%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP256-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 10:17:18 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 48
% Syntax : Number of formulae : 293 ( 20 unt; 23 def)
% Number of atoms : 801 ( 280 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 961 ( 453 ~; 485 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f73,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f81,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f97,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_5
<=> ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f91,f99,f105,f102,f99,f96,f93]) ).
fof(f109,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f111,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f115,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f113,f109]) ).
fof(f118,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f123,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f130,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f113,f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f140,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f148,f109]) ).
fof(f154,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f148,f128]) ).
fof(f159,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f161,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f159,f109]) ).
fof(f163,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f159,f118]) ).
fof(f164,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f159,f123]) ).
fof(f165,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f159,f128]) ).
fof(f170,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f172,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f170,f109]) ).
fof(f174,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f170,f118]) ).
fof(f175,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f170,f123]) ).
fof(f181,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f183,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_6
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f181,f109]) ).
fof(f187,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f181,f128]) ).
fof(f188,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f181,f133]) ).
fof(f189,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f181,f138]) ).
fof(f190,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f181,f143]) ).
fof(f192,definition,
( spl0_18
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f194,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f192,f109]) ).
fof(f198,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f192,f128]) ).
fof(f199,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f192,f133]) ).
fof(f200,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f192,f138]) ).
fof(f201,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f192,f143]) ).
fof(f206,plain,
( sk_c9 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f97,f1]) ).
fof(f208,definition,
( spl0_19
<=> sk_c8 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f210,plain,
( sk_c8 != inverse(identity)
| spl0_19 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl0_20
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f213,plain,
( sk_c9 = sk_c8
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f214,plain,
( sk_c9 != sk_c8
| spl0_20 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( ~ spl0_19
| ~ spl0_20
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f206,f96,f212,f208]) ).
fof(f216,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f183]) ).
fof(f218,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f3,f111]) ).
fof(f219,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f161]) ).
fof(f220,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f150]) ).
fof(f221,plain,
( identity != sk_c9
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2 ),
inference(superposition,[],[f97,f3]) ).
fof(f223,definition,
( spl0_21
<=> sk_c8 = inverse(inverse(sk_c8)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f225,plain,
( sk_c8 != inverse(inverse(sk_c8))
| spl0_21 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f227,definition,
( spl0_22
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f228,plain,
( identity = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f229,plain,
( identity != sk_c9
| spl0_22 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,plain,
( ~ spl0_21
| ~ spl0_22
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f221,f96,f227,f223]) ).
fof(f233,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f235,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f216]) ).
fof(f243,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f235,f1]) ).
fof(f244,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f233,f1]) ).
fof(f249,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f218]) ).
fof(f250,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f249,f1]) ).
fof(f260,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f243,f194]) ).
fof(f329,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f250,f120]) ).
fof(f377,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f244,f3]) ).
fof(f378,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f244,f244]) ).
fof(f384,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f244,f260]) ).
fof(f401,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f244,f172]) ).
fof(f412,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f401,f161]) ).
fof(f422,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f384,f3]) ).
fof(f426,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f377,f378]) ).
fof(f434,plain,
( $false
| ~ spl0_17
| ~ spl0_18
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f422,f229]) ).
fof(f435,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f436,plain,
( sk_c8 != inverse(sk_c9)
| spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f210,f228]) ).
fof(f437,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_22 ),
inference(superposition,[],[f1,f228]) ).
fof(f460,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f244,f412]) ).
fof(f463,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f460,f3]) ).
fof(f467,plain,
( sk_c9 = sk_c8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f463,f228]) ).
fof(f470,plain,
( spl0_20
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f467,f227,f170,f159,f212]) ).
fof(f474,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f220,f213]) ).
fof(f482,plain,
( identity = sk_c3
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f474,f437]) ).
fof(f483,plain,
( sk_c9 = sk_c3
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f482,f228]) ).
fof(f487,plain,
( sk_c8 = inverse(sk_c9)
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f150,f483]) ).
fof(f488,plain,
( $false
| ~ spl0_14
| spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f487,f436]) ).
fof(f489,plain,
( ~ spl0_14
| spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f494,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f130,f213]) ).
fof(f508,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f3,f494]) ).
fof(f509,plain,
( identity = sk_c5
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f508,f437]) ).
fof(f511,plain,
( sk_c9 = sk_c5
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f509,f228]) ).
fof(f512,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f494,f511]) ).
fof(f518,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f100,f194]) ).
fof(f519,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f100,f145]) ).
fof(f520,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f519]) ).
fof(f521,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f518]) ).
fof(f522,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f520,f140]) ).
fof(f523,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f522]) ).
fof(f524,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f521,f183]) ).
fof(f525,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f524]) ).
fof(f555,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f130]) ).
fof(f557,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f244,f555]) ).
fof(f560,plain,
( sk_c5 = inverse(sk_c8)
| ~ spl0_10 ),
inference(forward_demodulation,[],[f557,f426]) ).
fof(f562,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| sk_c9 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f94,f1]) ).
fof(f568,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f94,f250]) ).
fof(f569,plain,
( sk_c9 != sk_c8
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f568,f111]) ).
fof(f580,definition,
( spl0_26
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f582,plain,
( sk_c9 != inverse(sk_c3)
| spl0_26 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f599,plain,
( ~ spl0_20
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f569,f109,f93,f212]) ).
fof(f607,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_10
| spl0_21 ),
inference(superposition,[],[f225,f560]) ).
fof(f609,plain,
( identity = multiply(sk_c5,sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f3,f560]) ).
fof(f610,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f609,f135]) ).
fof(f611,plain,
( $false
| ~ spl0_10
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f607,f130]) ).
fof(f612,plain,
( ~ spl0_10
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f613,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f610,f229]) ).
fof(f614,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f618,plain,
( identity != sk_c8
| sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_5 ),
inference(superposition,[],[f106,f3]) ).
fof(f619,plain,
( sk_c8 != sk_c7
| sk_c9 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f106,f120]) ).
fof(f620,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f106,f115]) ).
fof(f621,plain,
( sk_c9 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f620]) ).
fof(f622,plain,
( ~ spl0_26
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f621,f113,f105,f580]) ).
fof(f623,plain,
( sk_c8 != sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f619,f111]) ).
fof(f626,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_22 ),
inference(superposition,[],[f1,f228]) ).
fof(f665,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f626,f125]) ).
fof(f672,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f125,f626]) ).
fof(f674,plain,
( identity = sk_c2
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f219,f626]) ).
fof(f681,plain,
( sk_c9 = sk_c2
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f674,f228]) ).
fof(f689,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f665,f623]) ).
fof(f690,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f689]) ).
fof(f701,plain,
( ! [X0,X1] :
( sk_c8 != multiply(X0,multiply(X1,sk_c9))
| sk_c8 != inverse(multiply(X0,X1)) )
| ~ spl0_4 ),
inference(superposition,[],[f103,f4]) ).
fof(f702,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c9))
| ~ spl0_4 ),
inference(superposition,[],[f103,f3]) ).
fof(f712,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f161,f681]) ).
fof(f723,plain,
( ! [X0] :
( sk_c9 != sk_c8
| sk_c8 != inverse(multiply(inverse(X0),X0)) )
| ~ spl0_4 ),
inference(superposition,[],[f701,f244]) ).
fof(f804,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f244,f329]) ).
fof(f806,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f804,f3]) ).
fof(f814,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_demodulation,[],[f806,f672]) ).
fof(f819,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_demodulation,[],[f814,f228]) ).
fof(f821,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f819,f214]) ).
fof(f822,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f821]) ).
fof(f833,plain,
( ! [X0] : sk_c8 != inverse(multiply(inverse(X0),X0))
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f723,f213]) ).
fof(f856,plain,
( sk_c8 != inverse(identity)
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f833,f3]) ).
fof(f873,plain,
( sk_c8 != inverse(sk_c9)
| ~ spl0_4
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f856,f228]) ).
fof(f889,plain,
( sk_c9 != sk_c8
| ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f873,f512]) ).
fof(f902,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f889,f213]) ).
fof(f903,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f902]) ).
fof(f908,plain,
( identity != sk_c9
| sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_5
| ~ spl0_20 ),
inference(forward_demodulation,[],[f618,f213]) ).
fof(f917,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f150,f213]) ).
fof(f944,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_5
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f908,f228]) ).
fof(f956,plain,
( $false
| ~ spl0_14
| ~ spl0_20
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f917,f582]) ).
fof(f957,plain,
( ~ spl0_14
| ~ spl0_20
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f956]) ).
fof(f968,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f944,f512]) ).
fof(f977,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f968,f512]) ).
fof(f978,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f977]) ).
fof(f987,plain,
( identity != sk_c9
| sk_c8 != inverse(inverse(sk_c9))
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f702,f213]) ).
fof(f1019,plain,
( sk_c8 != inverse(inverse(sk_c9))
| ~ spl0_4
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f987,f228]) ).
fof(f1052,plain,
( sk_c8 != inverse(sk_c9)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1019,f712]) ).
fof(f1074,plain,
( sk_c9 != sk_c8
| ~ spl0_4
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1052,f712]) ).
fof(f1083,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1074,f213]) ).
fof(f1084,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1083]) ).
fof(f1091,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(identity)
| ~ spl0_1
| ~ spl0_22 ),
inference(forward_demodulation,[],[f562,f626]) ).
fof(f1099,plain,
( sk_c9 != inverse(identity)
| ~ spl0_1
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1091,f213]) ).
fof(f1106,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1099,f228]) ).
fof(f1111,plain,
( $false
| ~ spl0_1
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1106,f712]) ).
fof(f1112,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1111]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f107]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f116]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s10,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s17,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
cnf(s18,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s19,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s24,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s25,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s26,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f175]) ).
cnf(s31,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f184]) ).
cnf(s34,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s35,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s38,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s41,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f198]) ).
cnf(s42,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f199]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f215]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f230]) ).
cnf(s52,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_22 ),
inference(sat_conversion,[],[f435]) ).
cnf(s53,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f470]) ).
cnf(s54,plain,
( ~ spl0_14
| spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f489]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f523]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f525]) ).
cnf(s64,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_20 ),
inference(sat_conversion,[],[f599]) ).
cnf(s67,plain,
( ~ spl0_10
| spl0_21 ),
inference(sat_conversion,[],[f612]) ).
cnf(s68,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f614]) ).
cnf(s69,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_26 ),
inference(sat_conversion,[],[f622]) ).
cnf(s71,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(sat_conversion,[],[f690]) ).
cnf(s76,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f822]) ).
cnf(s85,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f903]) ).
cnf(s89,plain,
( ~ spl0_14
| ~ spl0_20
| spl0_26 ),
inference(sat_conversion,[],[f957]) ).
cnf(s95,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f978]) ).
cnf(s117,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f1084]) ).
cnf(s125,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f1112]) ).
cnf(s126,plain,
( spl0_6
| ~ spl0_5 ),
inference(rat,[],[s69,s89,s53,s52,s3,s10,s17,s24,s31,s38]) ).
cnf(s127,plain,
( spl0_18
| spl0_22 ),
inference(rat,[],[s68,s41,s42]) ).
cnf(s128,plain,
( ~ spl0_18
| spl0_22 ),
inference(rat,[],[s68,s34,s35,s52]) ).
cnf(s129,plain,
spl0_22,
inference(rat,[],[s128,s127]) ).
cnf(s131,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s71,s25,s26,s126,s129]) ).
cnf(s132,plain,
( spl0_15
| ~ spl0_5 ),
inference(rat,[],[s71,s18,s19,s126,s129]) ).
cnf(s133,plain,
( ~ spl0_20
| ~ spl0_5 ),
inference(rat,[],[s69,s89,s6,s13,s95,s129]) ).
cnf(s134,plain,
~ spl0_5,
inference(rat,[],[s133,s53,s132,s131,s129]) ).
cnf(s135,plain,
( spl0_16
| spl0_20 ),
inference(rat,[],[s76,s24,s25,s26,s129]) ).
cnf(s136,plain,
( ~ spl0_16
| spl0_20 ),
inference(rat,[],[s76,s17,s18,s19,s53,s129]) ).
cnf(s137,plain,
spl0_20,
inference(rat,[],[s136,s135]) ).
cnf(s139,plain,
~ spl0_4,
inference(rat,[],[s20,s117,s85,s137,s129]) ).
cnf(s140,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s55,s43,s44]) ).
cnf(s141,plain,
( ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s55,s36,s37,s56]) ).
cnf(s142,plain,
~ spl0_3,
inference(rat,[],[s141,s140]) ).
cnf(s143,plain,
~ spl0_2,
inference(rat,[],[s13,s54,s67,s46,s47,s137,s129]) ).
cnf(s144,plain,
spl0_1,
inference(rat,[],[s2,s134,s139,s142,s143]) ).
cnf(s147,plain,
~ spl0_15,
inference(rat,[],[s125,s129,s137,s144]) ).
cnf(s148,plain,
~ spl0_6,
inference(rat,[],[s64,s137,s144]) ).
cnf(s155,plain,
$false,
inference(rat,[],[s17,s147,s148]) ).
fof(f1113,plain,
$false,
inference(avatar_sat_refutation,[],[s155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP256-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n019.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 09:40:04 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 % (2842343)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (2842348)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=606838641_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % TRYING [1]
% 0.17/0.51 % TRYING [2]
% 0.17/0.51 % (2842349)% WARNING: option uhcvi not known.
% 0.17/0.51 % TRYING [3]
% 0.17/0.51 % TRYING [4]
% 0.17/0.51 % (2842349)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2734476591:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (2842350)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1771508158:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (2842351)dis+10_1_sil=32000:sp=arity:random_seed=3183774109:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (2842352)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=606782035:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (2842353)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3079555483:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (2842354)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3183351035:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % TRYING [5]
% 0.17/0.51 % (2842351) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2842343-2842351"...
% 0.17/0.51 % (2842352) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2842343-2842352"...
% 0.17/0.51 % (2842352)...printing done.
% 0.17/0.51 % (2842351)...printing done.
% 0.17/0.51 % (2842352)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (2842352)------------------------------
% 0.17/0.51 % (2842352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (2842352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (2842352)CaDiCaL version: 2.1.3
% 0.17/0.51 % (2842352)Termination reason: Refutation
% 0.17/0.51 % (2842352)Time elapsed: 0.021 s
% 0.17/0.51 % (2842352)Peak memory usage: 12 MB
% 0.17/0.51 % (2842352)Instructions burned: 33 (million)
% 0.17/0.51 % (2842343)Success in time 0.059 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------