%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP248-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 2.28s 1.19s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 43
% Syntax : Number of formulae : 282 ( 18 unt; 23 def)
% Number of atoms : 836 ( 265 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1073 ( 519 ~; 531 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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 : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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(f13,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/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/sandbox2/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(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f51,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/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/sandbox2/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(f61,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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_c8) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| 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_c8) != 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/sandbox2/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_c8)
| 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_c8)
| 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
<=> ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c8) )
| ~ 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(f108,definition,
( spl0_6
<=> ! [X0] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0] :
( inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f91,f108,f105,f102,f99,f96,f93]) ).
fof(f116,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f118,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f121,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f123,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f126,definition,
( spl0_10
<=> sk_c9 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f128,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f131,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 != multiply(sk_c5,sk_c8)
| spl0_11 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f136,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f138,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f141,definition,
( spl0_13
<=> sk_c10 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f78,f116,f141]) ).
fof(f146,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f76,f116,f146]) ).
fof(f151,definition,
( spl0_15
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f153,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f159,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f64,f151,f141]) ).
fof(f160,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f62,f151,f146]) ).
fof(f162,definition,
( spl0_16
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f168,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f162,f131]) ).
fof(f169,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f162,f136]) ).
fof(f173,definition,
( spl0_17
<=> sk_c8 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f175,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f179,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f40,f173,f131]) ).
fof(f180,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f38,f173,f136]) ).
fof(f184,definition,
( spl0_18
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f186,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f188,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f184,f121]) ).
fof(f189,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f28,f184,f126]) ).
fof(f192,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f184,f141]) ).
fof(f193,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f184,f146]) ).
fof(f195,definition,
( spl0_19
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f196,plain,
( multiply(sk_c1,sk_c10) != sk_c9
| spl0_19 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f197,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f199,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f16,f195,f121]) ).
fof(f200,plain,
( spl0_10
| spl0_19 ),
inference(avatar_split_clause,[],[f14,f195,f126]) ).
fof(f203,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f8,f195,f141]) ).
fof(f204,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f6,f195,f146]) ).
fof(f214,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f97,f1]) ).
fof(f216,definition,
( spl0_20
<=> sk_c9 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f218,plain,
( sk_c9 != inverse(identity)
| spl0_20 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f220,definition,
( spl0_21
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f221,plain,
( sk_c9 = sk_c8
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f214,f96,f220,f216]) ).
fof(f224,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f186]) ).
fof(f225,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f148]) ).
fof(f226,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f138]) ).
fof(f228,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_16 ),
inference(superposition,[],[f3,f164]) ).
fof(f230,plain,
( identity != sk_c9
| sk_c9 != inverse(inverse(sk_c8))
| ~ spl0_2 ),
inference(superposition,[],[f97,f3]) ).
fof(f232,definition,
( spl0_22
<=> sk_c9 = inverse(inverse(sk_c8)) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f234,plain,
( sk_c9 != inverse(inverse(sk_c8))
| spl0_22 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl0_23
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f237,plain,
( identity = sk_c9
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,plain,
( ~ spl0_22
| ~ spl0_23
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f230,f96,f236,f232]) ).
fof(f242,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f243,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_19 ),
inference(superposition,[],[f4,f197]) ).
fof(f244,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f224]) ).
fof(f251,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c1,X0)) = X0
| ~ spl0_18 ),
inference(forward_demodulation,[],[f244,f1]) ).
fof(f252,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f242,f1]) ).
fof(f255,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c4,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f225]) ).
fof(f256,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c4,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f255,f1]) ).
fof(f265,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f251,f197]) ).
fof(f276,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c9,sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f243,f265]) ).
fof(f278,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f276,f197]) ).
fof(f292,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f256,f143]) ).
fof(f374,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f252,f278]) ).
fof(f380,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c9)
| ~ spl0_10 ),
inference(superposition,[],[f252,f128]) ).
fof(f385,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_17 ),
inference(superposition,[],[f252,f175]) ).
fof(f396,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f385,f164]) ).
fof(f398,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f380,f123]) ).
fof(f402,plain,
( identity = sk_c9
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f374,f3]) ).
fof(f415,plain,
( spl0_23
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f402,f195,f184,f236]) ).
fof(f416,plain,
( sk_c9 != inverse(sk_c9)
| spl0_20
| ~ spl0_23 ),
inference(superposition,[],[f218,f237]) ).
fof(f417,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_23 ),
inference(superposition,[],[f1,f237]) ).
fof(f425,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f252,f396]) ).
fof(f428,plain,
( identity = sk_c8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f425,f3]) ).
fof(f431,plain,
( sk_c9 = sk_c8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f428,f237]) ).
fof(f432,plain,
( spl0_21
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f431,f236,f173,f162,f220]) ).
fof(f435,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| ~ spl0_8
| ~ spl0_21 ),
inference(superposition,[],[f118,f221]) ).
fof(f437,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_21
| spl0_22 ),
inference(superposition,[],[f234,f221]) ).
fof(f444,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f252,f398]) ).
fof(f446,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f444,f3]) ).
fof(f455,plain,
( identity = sk_c5
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f226,f417]) ).
fof(f457,plain,
( identity = sk_c2
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f228,f417]) ).
fof(f465,plain,
( sk_c9 = sk_c2
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f457,f237]) ).
fof(f466,plain,
( sk_c9 = sk_c5
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f455,f237]) ).
fof(f475,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f164,f465]) ).
fof(f476,plain,
( $false
| ~ spl0_16
| spl0_20
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f475,f416]) ).
fof(f477,plain,
( ~ spl0_16
| spl0_20
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f476]) ).
fof(f481,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2) )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f103,f221]) ).
fof(f483,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f481,f220,f102,f99]) ).
fof(f484,plain,
( sk_c10 != sk_c10
| multiply(sk_c1,sk_c10) != sk_c9
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f109,f186]) ).
fof(f517,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f132,f466]) ).
fof(f519,plain,
( $false
| spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f517,f396]) ).
fof(f520,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f526,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f100,f153]) ).
fof(f527,plain,
( sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f526]) ).
fof(f550,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f435,f527]) ).
fof(f551,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_15
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f550]) ).
fof(f553,plain,
( sk_c9 = multiply(sk_c5,sk_c9)
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f133,f221]) ).
fof(f554,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f138,f466]) ).
fof(f555,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f100,f148]) ).
fof(f557,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f148]) ).
fof(f558,plain,
( sk_c10 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f555]) ).
fof(f560,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f558,f143]) ).
fof(f561,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f562,plain,
( spl0_23
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f446,f126,f121,f236]) ).
fof(f564,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_23 ),
inference(superposition,[],[f1,f237]) ).
fof(f573,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f133,f466]) ).
fof(f576,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f252,f573]) ).
fof(f578,plain,
( identity = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f576,f3]) ).
fof(f581,plain,
( sk_c9 = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f578,f237]) ).
fof(f582,plain,
( spl0_21
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f581,f236,f136,f131,f220]) ).
fof(f583,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_12
| ~ spl0_21
| spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f437,f554]) ).
fof(f584,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f553,f466]) ).
fof(f585,plain,
( $false
| ~ spl0_12
| ~ spl0_21
| spl0_22
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f583,f554]) ).
fof(f586,plain,
( ~ spl0_12
| ~ spl0_21
| spl0_22
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f585]) ).
fof(f608,plain,
( ! [X5] :
( sk_c9 != multiply(inverse(X5),sk_c9)
| sk_c9 != multiply(X5,inverse(X5)) )
| ~ spl0_1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f94,f221]) ).
fof(f611,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[],[f608,f138]) ).
fof(f627,plain,
( sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f611,f584]) ).
fof(f629,definition,
( spl0_32
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f631,plain,
( sk_c9 != multiply(sk_c4,sk_c10)
| spl0_32 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f637,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f627,f466]) ).
fof(f642,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f637,f584]) ).
fof(f643,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f642]) ).
fof(f647,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c4,sk_c10)
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f109,f148]) ).
fof(f652,plain,
( sk_c9 != multiply(sk_c4,sk_c10)
| ~ spl0_6
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f647]) ).
fof(f653,plain,
( ~ spl0_32
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f652,f146,f108,f629]) ).
fof(f656,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f557,f237]) ).
fof(f659,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_14
| ~ spl0_23 ),
inference(superposition,[],[f252,f656]) ).
fof(f689,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f252,f292]) ).
fof(f718,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f385,f221]) ).
fof(f750,plain,
( ! [X1] :
( sk_c9 != inverse(X1)
| sk_c9 != multiply(X1,sk_c9) )
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f106,f221]) ).
fof(f759,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[],[f750,f138]) ).
fof(f762,plain,
( sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f759]) ).
fof(f765,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f762,f466]) ).
fof(f769,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f765,f584]) ).
fof(f770,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f780,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c2),multiply(sk_c9,X0))
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f4,f718]) ).
fof(f781,plain,
( ! [X0] : multiply(inverse(sk_c2),X0) = X0
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f780,f564]) ).
fof(f803,plain,
( identity = sk_c2
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(superposition,[],[f3,f781]) ).
fof(f807,plain,
( sk_c9 = sk_c2
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f803,f237]) ).
fof(f830,plain,
( sk_c10 = sk_c4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(superposition,[],[f689,f659]) ).
fof(f855,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f164,f807]) ).
fof(f883,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f186]) ).
fof(f884,plain,
( sk_c9 = multiply(sk_c10,sk_c1)
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f883,f237]) ).
fof(f897,plain,
( identity != sk_c9
| sk_c9 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_1
| ~ spl0_21 ),
inference(superposition,[],[f608,f3]) ).
fof(f909,plain,
( sk_c9 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_1
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f897,f237]) ).
fof(f918,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f909,f564]) ).
fof(f927,plain,
( $false
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f918,f855]) ).
fof(f928,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f927]) ).
fof(f938,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(superposition,[],[f750,f855]) ).
fof(f942,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f938]) ).
fof(f943,plain,
( $false
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f942,f564]) ).
fof(f944,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f943]) ).
fof(f945,plain,
( multiply(sk_c1,sk_c10) != sk_c9
| ~ spl0_6
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f484]) ).
fof(f949,plain,
( ~ spl0_19
| ~ spl0_6
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f945,f184,f108,f195]) ).
fof(f994,plain,
( sk_c1 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_18
| ~ spl0_23 ),
inference(superposition,[],[f252,f884]) ).
fof(f997,plain,
( sk_c1 = sk_c10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f994,f689]) ).
fof(f999,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(superposition,[],[f196,f997]) ).
fof(f1001,plain,
( $false
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f999,f292]) ).
fof(f1002,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1001]) ).
fof(f1007,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_32 ),
inference(superposition,[],[f631,f830]) ).
fof(f1009,plain,
( $false
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_32 ),
inference(forward_subsumption_resolution,[],[f1007,f292]) ).
fof(f1010,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_32 ),
inference(avatar_contradiction_clause,[],[f1009]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f110]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s8,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s14,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s15,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s19,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s20,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f169]) ).
cnf(s26,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f179]) ).
cnf(s27,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s31,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f188]) ).
cnf(s32,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f189]) ).
cnf(s35,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f192]) ).
cnf(s36,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f193]) ).
cnf(s38,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f199]) ).
cnf(s39,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f200]) ).
cnf(s42,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f203]) ).
cnf(s43,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f204]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f223]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f239]) ).
cnf(s53,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_23 ),
inference(sat_conversion,[],[f415]) ).
cnf(s55,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f432]) ).
cnf(s56,plain,
( ~ spl0_16
| spl0_20
| ~ spl0_23 ),
inference(sat_conversion,[],[f477]) ).
cnf(s57,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_21 ),
inference(sat_conversion,[],[f483]) ).
cnf(s62,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(sat_conversion,[],[f520]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f551]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f561]) ).
cnf(s67,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_23 ),
inference(sat_conversion,[],[f562]) ).
cnf(s68,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f582]) ).
cnf(s69,plain,
( ~ spl0_12
| ~ spl0_21
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f586]) ).
cnf(s75,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f643]) ).
cnf(s78,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_32 ),
inference(sat_conversion,[],[f653]) ).
cnf(s83,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f770]) ).
cnf(s95,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f928]) ).
cnf(s98,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f944]) ).
cnf(s99,plain,
( ~ spl0_6
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f949]) ).
cnf(s107,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f1002]) ).
cnf(s108,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_32 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s110,plain,
( spl0_19
| ~ spl0_6 ),
inference(rat,[],[s67,s108,s78,s38,s39,s42,s43]) ).
cnf(s111,plain,
( ~ spl0_19
| ~ spl0_6 ),
inference(rat,[],[s67,s108,s78,s31,s32,s35,s36,s99]) ).
cnf(s112,plain,
~ spl0_6,
inference(rat,[],[s111,s110]) ).
cnf(s113,plain,
( spl0_19
| ~ spl0_18 ),
inference(rat,[],[s67,s107,s38,s39,s42,s43]) ).
cnf(s114,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_23
| ~ spl0_5 ),
inference(rat,[],[s83,s68]) ).
cnf(s115,plain,
( spl0_12
| ~ spl0_23
| ~ spl0_5 ),
inference(rat,[],[s98,s55,s20,s27]) ).
cnf(s116,plain,
( ~ spl0_12
| ~ spl0_23
| ~ spl0_5 ),
inference(rat,[],[s62,s19,s26,s114]) ).
cnf(s117,plain,
( ~ spl0_23
| ~ spl0_5 ),
inference(rat,[],[s116,s115]) ).
cnf(s118,plain,
( ~ spl0_18
| spl0_23 ),
inference(rat,[],[s53,s113]) ).
cnf(s119,plain,
spl0_23,
inference(rat,[],[s67,s31,s32,s118]) ).
cnf(s120,plain,
~ spl0_5,
inference(rat,[],[s117,s119]) ).
cnf(s121,plain,
( ~ spl0_12
| spl0_21 ),
inference(rat,[],[s62,s19,s26,s68,s119]) ).
cnf(s122,plain,
spl0_21,
inference(rat,[],[s55,s20,s27,s121,s119]) ).
cnf(s123,plain,
( spl0_3
| spl0_2
| spl0_1 ),
inference(rat,[],[s1,s57,s120,s112,s122]) ).
cnf(s124,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s65,s8,s15,s122]) ).
cnf(s125,plain,
( ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s65,s7,s14,s66,s122]) ).
cnf(s126,plain,
~ spl0_3,
inference(rat,[],[s125,s124]) ).
cnf(s128,plain,
~ spl0_2,
inference(rat,[],[s20,s56,s69,s45,s46,s119,s122]) ).
cnf(s129,plain,
spl0_1,
inference(rat,[],[s123,s126,s128]) ).
cnf(s131,plain,
~ spl0_12,
inference(rat,[],[s62,s19,s26,s75,s119,s122,s129]) ).
cnf(s132,plain,
spl0_17,
inference(rat,[],[s27,s131]) ).
cnf(s133,plain,
spl0_16,
inference(rat,[],[s20,s131]) ).
cnf(s136,plain,
$false,
inference(rat,[],[s95,s119,s122,s129,s132,s133]) ).
fof(f1011,plain,
$false,
inference(avatar_sat_refutation,[],[s136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP248-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:38:34 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.28/1.19 % (2292094)Input is clausal, will run a generic CNF schedule.
% 2.28/1.19 % (2292103)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=579228951:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.28/1.19 % (2292103)Instruction limit reached!
% 2.28/1.19 % (2292103)------------------------------
% 2.28/1.19 % (2292103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.19 % (2292103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.19 % (2292103)CaDiCaL version: 2.1.3
% 2.28/1.19 % (2292103)Termination reason: Instruction limit
% 2.28/1.19 % (2292103)Termination phase: Saturation
% 2.28/1.19 % (2292103)Time elapsed: 0.036 s
% 2.28/1.19 % (2292103)Peak memory usage: 89 MB
% 2.28/1.19 % (2292103)Instructions burned: 117 (million)
% 2.28/1.19 % (2292104)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2570930542:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.28/1.19 % (2292100)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2842025680:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.28/1.19 % (2292105)dis-21_1_sil=8000:lcm=predicate:random_seed=1686234615:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.28/1.19 % (2292099)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=888677727:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.28/1.19 % (2292101)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=107960539:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.28/1.19 % (2292102)lrs+10_1_sil=8000:sp=occurrence:random_seed=2918949635:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.28/1.19 % (2292105)Refutation not found, incomplete strategy
% 2.28/1.19 % (2292105)------------------------------
% 2.28/1.19 % (2292105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.19 % (2292105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.19 % (2292105)CaDiCaL version: 2.1.3
% 2.28/1.19 % (2292105)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.19 % (2292105)Time elapsed: 0.002 s
% 2.28/1.19 % (2292105)Peak memory usage: 88 MB
% 2.28/1.19 % (2292105)Instructions burned: 2 (million)
% 2.28/1.19 % (2292104)First to succeed.
% 2.28/1.19 % (2292104)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2292094"
% 2.28/1.19 % (2292102)Instruction limit reached!
% 2.28/1.19 % (2292102)------------------------------
% 2.28/1.19 % (2292102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.19 % (2292102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.19 % (2292102)CaDiCaL version: 2.1.3
% 2.28/1.19 % (2292102)Termination reason: Instruction limit
% 2.28/1.19 % (2292102)Termination phase: Saturation
% 2.28/1.19 % (2292102)Time elapsed: 0.054 s
% 2.28/1.19 % (2292102)Peak memory usage: 89 MB
% 2.28/1.19 % (2292102)Instructions burned: 108 (million)
% 2.28/1.19 % (2292113)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=236427748:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.28/1.19 % (2292104)Refutation found. Thanks to Tanya!
% 2.28/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.28/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/1.39 % (2292104)------------------------------
% 3.00/1.39 % (2292104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.39 % (2292104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.39 % (2292104)CaDiCaL version: 2.1.3
% 3.00/1.39 % (2292104)Termination reason: Refutation
% 3.00/1.39 % (2292104)Time elapsed: 0.012 s
% 3.00/1.39 % (2292104)Peak memory usage: 89 MB
% 3.00/1.39 % (2292104)Instructions burned: 35 (million)
% 3.00/1.39 % (2292104)------------------------------
% 3.00/1.39 % (2292104)------------------------------
% 3.00/1.39 % (2292094)Success in time 0.347 s
% 3.00/1.39 % Vampire exiting
%------------------------------------------------------------------------------