%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP300-1 : 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 : n015.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 10:17:25 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 200 ( 21 unt; 10 def)
% Number of atoms : 614 ( 195 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 783 ( 369 ~; 404 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 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_c6,sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
! [X2,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c4
| multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c6
| multiply(sk_c4,sk_c6) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(sk_c6) != sk_c4
| multiply(X2,sk_c4) != sk_c5
| inverse(X2) != sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c4
| sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != multiply(sk_c4,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4)
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c4 != inverse(sk_c6)
| sk_c5 != multiply(X2,sk_c4)
| sk_c4 != inverse(X2) ),
inference(reorient_equations,[],[f53]) ).
fof(f56,definition,
( spl0_1
<=> ! [X2] :
( sk_c5 != multiply(X2,sk_c4)
| sk_c4 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f57,plain,
( ! [X2] :
( sk_c5 != multiply(X2,sk_c4)
| sk_c4 != inverse(X2) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl0_2
<=> sk_c4 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f60,plain,
( sk_c4 = inverse(sk_c6)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( sk_c4 != inverse(sk_c6)
| spl0_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_3
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,definition,
( spl0_4
<=> sk_c6 = multiply(sk_c5,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f67,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( sk_c6 != multiply(sk_c5,sk_c4)
| spl0_4 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f70,definition,
( spl0_5
<=> sk_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( sk_c5 != multiply(sk_c4,sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl0_6
<=> multiply(sk_c6,sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c5) != sk_c4
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f54,f74,f63,f70,f66,f63,f59,f56]) ).
fof(f88,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f70,f59]) ).
fof(f90,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f70,f90]) ).
fof(f95,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f97,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f70,f95]) ).
fof(f99,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f70,f66]) ).
fof(f101,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f103,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,plain,
( spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f36,f101,f59]) ).
fof(f107,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f34,f101,f90]) ).
fof(f108,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f32,f101,f95]) ).
fof(f109,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f30,f101,f66]) ).
fof(f111,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f113,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,plain,
( spl0_2
| spl0_12 ),
inference(avatar_split_clause,[],[f24,f111,f59]) ).
fof(f117,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f22,f111,f90]) ).
fof(f118,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f20,f111,f95]) ).
fof(f119,plain,
( spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f18,f111,f66]) ).
fof(f122,plain,
( spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f59]) ).
fof(f123,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f90]) ).
fof(f124,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f95]) ).
fof(f125,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f66]) ).
fof(f126,plain,
( sk_c6 = multiply(sk_c5,inverse(sk_c6))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f67,f60]) ).
fof(f127,plain,
( multiply(sk_c6,sk_c5) != inverse(sk_c6)
| ~ spl0_2
| spl0_6 ),
inference(forward_demodulation,[],[f76,f60]) ).
fof(f131,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f92]) ).
fof(f133,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f134,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f133,f4]) ).
fof(f139,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c5,X0)
| ~ spl0_10 ),
inference(superposition,[],[f4,f97]) ).
fof(f144,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f131]) ).
fof(f145,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f144,f1]) ).
fof(f148,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f145,f97]) ).
fof(f157,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_2
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f127,f148]) ).
fof(f158,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c5,sk_c5)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f139,f148]) ).
fof(f160,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f158,f97]) ).
fof(f176,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f134,f3]) ).
fof(f178,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f134,f134]) ).
fof(f184,plain,
( sk_c5 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f134,f160]) ).
fof(f198,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f184,f3]) ).
fof(f201,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f176,f178]) ).
fof(f209,plain,
( sk_c6 = multiply(identity,inverse(sk_c6))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f126,f198]) ).
fof(f210,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f209,f1]) ).
fof(f213,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f210,f157]) ).
fof(f214,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f213]) ).
fof(f215,plain,
( sk_c5 != multiply(inverse(sk_c6),sk_c6)
| ~ spl0_2
| spl0_5 ),
inference(forward_demodulation,[],[f72,f60]) ).
fof(f217,plain,
( identity != sk_c5
| ~ spl0_2
| spl0_5 ),
inference(forward_demodulation,[],[f215,f3]) ).
fof(f219,plain,
( $false
| ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f217,f198]) ).
fof(f220,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f221,plain,
( ! [X2] :
( sk_c5 != multiply(X2,inverse(sk_c6))
| sk_c4 != inverse(X2) )
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f57,f60]) ).
fof(f223,plain,
( ! [X2] :
( sk_c5 != multiply(X2,sk_c6)
| sk_c4 != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f221,f210]) ).
fof(f225,plain,
( ! [X2] :
( identity != multiply(X2,sk_c6)
| sk_c4 != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f223,f198]) ).
fof(f226,plain,
( ! [X2] :
( inverse(sk_c6) != inverse(X2)
| identity != multiply(X2,sk_c6) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f225,f60]) ).
fof(f227,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| identity != multiply(X2,sk_c6) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f226,f210]) ).
fof(f228,plain,
( sk_c6 != sk_c6
| identity != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f227,f92]) ).
fof(f230,plain,
( identity != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f228]) ).
fof(f232,plain,
( identity != sk_c5
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f230,f97]) ).
fof(f234,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f232,f198]) ).
fof(f235,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f237,plain,
( ! [X1] :
( identity != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f64,f198]) ).
fof(f256,plain,
( identity != sk_c5
| sk_c6 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f237,f97]) ).
fof(f258,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f256,f198]) ).
fof(f269,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f258,f92]) ).
fof(f270,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f278,plain,
( sk_c5 = multiply(multiply(sk_c6,sk_c5),sk_c6)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f71,f75]) ).
fof(f279,plain,
( sk_c5 = multiply(sk_c6,multiply(sk_c5,sk_c6))
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f278,f4]) ).
fof(f287,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_11 ),
inference(superposition,[],[f3,f103]) ).
fof(f303,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f134,f113]) ).
fof(f305,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f303,f103]) ).
fof(f306,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f134,f287]) ).
fof(f309,plain,
( inverse(sk_c6) = sk_c1
| ~ spl0_11 ),
inference(forward_demodulation,[],[f306,f201]) ).
fof(f310,plain,
( multiply(sk_c5,sk_c6) = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f134,f279]) ).
fof(f314,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f113,f309]) ).
fof(f316,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f314,f3]) ).
fof(f319,plain,
( identity = multiply(sk_c6,multiply(identity,sk_c6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f279,f316]) ).
fof(f320,plain,
( sk_c6 = multiply(identity,sk_c4)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f67,f316]) ).
fof(f321,plain,
( sk_c6 = sk_c4
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f320,f1]) ).
fof(f322,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f319,f1]) ).
fof(f327,plain,
( sk_c6 != inverse(sk_c6)
| spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f61,f321]) ).
fof(f332,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f64,f113]) ).
fof(f333,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f332]) ).
fof(f334,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f333,f103]) ).
fof(f335,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f382,plain,
( sk_c6 = multiply(inverse(sk_c6),identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f134,f322]) ).
fof(f385,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f382,f201]) ).
fof(f386,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f385,f327]) ).
fof(f387,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f388,plain,
( sk_c6 != multiply(sk_c5,multiply(sk_c6,sk_c5))
| spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f68,f75]) ).
fof(f392,plain,
( sk_c6 != multiply(sk_c5,sk_c6)
| spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f388,f305]) ).
fof(f394,plain,
( sk_c6 != multiply(inverse(sk_c6),sk_c5)
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f392,f310]) ).
fof(f395,plain,
( sk_c6 != multiply(inverse(sk_c6),identity)
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f394,f316]) ).
fof(f396,plain,
( sk_c6 != inverse(sk_c6)
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f395,f201]) ).
fof(f397,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f396,f385]) ).
fof(f398,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f399,plain,
( ! [X2] :
( sk_c5 != multiply(X2,multiply(sk_c6,sk_c5))
| sk_c4 != inverse(X2) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f57,f75]) ).
fof(f403,plain,
( ! [X2] :
( sk_c5 != multiply(X2,sk_c6)
| sk_c4 != inverse(X2) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f399,f305]) ).
fof(f405,plain,
( ! [X2] :
( identity != multiply(X2,sk_c6)
| sk_c4 != inverse(X2) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f403,f316]) ).
fof(f407,plain,
( ! [X2] :
( multiply(sk_c6,sk_c5) != inverse(X2)
| identity != multiply(X2,sk_c6) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f405,f75]) ).
fof(f408,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| identity != multiply(X2,sk_c6) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f407,f305]) ).
fof(f433,plain,
( sk_c6 != sk_c6
| identity != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f408,f103]) ).
fof(f434,plain,
( identity != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f433]) ).
fof(f437,plain,
( identity != sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f434,f113]) ).
fof(f443,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f437,f316]) ).
fof(f444,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f443]) ).
cnf(s1,plain,
( spl0_3
| ~ spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f88]) ).
cnf(s6,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f93]) ).
cnf(s7,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f98]) ).
cnf(s8,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f99]) ).
cnf(s11,plain,
( spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f107]) ).
cnf(s13,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f108]) ).
cnf(s14,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f109]) ).
cnf(s17,plain,
( spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f116]) ).
cnf(s18,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s19,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s20,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s23,plain,
( spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f122]) ).
cnf(s24,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f123]) ).
cnf(s25,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f124]) ).
cnf(s26,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s27,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f214]) ).
cnf(s28,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f220]) ).
cnf(s29,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f235]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f270]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f335]) ).
cnf(s36,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f387]) ).
cnf(s37,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f398]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f444]) ).
cnf(s43,plain,
( spl0_2
| ~ spl0_12
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11 ),
inference(rat,[],[s37,s36]) ).
cnf(s44,plain,
spl0_2,
inference(rat,[],[s43,s5,s11,s17,s23]) ).
cnf(s45,plain,
spl0_4,
inference(rat,[],[s37,s8,s14,s20,s26]) ).
cnf(s46,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s31,s18,s19]) ).
cnf(s47,plain,
( ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s31,s12,s13,s35]) ).
cnf(s48,plain,
~ spl0_3,
inference(rat,[],[s47,s46]) ).
cnf(s49,plain,
spl0_6,
inference(rat,[],[s27,s24,s25,s44,s45]) ).
cnf(s50,plain,
spl0_5,
inference(rat,[],[s28,s6,s7,s44]) ).
cnf(s51,plain,
spl0_1,
inference(rat,[],[s2,s45,s44,s49,s48,s50]) ).
cnf(s52,plain,
spl0_12,
inference(rat,[],[s29,s18,s19,s51,s44,s45]) ).
cnf(s53,plain,
~ spl0_11,
inference(rat,[],[s41,s49,s51,s52]) ).
cnf(s54,plain,
spl0_10,
inference(rat,[],[s13,s53]) ).
cnf(s55,plain,
spl0_9,
inference(rat,[],[s12,s53]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s29,s45,s44,s51,s54,s55]) ).
fof(f448,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP300-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:52:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (1414426)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (1414436)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=53176671:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (1414432)% WARNING: option uhcvi not known.
% 0.11/0.45 % (1414436) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1414426-1414436"...
% 0.11/0.45 % (1414431)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3207826548_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (1414436)...printing done.
% 0.11/0.45 % (1414432)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2981369812:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (1414433)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=34628743:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (1414434)dis+10_1_sil=32000:sp=arity:random_seed=2120232758:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (1414435)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1712113052:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (1414436)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (1414436)------------------------------
% 0.11/0.45 % (1414436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (1414436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (1414436)CaDiCaL version: 2.1.3
% 0.11/0.45 % (1414436)Termination reason: Refutation
% 0.11/0.45 % (1414436)Time elapsed: 0.006 s
% 0.11/0.45 % (1414436)Peak memory usage: 12 MB
% 0.11/0.45 % (1414436)Instructions burned: 15 (million)
% 0.11/0.45 % (1414426)Success in time 0.032 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------