%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP245-1 : 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 : n016.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 3.17s 1.32s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 52
% Syntax : Number of formulae : 306 ( 17 unt; 23 def)
% Number of atoms : 833 ( 288 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 984 ( 457 ~; 504 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 3 ( 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 : 52 ( 0 sgn 52 !; 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_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,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_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f63]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
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_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,X6) != sk_c9
| inverse(X5) != X6
| multiply(X6,sk_c8) != 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_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c9 != multiply(X6,sk_c8) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X5] :
( sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X5] :
( sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f97,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c9 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_3
<=> ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_5
<=> ! [X0] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f91,f105,f102,f99,f99,f96,f93]) ).
fof(f109,definition,
( spl0_6
<=> sk_c9 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f111,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_7
<=> sk_c10 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f115,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f118,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f123,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f129,plain,
( sk_c9 != multiply(sk_c5,sk_c8)
| spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f130,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f140,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f78,f113,f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f113,f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f156,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f148,f138]) ).
fof(f157,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f148,f143]) ).
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(f166,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f159,f133]) ).
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(f176,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f170,f128]) ).
fof(f177,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f38,f170,f133]) ).
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(f185,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f181,f118]) ).
fof(f186,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f181,f123]) ).
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(f196,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f192,f118]) ).
fof(f197,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f192,f123]) ).
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(f202,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f97,f130]) ).
fof(f205,plain,
( sk_c9 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f202]) ).
fof(f206,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f205,f135]) ).
fof(f207,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f206]) ).
fof(f208,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f97,f1]) ).
fof(f210,definition,
( spl0_19
<=> sk_c9 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f211,plain,
( sk_c9 = inverse(identity)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f212,plain,
( sk_c9 != inverse(identity)
| spl0_19 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f214,definition,
( spl0_20
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f215,plain,
( sk_c9 = sk_c8
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( sk_c9 != sk_c8
| spl0_20 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( ~ spl0_19
| ~ spl0_20
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f208,f96,f214,f210]) ).
fof(f218,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f183]) ).
fof(f219,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f145]) ).
fof(f220,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_11 ),
inference(superposition,[],[f3,f135]) ).
fof(f222,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f161]) ).
fof(f230,definition,
( spl0_22
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f231,plain,
( identity = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f236,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f237,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_18 ),
inference(superposition,[],[f4,f194]) ).
fof(f238,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f140]) ).
fof(f244,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f236,f1]) ).
fof(f247,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f218]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f247,f1]) ).
fof(f249,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c4,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f219]) ).
fof(f250,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c4,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f249,f1]) ).
fof(f265,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f248,f194]) ).
fof(f275,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f237,f265]) ).
fof(f277,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f275,f194]) ).
fof(f290,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f250,f140]) ).
fof(f358,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f244,f290]) ).
fof(f360,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_13 ),
inference(superposition,[],[f244,f219]) ).
fof(f364,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f244,f277]) ).
fof(f368,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c9)
| ~ spl0_9 ),
inference(superposition,[],[f244,f125]) ).
fof(f373,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f244,f172]) ).
fof(f384,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f373,f161]) ).
fof(f386,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f368,f120]) ).
fof(f390,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f364,f3]) ).
fof(f401,plain,
( spl0_22
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f390,f192,f181,f230]) ).
fof(f402,plain,
( sk_c9 != inverse(sk_c9)
| spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f212,f231]) ).
fof(f403,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_22 ),
inference(superposition,[],[f1,f231]) ).
fof(f409,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f244,f384]) ).
fof(f412,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f409,f3]) ).
fof(f416,plain,
( sk_c9 = sk_c8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f412,f231]) ).
fof(f417,plain,
( spl0_20
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f416,f230,f170,f159,f214]) ).
fof(f419,plain,
( sk_c9 = multiply(sk_c7,sk_c9)
| ~ spl0_6
| ~ spl0_20 ),
inference(superposition,[],[f111,f215]) ).
fof(f427,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f244,f386]) ).
fof(f429,plain,
( identity = sk_c9
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f427,f3]) ).
fof(f437,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f220,f403]) ).
fof(f439,plain,
( identity = sk_c2
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f222,f403]) ).
fof(f447,plain,
( sk_c9 = sk_c2
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f439,f231]) ).
fof(f448,plain,
( sk_c9 = sk_c5
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f437,f231]) ).
fof(f457,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f161,f447]) ).
fof(f458,plain,
( $false
| ~ spl0_15
| spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f457,f402]) ).
fof(f459,plain,
( ~ spl0_15
| spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f463,plain,
( ! [X1] :
( sk_c9 != inverse(X1)
| sk_c9 != multiply(X1,sk_c9) )
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f103,f215]) ).
fof(f464,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f211,f231]) ).
fof(f468,plain,
( sk_c9 != sk_c7
| sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_20 ),
inference(superposition,[],[f463,f120]) ).
fof(f469,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f463,f161]) ).
fof(f471,plain,
( sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f469]) ).
fof(f475,plain,
( sk_c9 != sk_c8
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f471,f172]) ).
fof(f477,definition,
( spl0_24
<=> sk_c9 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f481,definition,
( spl0_25
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f482,plain,
( sk_c9 = sk_c7
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f484,plain,
( ~ spl0_24
| ~ spl0_25
| ~ spl0_4
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f468,f214,f118,f102,f481,f477]) ).
fof(f497,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f475,f215]) ).
fof(f498,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f497]) ).
fof(f501,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f129,f448]) ).
fof(f503,plain,
( $false
| spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f501,f384]) ).
fof(f504,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f508,plain,
( spl0_22
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f429,f123,f118,f230]) ).
fof(f512,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_22 ),
inference(superposition,[],[f1,f231]) ).
fof(f523,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f100,f145]) ).
fof(f527,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f100,f150]) ).
fof(f528,plain,
( sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f527]) ).
fof(f529,plain,
( sk_c10 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f523]) ).
fof(f530,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f528,f115]) ).
fof(f531,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f544,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f529,f140]) ).
fof(f545,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f544]) ).
fof(f550,plain,
( ! [X5] :
( sk_c9 != multiply(inverse(X5),sk_c9)
| sk_c9 != multiply(X5,inverse(X5)) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f94,f215]) ).
fof(f557,plain,
( sk_c9 != multiply(sk_c7,sk_c9)
| sk_c9 != multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_20 ),
inference(superposition,[],[f550,f120]) ).
fof(f560,plain,
( identity != sk_c9
| sk_c9 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_1
| ~ spl0_20 ),
inference(superposition,[],[f550,f3]) ).
fof(f572,plain,
( sk_c9 != multiply(sk_c7,sk_c9)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f557,f125]) ).
fof(f580,plain,
( sk_c9 != sk_c7
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f572,f386]) ).
fof(f581,plain,
( ~ spl0_25
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f580,f214,f123,f118,f93,f481]) ).
fof(f591,plain,
( ! [X0,X1] :
( sk_c9 != multiply(X0,multiply(X1,sk_c10))
| sk_c10 != inverse(multiply(X0,X1)) )
| ~ spl0_5 ),
inference(superposition,[],[f106,f4]) ).
fof(f593,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_18 ),
inference(superposition,[],[f106,f194]) ).
fof(f596,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f593]) ).
fof(f633,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| sk_c10 != inverse(multiply(sk_c4,sk_c9))
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f591,f238]) ).
fof(f642,plain,
( sk_c10 != inverse(multiply(sk_c4,sk_c9))
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f633,f290]) ).
fof(f660,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f642,f140]) ).
fof(f663,plain,
( sk_c9 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(superposition,[],[f386,f419]) ).
fof(f671,plain,
( spl0_25
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f663,f214,f123,f118,f109,f481]) ).
fof(f673,plain,
( sk_c9 = multiply(sk_c6,sk_c9)
| ~ spl0_9
| ~ spl0_25 ),
inference(superposition,[],[f125,f482]) ).
fof(f681,plain,
( spl0_24
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f673,f481,f123,f477]) ).
fof(f742,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f360,f231]) ).
fof(f834,plain,
( sk_c10 = sk_c4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f358,f742]) ).
fof(f861,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f145,f834]) ).
fof(f864,plain,
( $false
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f861,f660]) ).
fof(f865,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f864]) ).
fof(f868,plain,
( ~ spl0_17
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f596,f192,f105,f181]) ).
fof(f873,plain,
( sk_c9 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_1
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f560,f231]) ).
fof(f886,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f873,f512]) ).
fof(f895,plain,
( $false
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f886,f464]) ).
fof(f896,plain,
( ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f895]) ).
fof(f914,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_11 ),
inference(superposition,[],[f3,f135]) ).
fof(f915,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f914,f512]) ).
fof(f917,plain,
( sk_c9 = sk_c5
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f915,f231]) ).
fof(f940,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f130,f917]) ).
fof(f941,plain,
( sk_c9 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f940,f512]) ).
fof(f942,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f941,f216]) ).
fof(f943,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f942]) ).
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(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f141]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s15,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s16,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
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(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
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(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f185]) ).
cnf(s33,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
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(s39,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s40,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f197]) ).
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(s45,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f207]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f217]) ).
cnf(s53,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_22 ),
inference(sat_conversion,[],[f401]) ).
cnf(s55,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f417]) ).
cnf(s56,plain,
( ~ spl0_15
| spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f459]) ).
cnf(s57,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_20
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f484]) ).
cnf(s60,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(sat_conversion,[],[f498]) ).
cnf(s62,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f504]) ).
cnf(s63,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_22 ),
inference(sat_conversion,[],[f508]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f531]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f545]) ).
cnf(s72,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f581]) ).
cnf(s78,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| spl0_25 ),
inference(sat_conversion,[],[f671]) ).
cnf(s80,plain,
( ~ spl0_9
| spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f681]) ).
cnf(s84,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f865]) ).
cnf(s85,plain,
( ~ spl0_5
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f868]) ).
cnf(s93,plain,
( ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f896]) ).
cnf(s97,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f943]) ).
cnf(s99,plain,
( spl0_18
| ~ spl0_5 ),
inference(rat,[],[s63,s84,s39,s40,s43,s44]) ).
cnf(s100,plain,
( ~ spl0_18
| ~ spl0_5 ),
inference(rat,[],[s63,s84,s32,s33,s36,s37,s85]) ).
cnf(s101,plain,
~ spl0_5,
inference(rat,[],[s100,s99]) ).
cnf(s102,plain,
( spl0_18
| ~ spl0_4 ),
inference(rat,[],[s80,s57,s78,s97,s63,s38,s39,s40,s41,s42]) ).
cnf(s103,plain,
( ~ spl0_20
| ~ spl0_6
| ~ spl0_9
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s80,s57,s78]) ).
cnf(s104,plain,
( spl0_11
| spl0_20
| ~ spl0_22 ),
inference(rat,[],[s55,s21,s28]) ).
cnf(s105,plain,
( ~ spl0_11
| spl0_20
| ~ spl0_22 ),
inference(rat,[],[s62,s20,s27,s97]) ).
cnf(s106,plain,
( spl0_20
| ~ spl0_22 ),
inference(rat,[],[s105,s104]) ).
cnf(s107,plain,
( spl0_6
| ~ spl0_20
| ~ spl0_4 ),
inference(rat,[],[s60,s17,s24]) ).
cnf(s108,plain,
( spl0_9
| ~ spl0_20
| ~ spl0_4 ),
inference(rat,[],[s60,s19,s26]) ).
cnf(s109,plain,
( ~ spl0_9
| ~ spl0_20
| ~ spl0_4
| ~ spl0_6 ),
inference(rat,[],[s60,s18,s25,s103]) ).
cnf(s110,plain,
( ~ spl0_20
| ~ spl0_4 ),
inference(rat,[],[s109,s108,s107]) ).
cnf(s111,plain,
( spl0_22
| ~ spl0_18 ),
inference(rat,[],[s63,s32,s33,s53]) ).
cnf(s112,plain,
~ spl0_4,
inference(rat,[],[s111,s106,s110,s102]) ).
cnf(s113,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s65,s9,s16]) ).
cnf(s114,plain,
( ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s65,s8,s15,s67]) ).
cnf(s115,plain,
~ spl0_3,
inference(rat,[],[s114,s113]) ).
cnf(s116,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s45,s20,s21]) ).
cnf(s117,plain,
( ~ spl0_22
| ~ spl0_2 ),
inference(rat,[],[s46,s56,s106,s116]) ).
cnf(s118,plain,
~ spl0_2,
inference(rat,[],[s45,s41,s42,s111,s117]) ).
cnf(s119,plain,
spl0_1,
inference(rat,[],[s2,s101,s112,s115,s118]) ).
cnf(s120,plain,
( ~ spl0_20
| ~ spl0_22 ),
inference(rat,[],[s78,s72,s17,s18,s19,s56,s93,s119]) ).
cnf(s121,plain,
~ spl0_22,
inference(rat,[],[s120,s106]) ).
cnf(s122,plain,
~ spl0_18,
inference(rat,[],[s111,s121]) ).
cnf(s127,plain,
spl0_9,
inference(rat,[],[s40,s122]) ).
cnf(s128,plain,
spl0_8,
inference(rat,[],[s39,s122]) ).
cnf(s130,plain,
$false,
inference(rat,[],[s63,s121,s127,s128]) ).
fof(f944,plain,
$false,
inference(avatar_sat_refutation,[],[s130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP245-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:44:02 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.17/1.32 % (2379244)Input is clausal, will run a generic CNF schedule.
% 3.17/1.32 % (2379253)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=870806976:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.17/1.32 % (2379253)Instruction limit reached!
% 3.17/1.32 % (2379253)------------------------------
% 3.17/1.32 % (2379253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (2379253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (2379253)CaDiCaL version: 2.1.3
% 3.17/1.32 % (2379253)Termination reason: Instruction limit
% 3.17/1.32 % (2379253)Termination phase: Saturation
% 3.17/1.32 % (2379253)Time elapsed: 0.035 s
% 3.17/1.32 % (2379253)Peak memory usage: 89 MB
% 3.17/1.32 % (2379253)Instructions burned: 116 (million)
% 3.17/1.32 % (2379250)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=453445683:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.17/1.32 % (2379249)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=3872722671:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.17/1.32 % (2379251)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4214701601:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.17/1.32 % (2379252)lrs+10_1_sil=8000:sp=occurrence:random_seed=4252741043:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.17/1.32 % (2379255)dis-21_1_sil=8000:lcm=predicate:random_seed=2913977748: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)
% 3.17/1.32 % (2379254)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1849520649:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.17/1.32 % (2379255)Refutation not found, incomplete strategy
% 3.17/1.32 % (2379255)------------------------------
% 3.17/1.32 % (2379255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (2379255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (2379255)CaDiCaL version: 2.1.3
% 3.17/1.32 % (2379255)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.32 % (2379255)Time elapsed: 0.003 s
% 3.17/1.32 % (2379255)Peak memory usage: 88 MB
% 3.17/1.32 % (2379255)Instructions burned: 2 (million)
% 3.17/1.32 % (2379254)First to succeed.
% 3.17/1.32 % (2379254)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2379244"
% 3.17/1.32 % (2379252)Instruction limit reached!
% 3.17/1.32 % (2379252)------------------------------
% 3.17/1.32 % (2379252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (2379252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (2379252)CaDiCaL version: 2.1.3
% 3.17/1.32 % (2379252)Termination reason: Instruction limit
% 3.17/1.32 % (2379252)Termination phase: Saturation
% 3.17/1.32 % (2379252)Time elapsed: 0.056 s
% 3.17/1.32 % (2379252)Peak memory usage: 89 MB
% 3.17/1.32 % (2379252)Instructions burned: 107 (million)
% 3.17/1.32 % (2379257)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=4268979036:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.17/1.32 % (2379257)Instruction limit reached!
% 3.17/1.32 % (2379257)------------------------------
% 3.17/1.32 % (2379257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (2379257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (2379257)CaDiCaL version: 2.1.3
% 3.17/1.32 % (2379257)Termination reason: Instruction limit
% 3.17/1.32 % (2379257)Termination phase: Saturation
% 3.17/1.32 % (2379257)Time elapsed: 0.037 s
% 3.17/1.32 % (2379257)Peak memory usage: 90 MB
% 3.17/1.32 % (2379257)Instructions burned: 144 (million)
% 3.17/1.32 % (2379264)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=837207781: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)
% 3.17/1.32 % (2379255)------------------------------
% 3.17/1.32 % (2379255)------------------------------
% 3.17/1.32 % (2379266)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2595457699:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 3.17/1.32 % (2379254)Refutation found. Thanks to Tanya!
% 3.17/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.17/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.52 % (2379254)------------------------------
% 3.85/1.52 % (2379254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.52 % (2379254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.52 % (2379254)CaDiCaL version: 2.1.3
% 3.85/1.52 % (2379254)Termination reason: Refutation
% 3.85/1.52 % (2379254)Time elapsed: 0.021 s
% 3.85/1.52 % (2379254)Peak memory usage: 90 MB
% 3.85/1.52 % (2379254)Instructions burned: 32 (million)
% 3.85/1.52 % (2379254)------------------------------
% 3.85/1.52 % (2379254)------------------------------
% 3.85/1.52 % (2379244)Success in time 0.453 s
% 3.85/1.52 % Vampire exiting
%------------------------------------------------------------------------------