539)Instructions burned: 17 (million)
% 0.16/0.68 % (3305530)Success in time 0.046 s
% 0.16/0.68 % Vampire exiting
%------------------------------------------------------------------------------