%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP215-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:13:21 AM UTC 2026
% Result : Unsatisfiable 1.87s 1.67s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 39
% Syntax : Number of formulae : 212 ( 19 unt; 15 def)
% Number of atoms : 544 ( 194 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 617 ( 285 ~; 317 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 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 : 34 ( 0 sgn 34 !; 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_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(sk_c7,X3) != sk_c6
| multiply(X4,sk_c7) != X3
| inverse(X4) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(sk_c7,X3)
| multiply(X4,sk_c7) != X3
| sk_c7 != inverse(X4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) ),
inference(equality_resolution,[],[f46]) ).
fof(f49,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f53,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,definition,
( spl0_3
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,definition,
( spl0_4
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f59,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f47,f58,f55,f52,f49]) ).
fof(f62,definition,
( spl0_5
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f66,definition,
( spl0_6
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f68,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f44,f66,f62]) ).
fof(f71,definition,
( spl0_7
<=> sk_c5 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f73,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f42,f66,f71]) ).
fof(f76,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f40,f66,f76]) ).
fof(f81,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f83,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f38,f66,f81]) ).
fof(f86,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f88,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f36,f66,f86]) ).
fof(f91,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_5
| spl0_11 ),
inference(avatar_split_clause,[],[f34,f91,f62]) ).
fof(f95,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f32,f91,f71]) ).
fof(f96,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f30,f91,f76]) ).
fof(f97,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f28,f91,f81]) ).
fof(f98,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f26,f91,f86]) ).
fof(f100,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f24,f100,f62]) ).
fof(f104,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f22,f100,f71]) ).
fof(f105,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f20,f100,f76]) ).
fof(f106,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f18,f100,f81]) ).
fof(f107,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f16,f100,f86]) ).
fof(f109,definition,
( spl0_13
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f14,f109,f62]) ).
fof(f113,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f12,f109,f71]) ).
fof(f114,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f10,f109,f76]) ).
fof(f115,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f8,f109,f81]) ).
fof(f116,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f6,f109,f86]) ).
fof(f117,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f53,f83]) ).
fof(f118,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f117]) ).
fof(f119,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f118,f88]) ).
fof(f120,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f121,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f53,f93]) ).
fof(f122,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f123,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f122,f68]) ).
fof(f125,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_12 ),
inference(superposition,[],[f3,f102]) ).
fof(f135,definition,
( spl0_15
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f136,plain,
( identity = sk_c7
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f141,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f144,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f125]) ).
fof(f148,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c1,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f144,f1]) ).
fof(f149,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f141,f1]) ).
fof(f158,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f148,f111]) ).
fof(f252,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f149,f158]) ).
fof(f259,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f149,f73]) ).
fof(f261,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f149,f93]) ).
fof(f267,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f261,f68]) ).
fof(f269,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f259,f64]) ).
fof(f272,plain,
( identity = sk_c6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f252,f3]) ).
fof(f278,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f149,f267]) ).
fof(f280,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f278,f3]) ).
fof(f284,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f280,f91,f66,f135]) ).
fof(f285,plain,
( sk_c7 = sk_c6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f136,f272]) ).
fof(f290,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f285,f123]) ).
fof(f291,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f292,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c7,multiply(sk_c1,sk_c7))
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f50,f102]) ).
fof(f294,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c7,multiply(sk_c4,sk_c7))
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f50,f64]) ).
fof(f296,plain,
( sk_c6 != multiply(sk_c7,multiply(sk_c4,sk_c7))
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f294]) ).
fof(f298,plain,
( sk_c6 != multiply(sk_c7,multiply(sk_c1,sk_c7))
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f292]) ).
fof(f304,definition,
( spl0_20
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f305,plain,
( sk_c7 = sk_c6
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f306,plain,
( sk_c7 != sk_c6
| spl0_20 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f308,plain,
( sk_c6 != multiply(sk_c7,sk_c5)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f296,f73]) ).
fof(f309,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_12 ),
inference(forward_demodulation,[],[f298,f148]) ).
fof(f310,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f308,f78]) ).
fof(f311,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f312,plain,
( ~ spl0_20
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f309,f100,f49,f304]) ).
fof(f313,plain,
( sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f59,f102]) ).
fof(f314,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f59,f88]) ).
fof(f318,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f314]) ).
fof(f319,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f313]) ).
fof(f326,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f319,f111]) ).
fof(f327,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f329,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f56,f88]) ).
fof(f331,plain,
( sk_c6 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f56,f68]) ).
fof(f332,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f331]) ).
fof(f333,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f332,f93]) ).
fof(f334,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f349,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f285,f306]) ).
fof(f350,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f396,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f78,f269]) ).
fof(f404,plain,
( spl0_20
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f396,f76,f71,f62,f304]) ).
fof(f407,plain,
( sk_c7 = multiply(sk_c3,sk_c7)
| ~ spl0_9
| ~ spl0_20 ),
inference(superposition,[],[f83,f305]) ).
fof(f420,plain,
( sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f318,f407]) ).
fof(f424,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f420,f305]) ).
fof(f425,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f427,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f329,f305]) ).
fof(f434,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f427,f83]) ).
fof(f435,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f434]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s2,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f74]) ).
cnf(s4,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s6,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f89]) ).
cnf(s7,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f94]) ).
cnf(s8,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f95]) ).
cnf(s9,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f96]) ).
cnf(s10,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f97]) ).
cnf(s11,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s12,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f103]) ).
cnf(s13,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s14,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s15,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s16,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s17,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s18,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s19,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s20,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s21,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s22,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s28,plain,
( ~ spl0_6
| ~ spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f284]) ).
cnf(s30,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f291]) ).
cnf(s32,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f311]) ).
cnf(s33,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_20 ),
inference(sat_conversion,[],[f312]) ).
cnf(s35,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f327]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(sat_conversion,[],[f334]) ).
cnf(s42,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f350]) ).
cnf(s45,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_20 ),
inference(sat_conversion,[],[f404]) ).
cnf(s49,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(sat_conversion,[],[f425]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20 ),
inference(sat_conversion,[],[f435]) ).
cnf(s53,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s35,s12,s17]) ).
cnf(s54,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s45,s49,s18,s19,s20,s21,s53]) ).
cnf(s55,plain,
~ spl0_4,
inference(rat,[],[s45,s49,s13,s14,s15,s16,s35,s54,s53]) ).
cnf(s57,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s36,s6,s11]) ).
cnf(s58,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s36,s5,s10]) ).
cnf(s59,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s36,s4,s9]) ).
cnf(s60,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s36,s3,s8]) ).
cnf(s61,plain,
( ~ spl0_9
| ~ spl0_3
| ~ spl0_10 ),
inference(rat,[],[s36,s2,s7,s45,s60,s59,s50]) ).
cnf(s62,plain,
~ spl0_3,
inference(rat,[],[s61,s58,s57]) ).
cnf(s63,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s30,s28,s6,s11,s16,s21]) ).
cnf(s64,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s30,s28,s5,s10,s15,s20,s22]) ).
cnf(s65,plain,
~ spl0_2,
inference(rat,[],[s64,s63]) ).
cnf(s66,plain,
spl0_1,
inference(rat,[],[s1,s55,s62,s65]) ).
cnf(s68,plain,
( spl0_8
| ~ spl0_15 ),
inference(rat,[],[s42,s33,s14,s19,s66]) ).
cnf(s69,plain,
( ~ spl0_15
| ~ spl0_5 ),
inference(rat,[],[s42,s33,s13,s18,s32,s68,s66]) ).
cnf(s70,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s32,s8,s9,s66]) ).
cnf(s71,plain,
~ spl0_5,
inference(rat,[],[s32,s3,s4,s28,s70,s69,s66]) ).
cnf(s72,plain,
spl0_13,
inference(rat,[],[s17,s71]) ).
cnf(s73,plain,
spl0_12,
inference(rat,[],[s12,s71]) ).
cnf(s74,plain,
spl0_11,
inference(rat,[],[s7,s71]) ).
cnf(s75,plain,
spl0_6,
inference(rat,[],[s2,s71]) ).
cnf(s76,plain,
~ spl0_20,
inference(rat,[],[s33,s66,s73]) ).
cnf(s77,plain,
spl0_15,
inference(rat,[],[s28,s74,s75]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s42,s72,s73,s77,s76]) ).
fof(f441,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP215-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.42 % Computer : n026.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sun Sep 27 09:40:11 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.48 Running first-order theorem proving
% 0.24/0.48 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
% 1.87/1.67 % (2581490)Input is clausal, will run a generic CNF schedule.
% 1.87/1.67 % (2581505)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3831813524:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.87/1.67 % (2581501)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=70483085:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.87/1.67 % (2581507)dis-21_1_sil=8000:lcm=predicate:random_seed=4232898921: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)
% 1.87/1.67 % (2581507)Refutation not found, incomplete strategy
% 1.87/1.67 % (2581507)------------------------------
% 1.87/1.67 % (2581507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.67 % (2581507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.67 % (2581507)CaDiCaL version: 2.1.3
% 1.87/1.67 % (2581507)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.67 % (2581507)Time elapsed: 0.002 s
% 1.87/1.67 % (2581507)Peak memory usage: 88 MB
% 1.87/1.67 % (2581507)Instructions burned: 1 (million)
% 1.87/1.67 % (2581505)Instruction limit reached!
% 1.87/1.67 % (2581505)------------------------------
% 1.87/1.67 % (2581505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.67 % (2581502)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=585703062:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.87/1.67 % (2581505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.67 % (2581503)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=617221780:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.87/1.67 % (2581505)CaDiCaL version: 2.1.3
% 1.87/1.67 % (2581505)Termination reason: Instruction limit
% 1.87/1.67 % (2581505)Termination phase: Saturation
% 1.87/1.67 % (2581505)Time elapsed: 0.058 s
% 1.87/1.67 % (2581505)Peak memory usage: 89 MB
% 1.87/1.67 % (2581505)Instructions burned: 115 (million)
% 1.87/1.67 % (2581504)lrs+10_1_sil=8000:sp=occurrence:random_seed=1459839545:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.87/1.67 % (2581506)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=200405084:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.87/1.67 % (2581506)First to succeed.
% 1.87/1.67 % (2581506)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2581490"
% 1.87/1.67 % (2581504)Instruction limit reached!
% 1.87/1.67 % (2581504)------------------------------
% 1.87/1.67 % (2581504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.67 % (2581504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.67 % (2581504)CaDiCaL version: 2.1.3
% 1.87/1.67 % (2581504)Termination reason: Instruction limit
% 1.87/1.67 % (2581504)Termination phase: Saturation
% 1.87/1.67 % (2581504)Time elapsed: 0.098 s
% 1.87/1.67 % (2581504)Peak memory usage: 89 MB
% 1.87/1.67 % (2581504)Instructions burned: 107 (million)
% 1.87/1.67 % (2581515)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=1986664808:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.87/1.67 % (2581515)Also succeeded, but the first one will report.
% 1.87/1.67 % (2581520)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1575038874:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 1.87/1.67 % (2581507)------------------------------
% 1.87/1.67 % (2581507)------------------------------
% 1.87/1.67 % (2581506)Refutation found. Thanks to Tanya!
% 1.87/1.67 % SZS status Unsatisfiable for theBenchmark
% 1.87/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 5.58/2.01 % (2581506)------------------------------
% 5.58/2.01 % (2581506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.58/2.01 % (2581506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/2.01 % (2581506)CaDiCaL version: 2.1.3
% 5.58/2.01 % (2581506)Termination reason: Refutation
% 5.58/2.01 % (2581506)Time elapsed: 0.019 s
% 5.58/2.01 % (2581506)Peak memory usage: 89 MB
% 5.58/2.01 % (2581506)Instructions burned: 16 (million)
% 5.58/2.01 % (2581506)------------------------------
% 5.58/2.01 % (2581506)------------------------------
% 5.58/2.01 % (2581490)Success in time 0.663 s
% 5.58/2.01 % Vampire exiting
%------------------------------------------------------------------------------