%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP344-1 : 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 : n009.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 10:13:42 AM UTC 2026
% Result : Unsatisfiable 2.89s 1.28s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 33
% Syntax : Number of formulae : 210 ( 22 unt; 16 def)
% Number of atoms : 605 ( 185 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 780 ( 385 ~; 379 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 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 : 32 ( 0 sgn 32 !; 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(f5,negated_conjecture,
multiply(sk_c6,sk_c7) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f32]) ).
fof(f38,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c6
| inverse(X3) != sk_c5
| multiply(X3,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c5 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) ),
inference(reorient_equations,[],[f38]) ).
fof(f41,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f42,plain,
( ! [X3] :
( sk_c5 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f45,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,definition,
( spl0_3
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f48,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,definition,
( spl0_4
<=> ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f51,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_5
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f39,f53,f50,f47,f44,f41]) ).
fof(f58,definition,
( spl0_6
<=> sk_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f60,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f67,definition,
( spl0_8
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f69,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f72,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f74,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f33,f62,f72]) ).
fof(f77,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f31,f62,f77]) ).
fof(f82,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f84,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f87,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f25,f82,f72]) ).
fof(f88,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f23,f82,f77]) ).
fof(f90,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f21,f90,f58]) ).
fof(f94,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f19,f90,f67]) ).
fof(f95,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f17,f90,f72]) ).
fof(f96,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f15,f90,f77]) ).
fof(f98,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f13,f98,f58]) ).
fof(f102,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f11,f98,f67]) ).
fof(f103,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f9,f98,f72]) ).
fof(f104,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f7,f98,f77]) ).
fof(f105,plain,
spl0_5,
inference(avatar_split_clause,[],[f5,f53]) ).
fof(f107,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f45,f79]) ).
fof(f108,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f107]) ).
fof(f117,definition,
( spl0_15
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f118,plain,
( sk_c6 = sk_c5
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f121,plain,
( ~ spl0_9
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f108,f77,f44,f72]) ).
fof(f122,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f45,f92]) ).
fof(f123,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f122]) ).
fof(f124,plain,
( sk_c6 != sk_c7
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f123,f100]) ).
fof(f127,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f84]) ).
fof(f128,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f100]) ).
fof(f135,definition,
( spl0_17
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f136,plain,
( identity = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f141,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_5 ),
inference(superposition,[],[f4,f54]) ).
fof(f148,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f141,f1]) ).
fof(f153,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f127]) ).
fof(f154,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f153,f1]) ).
fof(f155,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f128]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c1,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f155,f1]) ).
fof(f171,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f154,f64]) ).
fof(f191,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f156,f92]) ).
fof(f205,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f142,f191]) ).
fof(f207,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f205,f171]) ).
fof(f263,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f148,f207]) ).
fof(f270,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f148,f60]) ).
fof(f283,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f263,f3]) ).
fof(f286,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f283,f98,f90,f82,f62,f53,f135]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_17 ),
inference(superposition,[],[f1,f136]) ).
fof(f289,plain,
( sk_c6 = sk_c7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f287,f191]) ).
fof(f294,plain,
( identity = sk_c1
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f128,f287]) ).
fof(f301,plain,
( sk_c7 = sk_c1
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f294,f136]) ).
fof(f305,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f289,f124]) ).
fof(f306,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f319,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f51,f100]) ).
fof(f328,definition,
( spl0_21
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f329,plain,
( sk_c6 = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f332,plain,
( sk_c5 != sk_c5
| sk_c5 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f42,f69]) ).
fof(f334,plain,
( sk_c7 != sk_c5
| sk_c5 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f42,f100]) ).
fof(f335,plain,
( sk_c5 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f332]) ).
fof(f336,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f335,f60]) ).
fof(f337,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f336]) ).
fof(f338,plain,
( spl0_21
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f289,f135,f98,f90,f328]) ).
fof(f340,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_13
| ~ spl0_21 ),
inference(superposition,[],[f128,f329]) ).
fof(f347,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f340,f301]) ).
fof(f349,plain,
( identity = sk_c5
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f347,f54]) ).
fof(f350,plain,
( sk_c7 = sk_c5
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f349,f136]) ).
fof(f354,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_demodulation,[],[f334,f329]) ).
fof(f355,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f350,f329]) ).
fof(f366,plain,
( sk_c7 != sk_c5
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_demodulation,[],[f354,f92]) ).
fof(f367,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f355,f328,f135,f98,f53,f117]) ).
fof(f368,plain,
( sk_c6 != sk_c5
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_demodulation,[],[f366,f329]) ).
fof(f369,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f368]) ).
fof(f370,plain,
( ~ spl0_15
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f369,f328,f98,f90,f41,f117]) ).
fof(f372,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f48,f84]) ).
fof(f373,plain,
( sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f372]) ).
fof(f384,plain,
( ~ spl0_7
| ~ spl0_3
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f373,f82,f47,f62]) ).
fof(f386,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f48,f69]) ).
fof(f389,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f48,f74]) ).
fof(f392,plain,
( sk_c6 != multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f389]) ).
fof(f455,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f148,f79]) ).
fof(f457,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f455,f74]) ).
fof(f459,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f54,f457]) ).
fof(f462,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f148,f457]) ).
fof(f464,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f462,f3]) ).
fof(f473,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f319]) ).
fof(f476,plain,
( ~ spl0_12
| ~ spl0_4
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f473,f98,f50,f90]) ).
fof(f477,plain,
( spl0_17
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f464,f77,f72,f135]) ).
fof(f478,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f459,f77,f72,f53,f117]) ).
fof(f483,plain,
( sk_c6 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f51,f74]) ).
fof(f486,plain,
( sk_c6 != sk_c7
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f483,f79]) ).
fof(f487,plain,
( ~ spl0_21
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f486,f77,f72,f50,f328]) ).
fof(f542,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f270,f118]) ).
fof(f543,plain,
( sk_c6 = multiply(sk_c5,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f542,f69]) ).
fof(f544,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f543,f118]) ).
fof(f547,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(superposition,[],[f148,f544]) ).
fof(f549,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f547,f3]) ).
fof(f556,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f136,f549]) ).
fof(f564,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f392,f118]) ).
fof(f565,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f386,f118]) ).
fof(f573,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f556,f135,f117,f67,f58,f328]) ).
fof(f574,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f564,f79]) ).
fof(f575,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f565,f118]) ).
fof(f578,plain,
( ~ spl0_21
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f574,f117,f77,f72,f47,f328]) ).
fof(f579,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f575,f60]) ).
fof(f580,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f579,f118]) ).
fof(f581,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f580]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f75]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f80]) ).
cnf(s8,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f87]) ).
cnf(s9,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f93]) ).
cnf(s11,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f94]) ).
cnf(s12,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f96]) ).
cnf(s14,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f101]) ).
cnf(s15,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f102]) ).
cnf(s16,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f103]) ).
cnf(s17,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f104]) ).
cnf(s18,plain,
spl0_5,
inference(sat_conversion,[],[f105]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f121]) ).
cnf(s26,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f286]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(sat_conversion,[],[f306]) ).
cnf(s31,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f337]) ).
cnf(s32,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f338]) ).
cnf(s38,plain,
( ~ spl0_5
| ~ spl0_13
| spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f367]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f370]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f384]) ).
cnf(s52,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f476]) ).
cnf(s54,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f477]) ).
cnf(s55,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f478]) ).
cnf(s59,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_21 ),
inference(sat_conversion,[],[f487]) ).
cnf(s62,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f573]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f578]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(sat_conversion,[],[f581]) ).
cnf(s68,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1,s18]) ).
cnf(s69,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s52,s10,s14]) ).
cnf(s70,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s62,s54,s55,s59,s15,s16,s17,s69,s18]) ).
cnf(s71,plain,
~ spl0_4,
inference(rat,[],[s62,s54,s55,s59,s11,s12,s13,s52,s70,s69,s18]) ).
cnf(s72,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s67,s55,s15,s16,s17,s18]) ).
cnf(s73,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s42,s5,s9]) ).
cnf(s74,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s42,s4,s8]) ).
cnf(s75,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s32,s11,s67,s72,s54,s65,s55,s73,s74,s18]) ).
cnf(s76,plain,
~ spl0_3,
inference(rat,[],[s32,s10,s14,s75,s65,s54,s55,s74,s73,s18]) ).
cnf(s77,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s26,s28,s5,s9,s13,s17,s18]) ).
cnf(s78,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s26,s28,s4,s8,s12,s16,s21,s18]) ).
cnf(s79,plain,
~ spl0_2,
inference(rat,[],[s78,s77]) ).
cnf(s80,plain,
spl0_1,
inference(rat,[],[s68,s76,s71,s79]) ).
cnf(s81,plain,
( ~ spl0_17
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s39,s38,s32,s18,s80]) ).
cnf(s82,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s81,s26,s18]) ).
cnf(s83,plain,
spl0_10,
inference(rat,[],[s82,s5,s9,s13,s17]) ).
cnf(s84,plain,
spl0_12,
inference(rat,[],[s31,s10,s11,s80]) ).
cnf(s85,plain,
spl0_13,
inference(rat,[],[s31,s14,s15,s80]) ).
cnf(s86,plain,
~ spl0_17,
inference(rat,[],[s81,s84,s85]) ).
cnf(s87,plain,
~ spl0_9,
inference(rat,[],[s54,s83,s86]) ).
cnf(s88,plain,
spl0_11,
inference(rat,[],[s8,s87]) ).
cnf(s89,plain,
spl0_7,
inference(rat,[],[s4,s87]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s82,s85,s84,s88,s89]) ).
fof(f582,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP344-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:54:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 2.89/1.28 % (1787300)Input is clausal, will run a generic CNF schedule.
% 2.89/1.28 % (1787309)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=612736211:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.89/1.28 % (1787309)Instruction limit reached!
% 2.89/1.28 % (1787309)------------------------------
% 2.89/1.28 % (1787309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (1787309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (1787309)CaDiCaL version: 2.1.3
% 2.89/1.28 % (1787309)Termination reason: Instruction limit
% 2.89/1.28 % (1787309)Termination phase: Saturation
% 2.89/1.28 % (1787309)Time elapsed: 0.037 s
% 2.89/1.28 % (1787309)Peak memory usage: 89 MB
% 2.89/1.28 % (1787309)Instructions burned: 117 (million)
% 2.89/1.28 % (1787308)lrs+10_1_sil=8000:sp=occurrence:random_seed=3200884467:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.89/1.28 % (1787305)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=860295473:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.89/1.28 % (1787310)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2409662462:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.89/1.28 % (1787311)dis-21_1_sil=8000:lcm=predicate:random_seed=3253534069: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)
% 2.89/1.28 % (1787307)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2010776169:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.89/1.28 % (1787306)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2018740637:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.89/1.28 % (1787311)Refutation not found, incomplete strategy
% 2.89/1.28 % (1787311)------------------------------
% 2.89/1.28 % (1787311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (1787311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (1787311)CaDiCaL version: 2.1.3
% 2.89/1.28 % (1787311)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.28 % (1787311)Time elapsed: 0.002 s
% 2.89/1.28 % (1787311)Peak memory usage: 88 MB
% 2.89/1.28 % (1787311)Instructions burned: 1 (million)
% 2.89/1.28 % (1787310)First to succeed.
% 2.89/1.28 % (1787310)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1787300"
% 2.89/1.28 % (1787308)Instruction limit reached!
% 2.89/1.28 % (1787308)------------------------------
% 2.89/1.28 % (1787308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (1787308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (1787308)CaDiCaL version: 2.1.3
% 2.89/1.28 % (1787308)Termination reason: Instruction limit
% 2.89/1.28 % (1787308)Termination phase: Saturation
% 2.89/1.28 % (1787308)Time elapsed: 0.053 s
% 2.89/1.28 % (1787308)Peak memory usage: 89 MB
% 2.89/1.28 % (1787308)Instructions burned: 109 (million)
% 2.89/1.28 % (1787319)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1941576825:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.89/1.28 % (1787319)Also succeeded, but the first one will report.
% 2.89/1.28 % (1787320)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=895403129:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.89/1.28 % (1787311)------------------------------
% 2.89/1.28 % (1787311)------------------------------
% 2.89/1.28 % (1787310)Refutation found. Thanks to Tanya!
% 2.89/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.89/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.48 % (1787310)------------------------------
% 3.74/1.48 % (1787310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.48 % (1787310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.48 % (1787310)CaDiCaL version: 2.1.3
% 3.74/1.48 % (1787310)Termination reason: Refutation
% 3.74/1.48 % (1787310)Time elapsed: 0.017 s
% 3.74/1.48 % (1787310)Peak memory usage: 89 MB
% 3.74/1.48 % (1787310)Instructions burned: 21 (million)
% 3.74/1.48 % (1787310)------------------------------
% 3.74/1.48 % (1787310)------------------------------
% 3.74/1.48 % (1787300)Success in time 0.452 s
% 3.74/1.48 % Vampire exiting
%------------------------------------------------------------------------------