%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n003.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 10:13:22 AM UTC 2026
% Result : Unsatisfiable 0.77s 0.92s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 35
% Syntax : Number of formulae : 201 ( 15 unt; 15 def)
% Number of atoms : 613 ( 188 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 786 ( 374 ~; 397 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',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(f42,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
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 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ 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(inverse(X1),sk_c7)
| sk_c6 != multiply(X1,inverse(X1)) )
| ~ 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(f65,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f43,f62,f58]) ).
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(f117,plain,
( ~ spl0_7
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f114,f77,f51,f72]) ).
fof(f130,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f69]) ).
fof(f131,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f84]) ).
fof(f133,plain,
( identity != sk_c6
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f52,f3]) ).
fof(f135,definition,
( spl0_15
<=> sk_c7 = inverse(inverse(sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f137,plain,
( sk_c7 != inverse(inverse(sk_c7))
| spl0_15 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl0_16
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f140,plain,
( identity = sk_c6
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f133,f51,f139,f135]) ).
fof(f145,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f150,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f64]) ).
fof(f152,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f145,f1]) ).
fof(f155,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f130]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f155,f1]) ).
fof(f157,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,multiply(sk_c2,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f131]) ).
fof(f158,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c2,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f157,f1]) ).
fof(f161,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f156,f60]) ).
fof(f181,plain,
( sk_c3 = multiply(sk_c3,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f158,f92]) ).
fof(f196,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c3,sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f150,f161]) ).
fof(f201,plain,
( sk_c3 = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f196,f181]) ).
fof(f246,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f152,f100]) ).
fof(f261,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f152,f64]) ).
fof(f262,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f152,f181]) ).
fof(f263,plain,
( sk_c2 = multiply(inverse(sk_c3),identity)
| ~ spl0_9 ),
inference(superposition,[],[f152,f131]) ).
fof(f268,plain,
( identity = sk_c6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f262,f3]) ).
fof(f275,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f246,f108]) ).
fof(f280,plain,
( spl0_16
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f268,f90,f82,f139]) ).
fof(f282,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_16 ),
inference(superposition,[],[f1,f140]) ).
fof(f292,plain,
( sk_c7 = sk_c3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f201,f282]) ).
fof(f295,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f92,f292]) ).
fof(f316,plain,
( sk_c2 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f263,f140]) ).
fof(f320,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f52,f295]) ).
fof(f323,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f320]) ).
fof(f326,plain,
( sk_c7 != sk_c3
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f323,f84]) ).
fof(f329,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f326,f292]) ).
fof(f330,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f332,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f150,f275]) ).
fof(f335,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f52,f275]) ).
fof(f338,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f335]) ).
fof(f341,plain,
( sk_c3 = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f332,f181]) ).
fof(f342,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f341,f282]) ).
fof(f373,plain,
( sk_c7 = sk_c2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f316,f261]) ).
fof(f378,plain,
( sk_c3 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_16 ),
inference(superposition,[],[f84,f373]) ).
fof(f379,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f378,f342]) ).
fof(f384,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f379,f338]) ).
fof(f385,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f391,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f137,f379]) ).
fof(f395,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f391,f379]) ).
fof(f396,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f395]) ).
fof(f400,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| sk_c6 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f55,f84]) ).
fof(f402,plain,
( identity != sk_c6
| sk_c6 != multiply(sk_c7,inverse(sk_c7))
| ~ spl0_3 ),
inference(superposition,[],[f55,f3]) ).
fof(f404,plain,
( sk_c6 != multiply(sk_c7,inverse(sk_c7))
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f402,f140]) ).
fof(f407,plain,
( sk_c6 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f400,f64]) ).
fof(f409,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f404,f379]) ).
fof(f410,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f407,f92]) ).
fof(f411,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f412,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f409,f275]) ).
fof(f413,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f412]) ).
fof(f419,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f49,f108]) ).
fof(f460,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| multiply(sk_c4,sk_c7) != sk_c6
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f55,f74]) ).
fof(f474,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f419]) ).
fof(f495,plain,
( ~ spl0_11
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f474,f106,f48,f98]) ).
fof(f506,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f49,f69]) ).
fof(f508,plain,
( sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f506]) ).
fof(f512,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f508,f60]) ).
fof(f513,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f519,definition,
( spl0_22
<=> sk_c6 = multiply(sk_c7,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f521,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| spl0_22 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f524,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f460,f79]) ).
fof(f530,plain,
( ~ spl0_22
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f524,f77,f72,f54,f519]) ).
fof(f547,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f161,f521]) ).
fof(f548,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f547]) ).
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(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f65]) ).
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(s24,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f117]) ).
cnf(s26,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f142]) ).
cnf(s30,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f280]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(sat_conversion,[],[f330]) ).
cnf(s34,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(sat_conversion,[],[f385]) ).
cnf(s35,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f396]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f411]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(sat_conversion,[],[f413]) ).
cnf(s47,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f495]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f513]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f530]) ).
cnf(s55,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_22 ),
inference(sat_conversion,[],[f548]) ).
cnf(s56,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s38,s30,s3,s7,s11,s15,s19]) ).
cnf(s57,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s55,s54,s12,s13,s14,s56]) ).
cnf(s58,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s55,s54,s8,s9,s10,s56]) ).
cnf(s59,plain,
~ spl0_3,
inference(rat,[],[s55,s54,s4,s5,s6,s37,s58,s57,s56]) ).
cnf(s60,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s24,s13,s14]) ).
cnf(s61,plain,
( ~ spl0_10
| ~ spl0_16
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(rat,[],[s35,s16,s20,s26,s32]) ).
cnf(s62,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_4
| ~ spl0_2 ),
inference(rat,[],[s61,s30,s60]) ).
cnf(s63,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s24,s9,s10]) ).
cnf(s64,plain,
( spl0_5
| ~ spl0_2 ),
inference(rat,[],[s24,s5,s6]) ).
cnf(s65,plain,
~ spl0_2,
inference(rat,[],[s34,s15,s19,s62,s64,s30,s63,s60]) ).
cnf(s66,plain,
spl0_1,
inference(rat,[],[s2,s59,s65]) ).
cnf(s67,plain,
spl0_6,
inference(rat,[],[s47,s16,s20,s66]) ).
cnf(s68,plain,
~ spl0_4,
inference(rat,[],[s50,s66,s67]) ).
cnf(s69,plain,
spl0_12,
inference(rat,[],[s19,s68]) ).
cnf(s70,plain,
spl0_11,
inference(rat,[],[s15,s68]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s47,s66,s69,s70]) ).
fof(f549,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n003.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:39:42 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.77/0.92 % (255718)Input is clausal, will run a generic CNF schedule.
% 0.77/0.92 % (255741)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2062983160:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.77/0.92 % (255741)First to succeed.
% 0.77/0.92 % (255741)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-255718"
% 0.77/0.92 % (255738)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3760163652:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.77/0.92 % (255740)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3087142111:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.77/0.92 % (255739)lrs+10_1_sil=8000:sp=occurrence:random_seed=1120637217:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.77/0.92 % (255737)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=276340705:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.77/0.92 % (255742)dis-21_1_sil=8000:lcm=predicate:random_seed=2478889155:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.77/0.92 % (255742)Refutation not found, incomplete strategy
% 0.77/0.92 % (255742)------------------------------
% 0.77/0.92 % (255742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.92 % (255742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.92 % (255742)CaDiCaL version: 2.1.3
% 0.77/0.92 % (255742)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.92 % (255742)Time elapsed: 0.002 s
% 0.77/0.92 % (255742)Peak memory usage: 88 MB
% 0.77/0.92 % (255742)Instructions burned: 1 (million)
% 0.77/0.92 % (255739)Instruction limit reached!
% 0.77/0.92 % (255739)------------------------------
% 0.77/0.92 % (255739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.92 % (255739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.92 % (255739)CaDiCaL version: 2.1.3
% 0.77/0.92 % (255739)Termination reason: Instruction limit
% 0.77/0.92 % (255739)Termination phase: Saturation
% 0.77/0.92 % (255739)Time elapsed: 0.052 s
% 0.77/0.92 % (255739)Peak memory usage: 89 MB
% 0.77/0.92 % (255739)Instructions burned: 108 (million)
% 0.77/0.92 % (255740)Instruction limit reached!
% 0.77/0.92 % (255740)------------------------------
% 0.77/0.92 % (255740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.92 % (255740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.92 % (255740)CaDiCaL version: 2.1.3
% 0.77/0.92 % (255740)Termination reason: Instruction limit
% 0.77/0.92 % (255740)Termination phase: Saturation
% 0.77/0.92 % (255740)Time elapsed: 0.064 s
% 0.77/0.92 % (255740)Peak memory usage: 89 MB
% 0.77/0.92 % (255740)Instructions burned: 114 (million)
% 0.77/0.92 % (255736)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=424683970:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.77/0.92 % (255741)Refutation found. Thanks to Tanya!
% 0.77/0.92 % SZS status Unsatisfiable for theBenchmark
% 0.77/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 0.77/1.02 % (255741)------------------------------
% 0.77/1.02 % (255741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/1.02 % (255741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/1.02 % (255741)CaDiCaL version: 2.1.3
% 0.77/1.02 % (255741)Termination reason: Refutation
% 0.77/1.02 % (255741)Time elapsed: 0.008 s
% 0.77/1.02 % (255741)Peak memory usage: 90 MB
% 0.77/1.02 % (255741)Instructions burned: 20 (million)
% 0.77/1.02 % (255741)------------------------------
% 0.77/1.02 % (255741)------------------------------
% 0.77/1.02 % (255718)Success in time 0.29 s
% 0.77/1.02 % Vampire exiting
%------------------------------------------------------------------------------