%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP250-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 10:13:26 AM UTC 2026
% Result : Unsatisfiable 1.88s 1.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 37
% Syntax : Number of formulae : 201 ( 16 unt; 17 def)
% Number of atoms : 532 ( 186 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 621 ( 290 ~; 314 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = inverse(sk_c2)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f50]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(X5) != sk_c7
| multiply(X5,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != inverse(X5)
| sk_c7 != multiply(X5,sk_c8) ),
inference(reorient_equations,[],[f76]) ).
fof(f79,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != inverse(X5)
| sk_c7 != multiply(X5,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f80,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c8)
| sk_c7 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_2
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f83,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_3
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_4
<=> ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f89,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f77,f85,f82,f88,f85,f82,f79]) ).
fof(f92,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f101,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f111,definition,
( spl0_9
<=> multiply(sk_c5,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f113,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f118,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f121,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f123,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f136,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f138,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f51,f136,f92]) ).
fof(f140,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f49,f136,f101]) ).
fof(f141,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f47,f136,f106]) ).
fof(f142,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f45,f136,f111]) ).
fof(f143,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f43,f136,f116]) ).
fof(f144,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f41,f136,f121]) ).
fof(f146,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f148,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f146,f92]) ).
fof(f150,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f146,f101]) ).
fof(f151,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f146,f106]) ).
fof(f152,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f146,f111]) ).
fof(f153,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f31,f146,f116]) ).
fof(f154,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f29,f146,f121]) ).
fof(f156,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f158,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f163,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f156,f116]) ).
fof(f164,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f17,f156,f121]) ).
fof(f166,definition,
( spl0_16
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f168,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f173,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f8,f166,f116]) ).
fof(f174,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f6,f166,f121]) ).
fof(f176,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f83,f113]) ).
fof(f177,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f176]) ).
fof(f182,plain,
( ~ spl0_8
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f177,f111,f82,f106]) ).
fof(f183,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f83,f148]) ).
fof(f184,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f183]) ).
fof(f185,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f184,f138]) ).
fof(f186,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f187,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f80,f94]) ).
fof(f189,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f80,f148]) ).
fof(f190,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f189]) ).
fof(f192,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f187]) ).
fof(f193,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f190,f138]) ).
fof(f194,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f192,f103]) ).
fof(f195,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f197,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f158]) ).
fof(f208,definition,
( spl0_18
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f209,plain,
( identity = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f213,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f222,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f213,f1]) ).
fof(f224,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f197]) ).
fof(f225,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c1,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f224,f1]) ).
fof(f234,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f225,f168]) ).
fof(f336,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_11 ),
inference(superposition,[],[f222,f123]) ).
fof(f338,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f222,f234]) ).
fof(f340,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f222,f113]) ).
fof(f342,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f222,f148]) ).
fof(f352,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f342,f138]) ).
fof(f355,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f338,f3]) ).
fof(f357,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f336,f118]) ).
fof(f386,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f86,f168]) ).
fof(f447,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f222,f352]) ).
fof(f449,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f447,f3]) ).
fof(f461,plain,
( sk_c8 = sk_c7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f449,f355]) ).
fof(f464,definition,
( spl0_24
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f465,plain,
( sk_c8 = sk_c7
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f466,plain,
( sk_c8 != sk_c7
| spl0_24 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f470,plain,
( spl0_24
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f461,f166,f156,f146,f136,f464]) ).
fof(f471,plain,
( ~ spl0_24
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f193,f146,f136,f79,f464]) ).
fof(f472,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f386]) ).
fof(f473,plain,
( ~ spl0_15
| ~ spl0_3
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f472,f166,f85,f156]) ).
fof(f484,definition,
( spl0_27
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f485,plain,
( identity = sk_c8
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f488,plain,
( spl0_18
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f449,f146,f136,f208]) ).
fof(f501,plain,
( sk_c8 = sk_c7
| ~ spl0_18
| ~ spl0_27 ),
inference(superposition,[],[f209,f485]) ).
fof(f503,plain,
( spl0_24
| ~ spl0_18
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f501,f484,f208,f464]) ).
fof(f505,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f86,f123]) ).
fof(f509,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f505]) ).
fof(f512,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f509,f118]) ).
fof(f513,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f528,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_4
| ~ spl0_24 ),
inference(forward_demodulation,[],[f89,f465]) ).
fof(f530,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24 ),
inference(superposition,[],[f528,f108]) ).
fof(f532,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_24 ),
inference(superposition,[],[f528,f138]) ).
fof(f535,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f532]) ).
fof(f536,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f530]) ).
fof(f537,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_demodulation,[],[f535,f148]) ).
fof(f539,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[],[f536,f113]) ).
fof(f540,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f537,f465]) ).
fof(f541,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f543,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f539,f465]) ).
fof(f544,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f578,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f222,f357]) ).
fof(f580,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f578,f3]) ).
fof(f582,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f580,f121,f116,f484]) ).
fof(f587,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_27 ),
inference(superposition,[],[f1,f485]) ).
fof(f676,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f340,f108]) ).
fof(f677,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_27 ),
inference(forward_demodulation,[],[f676,f587]) ).
fof(f678,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| spl0_24
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f677,f466]) ).
fof(f679,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_24
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f678]) ).
cnf(s1,plain,
( spl0_2
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s15,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s16,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s17,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f141]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s20,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s21,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s23,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s24,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s25,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s26,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s31,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s32,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s37,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s38,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f182]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f186]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f195]) ).
cnf(s53,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_24 ),
inference(sat_conversion,[],[f470]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(sat_conversion,[],[f471]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f473]) ).
cnf(s59,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f488]) ).
cnf(s61,plain,
( ~ spl0_18
| spl0_24
| ~ spl0_27 ),
inference(sat_conversion,[],[f503]) ).
cnf(s63,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f513]) ).
cnf(s66,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(sat_conversion,[],[f541]) ).
cnf(s67,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(sat_conversion,[],[f544]) ).
cnf(s72,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_27 ),
inference(sat_conversion,[],[f582]) ).
cnf(s76,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_24
| ~ spl0_27 ),
inference(sat_conversion,[],[f679]) ).
cnf(s78,plain,
( spl0_16
| spl0_27 ),
inference(rat,[],[s72,s37,s38]) ).
cnf(s79,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s72,s31,s32,s53,s78,s61,s66,s59]) ).
cnf(s80,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s67,s76,s72,s23,s24,s25,s26]) ).
cnf(s81,plain,
( ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s67,s76,s72,s17,s18,s19,s20,s79]) ).
cnf(s82,plain,
~ spl0_4,
inference(rat,[],[s81,s80]) ).
cnf(s83,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s63,s31,s32]) ).
cnf(s84,plain,
( ~ spl0_15
| ~ spl0_3 ),
inference(rat,[],[s63,s37,s38,s55]) ).
cnf(s85,plain,
~ spl0_3,
inference(rat,[],[s84,s83]) ).
cnf(s86,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s40,s23,s24]) ).
cnf(s87,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s40,s17,s18,s41]) ).
cnf(s88,plain,
~ spl0_2,
inference(rat,[],[s87,s86]) ).
cnf(s89,plain,
spl0_1,
inference(rat,[],[s2,s82,s85,s88]) ).
cnf(s90,plain,
( ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s72,s31,s32,s53,s78,s61,s54,s59,s89]) ).
cnf(s91,plain,
spl0_14,
inference(rat,[],[s42,s21,s22,s89]) ).
cnf(s92,plain,
~ spl0_13,
inference(rat,[],[s90,s91]) ).
cnf(s97,plain,
spl0_7,
inference(rat,[],[s16,s92]) ).
cnf(s98,plain,
spl0_5,
inference(rat,[],[s15,s92]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s42,s89,s97,s98]) ).
fof(f680,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP250-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:45:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.88/1.30 % (2085574)Input is clausal, will run a generic CNF schedule.
% 1.88/1.30 % (2085581)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=652467698:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.88/1.30 % (2085579)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=93511596:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.88/1.30 % (2085583)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=560812644:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.88/1.30 % (2085584)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3769745080:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.88/1.30 % (2085580)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=366060481:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.88/1.30 % (2085582)lrs+10_1_sil=8000:sp=occurrence:random_seed=1261933504:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.88/1.30 % (2085584)First to succeed.
% 1.88/1.30 % (2085584)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2085574"
% 1.88/1.30 % (2085585)dis-21_1_sil=8000:lcm=predicate:random_seed=547795661: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)
% 1.88/1.30 % (2085585)Refutation not found, incomplete strategy
% 1.88/1.30 % (2085585)------------------------------
% 1.88/1.30 % (2085585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.30 % (2085585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.30 % (2085585)CaDiCaL version: 2.1.3
% 1.88/1.30 % (2085585)Termination reason: Refutation not found, incomplete strategy
% 1.88/1.30 % (2085585)Time elapsed: 0.002 s
% 1.88/1.30 % (2085585)Peak memory usage: 88 MB
% 1.88/1.30 % (2085585)Instructions burned: 2 (million)
% 1.88/1.30 % (2085582)Instruction limit reached!
% 1.88/1.30 % (2085582)------------------------------
% 1.88/1.30 % (2085582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.30 % (2085582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.30 % (2085582)CaDiCaL version: 2.1.3
% 1.88/1.30 % (2085582)Termination reason: Instruction limit
% 1.88/1.30 % (2085582)Termination phase: Saturation
% 1.88/1.30 % (2085582)Time elapsed: 0.053 s
% 1.88/1.30 % (2085582)Peak memory usage: 89 MB
% 1.88/1.30 % (2085582)Instructions burned: 108 (million)
% 1.88/1.30 % (2085583)Instruction limit reached!
% 1.88/1.30 % (2085583)------------------------------
% 1.88/1.30 % (2085583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.30 % (2085583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.30 % (2085583)CaDiCaL version: 2.1.3
% 1.88/1.30 % (2085583)Termination reason: Instruction limit
% 1.88/1.30 % (2085583)Termination phase: Saturation
% 1.88/1.30 % (2085583)Time elapsed: 0.065 s
% 1.88/1.30 % (2085583)Peak memory usage: 89 MB
% 1.88/1.30 % (2085583)Instructions burned: 115 (million)
% 1.88/1.30 % (2085593)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=3773997385:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.88/1.30 % (2085594)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1556127005: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)
% 1.88/1.30 % (2085584)Refutation found. Thanks to Tanya!
% 1.88/1.30 % SZS status Unsatisfiable for theBenchmark
% 1.88/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.40 % (2085584)------------------------------
% 0.19/1.40 % (2085584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.40 % (2085584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.40 % (2085584)CaDiCaL version: 2.1.3
% 0.19/1.40 % (2085584)Termination reason: Refutation
% 0.19/1.40 % (2085584)Time elapsed: 0.017 s
% 0.19/1.40 % (2085584)Peak memory usage: 89 MB
% 0.19/1.40 % (2085584)Instructions burned: 24 (million)
% 0.19/1.40 % (2085584)------------------------------
% 0.19/1.40 % (2085584)------------------------------
% 0.19/1.40 % (2085574)Success in time 0.437 s
% 0.19/1.40 % Vampire exiting
%------------------------------------------------------------------------------