%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP285-1 : 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 : n019.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 10:13:32 AM UTC 2026
% Result : Unsatisfiable 2.97s 1.24s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 39
% Syntax : Number of formulae : 194 ( 17 unt; 16 def)
% Number of atoms : 496 ( 186 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 543 ( 241 ~; 286 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/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_c9,sk_c8) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f45]) ).
fof(f61,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X1,sk_c9) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c7
| multiply(sk_c9,X4) != sk_c7
| multiply(X5,sk_c9) != X4
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c9)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c9)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f62]) ).
fof(f65,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f66,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(sk_c9,multiply(X5,sk_c9)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_3
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f72,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_4
<=> ! [X1] : sk_c7 != multiply(X1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f75,plain,
( ! [X1] : sk_c7 != multiply(X1,sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl0_5
<=> multiply(sk_c9,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f78,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| spl0_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f63,f77,f71,f74,f71,f68,f65]) ).
fof(f82,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f84,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f91,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f93,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f96,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c9,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f98,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f101,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f108,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f111,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f113,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f118,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f121,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f123,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f121,f82]) ).
fof(f125,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f121,f91]) ).
fof(f126,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f121,f96]) ).
fof(f127,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f121,f101]) ).
fof(f128,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f121,f106]) ).
fof(f129,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f121,f111]) ).
fof(f130,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f121,f116]) ).
fof(f132,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f134,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f132,f82]) ).
fof(f136,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f132,f91]) ).
fof(f137,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f132,f96]) ).
fof(f138,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f132,f101]) ).
fof(f139,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f132,f106]) ).
fof(f140,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f132,f111]) ).
fof(f141,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f132,f116]) ).
fof(f142,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f77,f82]) ).
fof(f143,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f77,f91]) ).
fof(f144,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f77,f96]) ).
fof(f147,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f77,f111]) ).
fof(f148,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f77,f116]) ).
fof(f149,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f84]) ).
fof(f154,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f156,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f149]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f156,f1]) ).
fof(f161,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f154,f1]) ).
fof(f168,plain,
( sk_c9 = multiply(sk_c9,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f160,f93]) ).
fof(f174,plain,
( sk_c9 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f168,f98]) ).
fof(f235,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f161,f118]) ).
fof(f250,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f235,f113]) ).
fof(f262,plain,
( sk_c9 != sk_c7
| spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f79,f250]) ).
fof(f271,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f262,f174]) ).
fof(f272,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f276,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f72,f113]) ).
fof(f277,plain,
( sk_c8 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f276]) ).
fof(f279,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f277,f118]) ).
fof(f280,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f284,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f72,f123]) ).
fof(f287,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f284]) ).
fof(f289,plain,
( ~ spl0_15
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f287,f121,f71,f132]) ).
fof(f291,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f161,f134]) ).
fof(f293,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f291,f123]) ).
fof(f323,plain,
( sk_c9 != sk_c9
| sk_c7 != multiply(sk_c9,multiply(sk_c5,sk_c9))
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f66,f84]) ).
fof(f325,plain,
( sk_c9 != sk_c9
| sk_c7 != multiply(sk_c9,multiply(sk_c1,sk_c9))
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f66,f123]) ).
fof(f326,plain,
( sk_c7 != multiply(sk_c9,multiply(sk_c1,sk_c9))
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f325]) ).
fof(f327,plain,
( sk_c7 != multiply(sk_c9,multiply(sk_c5,sk_c9))
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f323]) ).
fof(f328,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f326,f134]) ).
fof(f334,definition,
( spl0_17
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f335,plain,
( sk_c9 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f338,plain,
( sk_c9 != sk_c7
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f327,f160]) ).
fof(f339,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f328,f78]) ).
fof(f340,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f341,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f338,f82,f65,f334]) ).
fof(f347,plain,
( sk_c7 != sk_c7
| sk_c8 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f69,f103]) ).
fof(f348,plain,
( sk_c9 != sk_c7
| sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f69,f123]) ).
fof(f349,plain,
( sk_c8 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f347]) ).
fof(f351,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f353,plain,
( sk_c8 != multiply(sk_c1,sk_c7)
| spl0_18 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f354,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f348,f121,f68,f334,f351]) ).
fof(f355,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f349,f108]) ).
fof(f356,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f363,plain,
( sk_c9 = sk_c7
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f78,f293]) ).
fof(f373,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f363,f132,f121,f77,f334]) ).
fof(f376,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_17
| spl0_18 ),
inference(forward_demodulation,[],[f353,f335]) ).
fof(f377,plain,
( $false
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f376,f134]) ).
fof(f378,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f379,plain,
( ! [X1] : sk_c9 != multiply(X1,sk_c9)
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f75,f335]) ).
fof(f381,plain,
( sk_c9 != sk_c9
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f379,f1]) ).
fof(f387,plain,
( $false
| ~ spl0_4
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f381]) ).
fof(f388,plain,
( ~ spl0_4
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f392,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f174,f96,f91,f82,f334]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s10,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s15,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s16,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s17,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f137]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f138]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s22,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f140]) ).
cnf(s23,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f141]) ).
cnf(s24,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f142]) ).
cnf(s25,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f143]) ).
cnf(s26,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f144]) ).
cnf(s29,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f147]) ).
cnf(s30,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s31,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f272]) ).
cnf(s32,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f280]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f289]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f340]) ).
cnf(s38,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_17 ),
inference(sat_conversion,[],[f341]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f354]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f356]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f373]) ).
cnf(s46,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f378]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_17 ),
inference(sat_conversion,[],[f388]) ).
cnf(s49,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f392]) ).
cnf(s50,plain,
spl0_5,
inference(rat,[],[s31,s24,s25,s26,s29,s30]) ).
cnf(s52,plain,
( spl0_9
| spl0_17 ),
inference(rat,[],[s44,s12,s19,s50]) ).
cnf(s53,plain,
( spl0_8
| spl0_17 ),
inference(rat,[],[s44,s11,s18,s50]) ).
cnf(s54,plain,
( ~ spl0_8
| spl0_17
| ~ spl0_9 ),
inference(rat,[],[s44,s10,s17,s49,s50]) ).
cnf(s55,plain,
spl0_17,
inference(rat,[],[s54,s53,s52]) ).
cnf(s56,plain,
~ spl0_4,
inference(rat,[],[s47,s55]) ).
cnf(s58,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s32,s22,s23]) ).
cnf(s59,plain,
( ~ spl0_15
| ~ spl0_3 ),
inference(rat,[],[s32,s15,s16,s33]) ).
cnf(s60,plain,
~ spl0_3,
inference(rat,[],[s59,s58]) ).
cnf(s61,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s40,s20,s21]) ).
cnf(s62,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s40,s13,s14,s39,s55]) ).
cnf(s63,plain,
~ spl0_2,
inference(rat,[],[s62,s46,s61,s55]) ).
cnf(s64,plain,
spl0_1,
inference(rat,[],[s2,s56,s60,s50,s63]) ).
cnf(s65,plain,
~ spl0_6,
inference(rat,[],[s38,s55,s64]) ).
cnf(s66,plain,
spl0_15,
inference(rat,[],[s17,s65]) ).
cnf(s67,plain,
spl0_14,
inference(rat,[],[s10,s65]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s37,s64,s50,s66,s67]) ).
fof(f393,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP285-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 09:44:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 2.97/1.24 % (2844003)Input is clausal, will run a generic CNF schedule.
% 2.97/1.24 % (2844012)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=666177253:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.97/1.24 % (2844012)Instruction limit reached!
% 2.97/1.24 % (2844012)------------------------------
% 2.97/1.24 % (2844012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.24 % (2844012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.24 % (2844012)CaDiCaL version: 2.1.3
% 2.97/1.24 % (2844012)Termination reason: Instruction limit
% 2.97/1.24 % (2844012)Termination phase: Saturation
% 2.97/1.24 % (2844012)Time elapsed: 0.036 s
% 2.97/1.24 % (2844012)Peak memory usage: 89 MB
% 2.97/1.24 % (2844012)Instructions burned: 116 (million)
% 2.97/1.24 % (2844011)lrs+10_1_sil=8000:sp=occurrence:random_seed=2868264381:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.97/1.24 % (2844014)dis-21_1_sil=8000:lcm=predicate:random_seed=1836426744: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)
% 2.97/1.24 % (2844008)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=3226041672:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.97/1.24 % (2844009)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1252060033:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.97/1.24 % (2844013)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=700534059:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.97/1.24 % (2844010)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=284184843:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.97/1.24 % (2844014)Refutation not found, incomplete strategy
% 2.97/1.24 % (2844014)------------------------------
% 2.97/1.24 % (2844014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.24 % (2844014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.24 % (2844014)CaDiCaL version: 2.1.3
% 2.97/1.24 % (2844014)Termination reason: Refutation not found, incomplete strategy
% 2.97/1.24 % (2844014)Time elapsed: 0.002 s
% 2.97/1.24 % (2844014)Peak memory usage: 88 MB
% 2.97/1.24 % (2844014)Instructions burned: 1 (million)
% 2.97/1.24 % (2844011)Refutation not found, incomplete strategy
% 2.97/1.24 % (2844011)------------------------------
% 2.97/1.24 % (2844011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.24 % (2844011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.24 % (2844011)CaDiCaL version: 2.1.3
% 2.97/1.24 % (2844011)Termination reason: Refutation not found, incomplete strategy
% 2.97/1.24 % (2844011)Time elapsed: 0.003 s
% 2.97/1.24 % (2844011)Peak memory usage: 88 MB
% 2.97/1.24 % (2844011)Instructions burned: 4 (million)
% 2.97/1.24 % (2844013)First to succeed.
% 2.97/1.24 % (2844013)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2844003"
% 2.97/1.24 % (2844022)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=2290755796:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.97/1.24 % (2844022)Refutation not found, incomplete strategy
% 2.97/1.24 % (2844022)------------------------------
% 2.97/1.24 % (2844022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.24 % (2844022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.24 % (2844022)CaDiCaL version: 2.1.3
% 2.97/1.24 % (2844022)Termination reason: Refutation not found, incomplete strategy
% 2.97/1.24 % (2844022)Time elapsed: 0.002 s
% 2.97/1.24 % (2844022)Peak memory usage: 88 MB
% 2.97/1.24 % (2844022)Instructions burned: 4 (million)
% 2.97/1.24 % (2844011)------------------------------
% 2.97/1.24 % (2844011)------------------------------
% 2.97/1.24 % (2844014)------------------------------
% 2.97/1.24 % (2844014)------------------------------
% 2.97/1.24 % (2844022)------------------------------
% 2.97/1.24 % (2844022)------------------------------
% 2.97/1.24 % (2844013)Refutation found. Thanks to Tanya!
% 2.97/1.24 % SZS status Unsatisfiable for theBenchmark
% 2.97/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.42 % (2844013)------------------------------
% 3.46/1.42 % (2844013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.42 % (2844013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.42 % (2844013)CaDiCaL version: 2.1.3
% 3.46/1.42 % (2844013)Termination reason: Refutation
% 3.46/1.42 % (2844013)Time elapsed: 0.010 s
% 3.46/1.42 % (2844013)Peak memory usage: 89 MB
% 3.46/1.42 % (2844013)Instructions burned: 15 (million)
% 3.46/1.42 % (2844013)------------------------------
% 3.46/1.42 % (2844013)------------------------------
% 3.46/1.42 % (2844003)Success in time 0.407 s
% 3.46/1.42 % Vampire exiting
%------------------------------------------------------------------------------