%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP215-1 : 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 : n010.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 10:17:11 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.56s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 40
% Syntax : Number of formulae : 230 ( 18 unt; 16 def)
% Number of atoms : 628 ( 211 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 740 ( 342 ~; 382 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 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(f5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(sk_c7,X3) != sk_c6
| multiply(X4,sk_c7) != X3
| inverse(X4) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(sk_c7,X3)
| multiply(X4,sk_c7) != X3
| sk_c7 != inverse(X4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) ),
inference(equality_resolution,[],[f46]) ).
fof(f49,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X4] :
( sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f53,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,definition,
( spl0_3
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,definition,
( spl0_4
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f59,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f47,f58,f55,f52,f49]) ).
fof(f62,definition,
( spl0_5
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f66,definition,
( spl0_6
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f68,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f44,f66,f62]) ).
fof(f71,definition,
( spl0_7
<=> sk_c5 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f72,plain,
( sk_c5 != multiply(sk_c4,sk_c7)
| spl0_7 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f42,f66,f71]) ).
fof(f76,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f40,f66,f76]) ).
fof(f81,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f84,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f38,f66,f81]) ).
fof(f86,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f88,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f36,f66,f86]) ).
fof(f91,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_5
| spl0_11 ),
inference(avatar_split_clause,[],[f34,f91,f62]) ).
fof(f95,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f32,f91,f71]) ).
fof(f96,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f30,f91,f76]) ).
fof(f97,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f28,f91,f81]) ).
fof(f98,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f26,f91,f86]) ).
fof(f100,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f24,f100,f62]) ).
fof(f104,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f22,f100,f71]) ).
fof(f105,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f20,f100,f76]) ).
fof(f106,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f18,f100,f81]) ).
fof(f107,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f16,f100,f86]) ).
fof(f109,definition,
( spl0_13
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f14,f109,f62]) ).
fof(f113,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f12,f109,f71]) ).
fof(f114,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f10,f109,f76]) ).
fof(f115,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f8,f109,f81]) ).
fof(f116,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f6,f109,f86]) ).
fof(f118,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f53,f88]) ).
fof(f119,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f118]) ).
fof(f121,plain,
( ~ spl0_9
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f119,f86,f52,f81]) ).
fof(f122,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f53,f68]) ).
fof(f124,definition,
( spl0_14
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f125,plain,
( sk_c7 = sk_c6
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f122,f66,f52,f124,f91]) ).
fof(f130,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_12 ),
inference(superposition,[],[f3,f102]) ).
fof(f131,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f88]) ).
fof(f132,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_5 ),
inference(superposition,[],[f3,f64]) ).
fof(f136,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f138,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f130]) ).
fof(f141,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f132]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c6,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f93]) ).
fof(f181,plain,
( multiply(identity,sk_c1) = multiply(inverse(sk_c7),identity)
| ~ spl0_12 ),
inference(superposition,[],[f136,f130]) ).
fof(f182,plain,
( multiply(inverse(sk_c7),identity) = multiply(identity,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f136,f131]) ).
fof(f184,plain,
( multiply(inverse(sk_c7),identity) = multiply(identity,sk_c4)
| ~ spl0_5 ),
inference(superposition,[],[f136,f132]) ).
fof(f191,plain,
( multiply(identity,sk_c7) = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f136,f73]) ).
fof(f193,plain,
( multiply(identity,sk_c6) = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f136,f93]) ).
fof(f204,plain,
( multiply(identity,sk_c1) = multiply(identity,sk_c3)
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f181,f182]) ).
fof(f211,plain,
( multiply(identity,sk_c3) = multiply(identity,sk_c4)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f182,f184]) ).
fof(f217,plain,
( multiply(sk_c7,sk_c5) = multiply(identity,sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f191,f64]) ).
fof(f220,plain,
( multiply(identity,sk_c6) = multiply(sk_c6,sk_c7)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f193,f68]) ).
fof(f238,plain,
( sk_c4 = multiply(identity,sk_c3)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f1,f211]) ).
fof(f244,plain,
( sk_c4 = multiply(identity,sk_c1)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f204,f238]) ).
fof(f245,plain,
( sk_c3 = sk_c4
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f1,f238]) ).
fof(f311,plain,
( sk_c1 = sk_c4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f1,f244]) ).
fof(f341,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f78,f217]) ).
fof(f347,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f1,f341]) ).
fof(f351,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f347,f76,f71,f62,f124]) ).
fof(f352,plain,
( multiply(sk_c1,sk_c7) != sk_c5
| ~ spl0_5
| spl0_7
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f72,f311]) ).
fof(f356,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c2,multiply(identity,sk_c6))
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f144,f220]) ).
fof(f361,plain,
( sk_c6 != sk_c5
| ~ spl0_5
| spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f352,f111]) ).
fof(f421,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f356,f1]) ).
fof(f428,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f93,f421]) ).
fof(f435,plain,
( multiply(identity,sk_c7) = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f136,f428]) ).
fof(f444,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f3,f435]) ).
fof(f449,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f1,f444]) ).
fof(f454,plain,
( sk_c6 = multiply(identity,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f78,f449]) ).
fof(f456,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f130,f449]) ).
fof(f482,plain,
( sk_c6 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f1,f454]) ).
fof(f487,plain,
( sk_c6 != sk_c6
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f361,f482]) ).
fof(f490,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f487]) ).
fof(f491,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f503,plain,
( identity = sk_c1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f456]) ).
fof(f508,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f111,f503]) ).
fof(f610,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1,f508]) ).
fof(f614,plain,
( spl0_14
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f610,f109,f100,f91,f66,f124]) ).
fof(f648,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f56,f64]) ).
fof(f649,plain,
( sk_c6 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f56,f68]) ).
fof(f650,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f649]) ).
fof(f651,plain,
( ~ spl0_11
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f650,f66,f55,f91]) ).
fof(f653,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f654,plain,
( sk_c7 = multiply(sk_c4,sk_c6)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f655,plain,
( sk_c7 != multiply(sk_c4,sk_c6)
| spl0_15 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f677,plain,
( sk_c7 = multiply(sk_c4,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f654,f125]) ).
fof(f790,plain,
( sk_c6 != multiply(identity,sk_c7)
| sk_c7 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f50,f138]) ).
fof(f791,plain,
( sk_c6 != multiply(identity,sk_c7)
| sk_c7 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f50,f141]) ).
fof(f793,definition,
( spl0_18
<=> sk_c6 = multiply(identity,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f795,plain,
( sk_c6 != multiply(identity,sk_c7)
| spl0_18 ),
inference(avatar_component_clause,[],[f793]) ).
fof(f796,plain,
( ~ spl0_5
| ~ spl0_18
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f791,f62,f49,f793,f62]) ).
fof(f797,plain,
( ~ spl0_12
| ~ spl0_18
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f790,f100,f49,f793,f100]) ).
fof(f892,plain,
( sk_c6 != sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(superposition,[],[f795,f508]) ).
fof(f894,plain,
( sk_c7 != sk_c6
| spl0_18 ),
inference(superposition,[],[f795,f1]) ).
fof(f895,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(trivial_inequality_removal,[],[f892]) ).
fof(f896,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f895]) ).
fof(f897,plain,
( ~ spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f894,f793,f124]) ).
fof(f953,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f59,f111]) ).
fof(f959,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f59,f677]) ).
fof(f962,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f953]) ).
fof(f965,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f959,f653,f124,f58,f124,f62]) ).
fof(f978,plain,
( ~ spl0_12
| ~ spl0_4
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f962,f109,f58,f100]) ).
fof(f985,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f648,f62,f55,f124,f653]) ).
fof(f1023,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_10
| spl0_15 ),
inference(superposition,[],[f655,f245]) ).
fof(f1026,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f1023,f653,f86,f62,f81]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s2,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f74]) ).
cnf(s4,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s6,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f89]) ).
cnf(s7,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f94]) ).
cnf(s8,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f95]) ).
cnf(s9,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f96]) ).
cnf(s10,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f97]) ).
cnf(s11,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s12,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f103]) ).
cnf(s13,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s14,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s15,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s16,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s17,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s18,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s19,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s20,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s21,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s22,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f121]) ).
cnf(s23,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s24,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f351]) ).
cnf(s26,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f491]) ).
cnf(s27,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f614]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(sat_conversion,[],[f651]) ).
cnf(s36,plain,
( ~ spl0_5
| ~ spl0_1
| ~ spl0_5
| ~ spl0_18 ),
inference(sat_conversion,[],[f796]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_18 ),
inference(rat,[],[s36]) ).
cnf(s38,plain,
( ~ spl0_12
| ~ spl0_1
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f797]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_18 ),
inference(rat,[],[s38]) ).
cnf(s57,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f896]) ).
cnf(s58,plain,
( ~ spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f897]) ).
cnf(s67,plain,
( ~ spl0_14
| ~ spl0_5
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f965]) ).
cnf(s68,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(rat,[],[s67]) ).
cnf(s73,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f978]) ).
cnf(s81,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f985]) ).
cnf(s85,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f1026]) ).
cnf(s86,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s73,s12,s17]) ).
cnf(s87,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s68,s24,s85,s18,s19,s20,s21,s86]) ).
cnf(s88,plain,
~ spl0_4,
inference(rat,[],[s68,s24,s85,s13,s14,s15,s16,s73,s87,s86]) ).
cnf(s89,plain,
( spl0_13
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s81,s24,s85,s18,s19,s20,s21]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s29,s6,s11]) ).
cnf(s91,plain,
( spl0_8
| spl0_14
| ~ spl0_13 ),
inference(rat,[],[s27,s4,s9,s14]) ).
cnf(s92,plain,
( spl0_14
| ~ spl0_13
| ~ spl0_5
| ~ spl0_10 ),
inference(rat,[],[s26,s3,s8,s13,s24,s91]) ).
cnf(s93,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s29,s5,s10]) ).
cnf(s94,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s81,s92,s85,s89,s90,s93]) ).
cnf(s95,plain,
~ spl0_3,
inference(rat,[],[s29,s2,s7,s94]) ).
cnf(s96,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s23,s27,s6,s11,s16,s21]) ).
cnf(s97,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s27,s23,s5,s10,s15,s20,s22]) ).
cnf(s98,plain,
~ spl0_2,
inference(rat,[],[s97,s96]) ).
cnf(s99,plain,
spl0_1,
inference(rat,[],[s1,s88,s95,s98]) ).
cnf(s100,plain,
spl0_10,
inference(rat,[],[s57,s39,s6,s11,s16,s21,s99]) ).
cnf(s101,plain,
~ spl0_18,
inference(rat,[],[s12,s37,s39,s99]) ).
cnf(s102,plain,
~ spl0_14,
inference(rat,[],[s58,s101]) ).
cnf(s103,plain,
~ spl0_13,
inference(rat,[],[s57,s2,s7,s12,s92,s101,s102,s100]) ).
cnf(s104,plain,
spl0_8,
inference(rat,[],[s19,s103]) ).
cnf(s105,plain,
spl0_7,
inference(rat,[],[s18,s103]) ).
cnf(s106,plain,
spl0_5,
inference(rat,[],[s17,s103]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s24,s102,s106,s105,s104]) ).
fof(f1027,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP215-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.48 % Computer : n010.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sun Sep 27 09:37:46 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.52 Running first-order model finding
% 0.25/0.52 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
% 0.25/0.56 % (702266)Will run a generic schedule for satisfiability detection.
% 0.25/0.56 % (702277)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3606816298:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.56 % (702272)% WARNING: option uhcvi not known.
% 0.25/0.56 % (702271)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2742756719_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.56 % (702274)dis+10_1_sil=32000:sp=arity:random_seed=2548438492:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.56 % (702273)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2968948029:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.56 % (702272)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2520191600:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.56 % (702275)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=813258762:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.56 % (702276)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2469177012:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.56 % TRYING [1]
% 0.25/0.56 % TRYING [2]
% 0.25/0.56 % TRYING [3]
% 0.25/0.56 % TRYING [4]
% 0.25/0.56 % (702277) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-702266-702277"...
% 0.25/0.56 % (702277)...printing done.
% 0.25/0.56 % (702277)Refutation found. Thanks to Tanya!
% 0.25/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.57 % (702277)------------------------------
% 0.25/0.57 % (702277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.57 % (702277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.57 % (702277)CaDiCaL version: 2.1.3
% 0.25/0.57 % (702277)Termination reason: Refutation
% 0.25/0.57 % (702277)Time elapsed: 0.017 s
% 0.25/0.57 % (702277)Peak memory usage: 13 MB
% 0.25/0.57 % (702277)Instructions burned: 48 (million)
% 0.25/0.57 % (702266)Success in time 0.039 s
% 0.25/0.57 % Vampire exiting
%------------------------------------------------------------------------------