%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP243-1 : 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 : n007.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 10:13:25 AM UTC 2026
% Result : Unsatisfiable 0.52s 0.90s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 41
% Syntax : Number of formulae : 288 ( 18 unt; 21 def)
% Number of atoms : 879 ( 292 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1147 ( 556 ~; 570 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 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_c12) = sk_c11
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c12 = inverse(sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c12 = multiply(sk_c6,sk_c11) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c11 = inverse(sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c11 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c9 = inverse(sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c12 = inverse(sk_c1)
| sk_c12 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c12 = inverse(sk_c1)
| sk_c11 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c12 = inverse(sk_c1)
| sk_c9 = inverse(sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c11 = inverse(sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f39]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = inverse(sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f53]) ).
fof(f61,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c12 = inverse(sk_c3)
| sk_c12 = inverse(sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c12 = inverse(sk_c3)
| sk_c12 = multiply(sk_c6,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c12 = multiply(sk_c3,sk_c11)
| sk_c12 = inverse(sk_c6) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c12 = multiply(sk_c3,sk_c11)
| sk_c12 = multiply(sk_c6,sk_c11) ),
inference(reorient_equations,[],[f77]) ).
fof(f131,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(X0,sk_c12) != sk_c11
| inverse(X0) != sk_c12
| multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| inverse(X2) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,X4) != sk_c11
| inverse(X3) != X4
| multiply(X4,sk_c10) != sk_c11
| inverse(X5) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| inverse(X6) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| multiply(X7,X8) != sk_c11
| inverse(X7) != X8
| multiply(X8,sk_c10) != sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_64) ).
fof(f132,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12
| sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c12 != inverse(X2)
| sk_c12 != multiply(X2,sk_c11)
| sk_c11 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c11 != multiply(X4,sk_c10)
| sk_c12 != inverse(X5)
| sk_c12 != multiply(X5,sk_c11)
| sk_c11 != inverse(X6)
| sk_c11 != multiply(X6,sk_c10)
| sk_c11 != multiply(X7,X8)
| inverse(X7) != X8
| sk_c11 != multiply(X8,sk_c10) ),
inference(reorient_equations,[],[f131]) ).
fof(f133,plain,
! [X2,X3,X0,X1,X8,X6,X7,X5] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12
| sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c12 != inverse(X2)
| sk_c12 != multiply(X2,sk_c11)
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c12 != inverse(X5)
| sk_c12 != multiply(X5,sk_c11)
| sk_c11 != inverse(X6)
| sk_c11 != multiply(X6,sk_c10)
| sk_c11 != multiply(X7,X8)
| inverse(X7) != X8
| sk_c11 != multiply(X8,sk_c10) ),
inference(equality_resolution,[],[f132]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X6,X7,X5] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12
| sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c12 != inverse(X2)
| sk_c12 != multiply(X2,sk_c11)
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c12 != inverse(X5)
| sk_c12 != multiply(X5,sk_c11)
| sk_c11 != inverse(X6)
| sk_c11 != multiply(X6,sk_c10)
| sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10) ),
inference(equality_resolution,[],[f133]) ).
fof(f136,definition,
( spl0_1
<=> ! [X7] :
( sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f137,plain,
( ! [X7] :
( sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,definition,
( spl0_2
<=> ! [X6] :
( sk_c11 != inverse(X6)
| sk_c11 != multiply(X6,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f140,plain,
( ! [X6] :
( sk_c11 != multiply(X6,sk_c10)
| sk_c11 != inverse(X6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,definition,
( spl0_3
<=> ! [X5] :
( sk_c12 != inverse(X5)
| sk_c12 != multiply(X5,sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f143,plain,
( ! [X5] :
( sk_c12 != inverse(X5)
| sk_c12 != multiply(X5,sk_c11) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,definition,
( spl0_4
<=> ! [X1] :
( sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f146,plain,
( ! [X1] :
( sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,definition,
( spl0_5
<=> ! [X0] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f149,plain,
( ! [X0] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f150,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f134,f148,f145,f142,f136,f142,f139,f136]) ).
fof(f161,definition,
( spl0_8
<=> sk_c9 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f163,plain,
( sk_c9 = inverse(sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f166,definition,
( spl0_9
<=> sk_c11 = multiply(sk_c8,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f168,plain,
( sk_c11 = multiply(sk_c8,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f171,definition,
( spl0_10
<=> sk_c11 = multiply(sk_c7,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f172,plain,
( sk_c11 != multiply(sk_c7,sk_c10)
| spl0_10 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f173,plain,
( sk_c11 = multiply(sk_c7,sk_c10)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f176,definition,
( spl0_11
<=> sk_c11 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f178,plain,
( sk_c11 = inverse(sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f181,definition,
( spl0_12
<=> sk_c12 = multiply(sk_c6,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f183,plain,
( sk_c12 = multiply(sk_c6,sk_c11)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f186,definition,
( spl0_13
<=> sk_c12 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f188,plain,
( sk_c12 = inverse(sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f213,definition,
( spl0_16
<=> sk_c12 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f215,plain,
( sk_c12 = multiply(sk_c3,sk_c11)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f221,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f78,f213,f181]) ).
fof(f222,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f76,f213,f186]) ).
fof(f224,definition,
( spl0_17
<=> sk_c12 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f226,plain,
( sk_c12 = inverse(sk_c3)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f232,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f224,f181]) ).
fof(f233,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f62,f224,f186]) ).
fof(f235,definition,
( spl0_18
<=> sk_c11 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f237,plain,
( sk_c11 = inverse(sk_c2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f241,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f54,f235,f171]) ).
fof(f242,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f52,f235,f176]) ).
fof(f246,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f248,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f252,plain,
( spl0_10
| spl0_19 ),
inference(avatar_split_clause,[],[f40,f246,f171]) ).
fof(f253,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f38,f246,f176]) ).
fof(f257,definition,
( spl0_20
<=> sk_c12 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f258,plain,
( sk_c12 != inverse(sk_c1)
| spl0_20 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( sk_c12 = inverse(sk_c1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,plain,
( spl0_8
| spl0_20 ),
inference(avatar_split_clause,[],[f30,f257,f161]) ).
fof(f262,plain,
( spl0_9
| spl0_20 ),
inference(avatar_split_clause,[],[f28,f257,f166]) ).
fof(f266,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f20,f257,f186]) ).
fof(f268,definition,
( spl0_21
<=> multiply(sk_c1,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f269,plain,
( multiply(sk_c1,sk_c12) != sk_c11
| spl0_21 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f270,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f272,plain,
( spl0_8
| spl0_21 ),
inference(avatar_split_clause,[],[f16,f268,f161]) ).
fof(f273,plain,
( spl0_9
| spl0_21 ),
inference(avatar_split_clause,[],[f14,f268,f166]) ).
fof(f275,plain,
( spl0_11
| spl0_21 ),
inference(avatar_split_clause,[],[f10,f268,f176]) ).
fof(f276,plain,
( spl0_12
| spl0_21 ),
inference(avatar_split_clause,[],[f8,f268,f181]) ).
fof(f277,plain,
( spl0_13
| spl0_21 ),
inference(avatar_split_clause,[],[f6,f268,f186]) ).
fof(f278,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f140,f173]) ).
fof(f281,plain,
( sk_c11 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f278]) ).
fof(f282,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f281,f178]) ).
fof(f283,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f288,definition,
( spl0_22
<=> sk_c11 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f289,plain,
( sk_c11 = inverse(identity)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( sk_c11 != inverse(identity)
| spl0_22 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f292,definition,
( spl0_23
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f293,plain,
( sk_c11 = sk_c10
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_20 ),
inference(superposition,[],[f3,f259]) ).
fof(f297,plain,
( identity = multiply(sk_c12,sk_c6)
| ~ spl0_13 ),
inference(superposition,[],[f3,f188]) ).
fof(f298,plain,
( identity = multiply(sk_c11,sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f3,f178]) ).
fof(f299,plain,
( identity = multiply(sk_c9,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f3,f163]) ).
fof(f300,plain,
( identity = multiply(sk_c11,sk_c2)
| ~ spl0_18 ),
inference(superposition,[],[f3,f237]) ).
fof(f303,plain,
( identity != sk_c11
| sk_c11 != inverse(inverse(sk_c10))
| ~ spl0_2 ),
inference(superposition,[],[f140,f3]) ).
fof(f305,definition,
( spl0_24
<=> sk_c11 = inverse(inverse(sk_c10)) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f307,plain,
( sk_c11 != inverse(inverse(sk_c10))
| spl0_24 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f309,definition,
( spl0_25
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f310,plain,
( identity = sk_c11
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,plain,
( ~ spl0_24
| ~ spl0_25
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f303,f139,f309,f305]) ).
fof(f315,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f316,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c12,X0)) = multiply(sk_c11,X0)
| ~ spl0_21 ),
inference(superposition,[],[f4,f270]) ).
fof(f317,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(sk_c6,multiply(sk_c11,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f183]) ).
fof(f325,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f315,f1]) ).
fof(f328,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c1,X0))
| ~ spl0_20 ),
inference(superposition,[],[f4,f296]) ).
fof(f329,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c1,X0)) = X0
| ~ spl0_20 ),
inference(forward_demodulation,[],[f328,f1]) ).
fof(f330,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c6,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f297]) ).
fof(f331,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c6,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f330,f1]) ).
fof(f334,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f299]) ).
fof(f335,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c8,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f334,f1]) ).
fof(f342,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f329,f270]) ).
fof(f353,plain,
( multiply(sk_c1,sk_c12) = multiply(sk_c11,sk_c11)
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f316,f342]) ).
fof(f355,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f353,f270]) ).
fof(f356,plain,
( multiply(sk_c12,sk_c7) = multiply(sk_c6,identity)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f317,f298]) ).
fof(f369,plain,
( sk_c11 = multiply(sk_c12,sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f331,f183]) ).
fof(f407,plain,
( sk_c9 = multiply(sk_c9,sk_c11)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f335,f168]) ).
fof(f471,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(inverse(sk_c1),multiply(sk_c11,X0))
| ~ spl0_21 ),
inference(superposition,[],[f325,f316]) ).
fof(f477,plain,
( sk_c6 = multiply(inverse(sk_c12),identity)
| ~ spl0_13 ),
inference(superposition,[],[f325,f297]) ).
fof(f480,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f325,f355]) ).
fof(f484,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c6),multiply(sk_c12,X0))
| ~ spl0_12 ),
inference(superposition,[],[f325,f317]) ).
fof(f490,plain,
( sk_c11 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f325,f407]) ).
fof(f493,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_19 ),
inference(superposition,[],[f325,f248]) ).
fof(f511,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f493,f237]) ).
fof(f512,plain,
( identity = sk_c11
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f490,f3]) ).
fof(f516,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c12,multiply(sk_c12,X0))
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f484,f188]) ).
fof(f518,plain,
( identity = sk_c11
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f480,f3]) ).
fof(f530,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f512,f166,f161,f309]) ).
fof(f532,plain,
( spl0_25
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f518,f268,f257,f309]) ).
fof(f533,plain,
( sk_c11 != inverse(sk_c11)
| spl0_22
| ~ spl0_25 ),
inference(superposition,[],[f290,f310]) ).
fof(f534,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_25 ),
inference(superposition,[],[f1,f310]) ).
fof(f545,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f325,f511]) ).
fof(f548,plain,
( identity = sk_c10
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f545,f3]) ).
fof(f552,plain,
( sk_c11 = sk_c10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f548,f310]) ).
fof(f553,plain,
( spl0_23
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f552,f309,f246,f235,f292]) ).
fof(f558,plain,
( sk_c11 != inverse(inverse(sk_c11))
| ~ spl0_23
| spl0_24 ),
inference(superposition,[],[f307,f293]) ).
fof(f572,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f298,f534]) ).
fof(f574,plain,
( identity = sk_c2
| ~ spl0_18
| ~ spl0_25 ),
inference(superposition,[],[f300,f534]) ).
fof(f582,plain,
( sk_c11 = sk_c2
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f574,f310]) ).
fof(f583,plain,
( sk_c11 = sk_c7
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f572,f310]) ).
fof(f592,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_18
| ~ spl0_25 ),
inference(superposition,[],[f237,f582]) ).
fof(f593,plain,
( $false
| ~ spl0_18
| spl0_22
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f592,f533]) ).
fof(f594,plain,
( ~ spl0_18
| spl0_22
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f593]) ).
fof(f598,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_demodulation,[],[f289,f310]) ).
fof(f602,plain,
( sk_c11 != sk_c11
| sk_c12 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_21 ),
inference(superposition,[],[f149,f270]) ).
fof(f623,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f172,f583]) ).
fof(f625,plain,
( $false
| spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f623,f511]) ).
fof(f626,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f625]) ).
fof(f631,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(inverse(sk_c1),X0)
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f471,f534]) ).
fof(f637,plain,
( sk_c12 != sk_c12
| sk_c12 != multiply(sk_c6,sk_c11)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f143,f188]) ).
fof(f641,plain,
( sk_c12 != sk_c12
| sk_c12 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f143,f226]) ).
fof(f643,plain,
( sk_c12 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f641]) ).
fof(f644,plain,
( sk_c12 != multiply(sk_c6,sk_c11)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f637]) ).
fof(f654,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f643,f215]) ).
fof(f655,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f654]) ).
fof(f667,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f644,f183]) ).
fof(f668,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f675,plain,
( ! [X7] :
( sk_c11 != multiply(inverse(X7),sk_c11)
| sk_c11 != multiply(X7,inverse(X7)) )
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f137,f293]) ).
fof(f677,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c7,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_23 ),
inference(superposition,[],[f675,f178]) ).
fof(f679,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_1
| ~ spl0_18
| ~ spl0_23 ),
inference(superposition,[],[f675,f237]) ).
fof(f694,plain,
( sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_1
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f679,f534]) ).
fof(f696,plain,
( sk_c11 != multiply(sk_c7,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f677,f534]) ).
fof(f704,plain,
( sk_c11 != sk_c10
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f694,f248]) ).
fof(f706,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f696,f583]) ).
fof(f707,plain,
( $false
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f704,f293]) ).
fof(f708,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f707]) ).
fof(f709,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f706,f534]) ).
fof(f710,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f711,plain,
( sk_c12 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f602]) ).
fof(f716,plain,
( ~ spl0_20
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f711,f268,f148,f257]) ).
fof(f816,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_22
| ~ spl0_23
| spl0_24
| ~ spl0_25 ),
inference(forward_demodulation,[],[f558,f598]) ).
fof(f817,plain,
( $false
| ~ spl0_22
| ~ spl0_23
| spl0_24
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f816,f598]) ).
fof(f818,plain,
( ~ spl0_22
| ~ spl0_23
| spl0_24
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f817]) ).
fof(f824,plain,
( sk_c6 = multiply(inverse(sk_c12),sk_c11)
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f477,f310]) ).
fof(f898,plain,
( multiply(sk_c6,sk_c11) = multiply(sk_c12,sk_c7)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f356,f310]) ).
fof(f899,plain,
( multiply(sk_c6,sk_c11) = multiply(sk_c12,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f898,f583]) ).
fof(f900,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f899,f183]) ).
fof(f960,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f3,f631]) ).
fof(f971,plain,
( sk_c11 = multiply(sk_c12,sk_c1)
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f960,f310]) ).
fof(f975,plain,
( sk_c1 = multiply(inverse(sk_c12),sk_c11)
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f325,f971]) ).
fof(f978,plain,
( sk_c1 = sk_c6
| ~ spl0_13
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f975,f824]) ).
fof(f981,plain,
( sk_c12 != inverse(sk_c6)
| ~ spl0_13
| spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f258,f978]) ).
fof(f996,plain,
( $false
| ~ spl0_13
| spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f981,f188]) ).
fof(f997,plain,
( ~ spl0_13
| spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f996]) ).
fof(f998,plain,
( ! [X1] :
( sk_c11 != inverse(X1)
| sk_c11 != multiply(X1,sk_c11) )
| ~ spl0_4
| ~ spl0_23 ),
inference(forward_demodulation,[],[f146,f293]) ).
fof(f1003,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c7,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_23 ),
inference(superposition,[],[f998,f178]) ).
fof(f1005,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_23 ),
inference(superposition,[],[f998,f237]) ).
fof(f1008,plain,
( sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1005]) ).
fof(f1009,plain,
( sk_c11 != multiply(sk_c7,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1003]) ).
fof(f1012,plain,
( sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1008,f248]) ).
fof(f1014,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1009,f583]) ).
fof(f1018,plain,
( $false
| ~ spl0_4
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1012,f293]) ).
fof(f1019,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1018]) ).
fof(f1021,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1014,f534]) ).
fof(f1022,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1021]) ).
fof(f1027,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f173,f583]) ).
fof(f1032,plain,
( sk_c11 = sk_c10
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1027,f534]) ).
fof(f1033,plain,
( spl0_23
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1032,f309,f176,f171,f292]) ).
fof(f1057,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_20 ),
inference(superposition,[],[f3,f259]) ).
fof(f1058,plain,
( sk_c11 = multiply(sk_c12,sk_c1)
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1057,f310]) ).
fof(f1084,plain,
( ! [X0,X1] :
( sk_c11 != multiply(X0,multiply(X1,sk_c12))
| sk_c12 != inverse(multiply(X0,X1)) )
| ~ spl0_5 ),
inference(superposition,[],[f149,f4]) ).
fof(f1141,plain,
( sk_c11 != multiply(sk_c12,sk_c12)
| sk_c12 != inverse(multiply(sk_c6,sk_c11))
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f1084,f317]) ).
fof(f1155,plain,
( sk_c12 != inverse(multiply(sk_c6,sk_c11))
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1141,f369]) ).
fof(f1164,plain,
( sk_c12 != inverse(sk_c12)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1155,f183]) ).
fof(f1287,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c12,X0)) = X0
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f516,f534]) ).
fof(f1289,plain,
( sk_c1 = multiply(sk_c12,sk_c11)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20
| ~ spl0_25 ),
inference(superposition,[],[f1287,f1058]) ).
fof(f1293,plain,
( sk_c6 = multiply(sk_c12,identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(superposition,[],[f1287,f297]) ).
fof(f1298,plain,
( sk_c6 = multiply(sk_c12,sk_c11)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1293,f310]) ).
fof(f1300,plain,
( sk_c1 = sk_c12
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1289,f900]) ).
fof(f1301,plain,
( sk_c12 = sk_c6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1298,f900]) ).
fof(f1305,plain,
( sk_c11 != multiply(sk_c12,sk_c12)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20
| spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f269,f1300]) ).
fof(f1309,plain,
( $false
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20
| spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1305,f369]) ).
fof(f1310,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20
| spl0_21
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1309]) ).
fof(f1312,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(superposition,[],[f188,f1301]) ).
fof(f1320,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1312,f1164]) ).
fof(f1321,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1320]) ).
cnf(s1,plain,
( spl0_1
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f150]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f221]) ).
cnf(s30,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f222]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f232]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f233]) ).
cnf(s41,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f241]) ).
cnf(s42,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f242]) ).
cnf(s48,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f252]) ).
cnf(s49,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f253]) ).
cnf(s53,plain,
( spl0_8
| spl0_20 ),
inference(sat_conversion,[],[f261]) ).
cnf(s54,plain,
( spl0_9
| spl0_20 ),
inference(sat_conversion,[],[f262]) ).
cnf(s58,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f266]) ).
cnf(s60,plain,
( spl0_8
| spl0_21 ),
inference(sat_conversion,[],[f272]) ).
cnf(s61,plain,
( spl0_9
| spl0_21 ),
inference(sat_conversion,[],[f273]) ).
cnf(s63,plain,
( spl0_11
| spl0_21 ),
inference(sat_conversion,[],[f275]) ).
cnf(s64,plain,
( spl0_12
| spl0_21 ),
inference(sat_conversion,[],[f276]) ).
cnf(s65,plain,
( spl0_13
| spl0_21 ),
inference(sat_conversion,[],[f277]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f283]) ).
cnf(s68,plain,
( ~ spl0_2
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f312]) ).
cnf(s74,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_25 ),
inference(sat_conversion,[],[f530]) ).
cnf(s76,plain,
( ~ spl0_20
| ~ spl0_21
| spl0_25 ),
inference(sat_conversion,[],[f532]) ).
cnf(s78,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f553]) ).
cnf(s79,plain,
( ~ spl0_18
| spl0_22
| ~ spl0_25 ),
inference(sat_conversion,[],[f594]) ).
cnf(s83,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(sat_conversion,[],[f626]) ).
cnf(s85,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f655]) ).
cnf(s87,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f668]) ).
cnf(s92,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f708]) ).
cnf(s93,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f710]) ).
cnf(s95,plain,
( ~ spl0_5
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f716]) ).
cnf(s101,plain,
( ~ spl0_22
| ~ spl0_23
| spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f818]) ).
cnf(s103,plain,
( ~ spl0_13
| spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f997]) ).
cnf(s105,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f1019]) ).
cnf(s106,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f1022]) ).
cnf(s109,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s115,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20
| spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f1310]) ).
cnf(s117,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(sat_conversion,[],[f1321]) ).
cnf(s119,plain,
( spl0_21
| ~ spl0_5 ),
inference(rat,[],[s74,s117,s60,s61,s63,s64,s65]) ).
cnf(s120,plain,
( ~ spl0_21
| ~ spl0_5 ),
inference(rat,[],[s74,s103,s53,s54,s58,s95]) ).
cnf(s121,plain,
~ spl0_5,
inference(rat,[],[s120,s119]) ).
cnf(s122,plain,
( spl0_21
| ~ spl0_20 ),
inference(rat,[],[s74,s115,s60,s61,s63,s64,s65]) ).
cnf(s123,plain,
( spl0_23
| ~ spl0_11
| ~ spl0_25 ),
inference(rat,[],[s78,s41,s48,s109]) ).
cnf(s124,plain,
( ~ spl0_11
| ~ spl0_25
| ~ spl0_4 ),
inference(rat,[],[s123,s106]) ).
cnf(s125,plain,
( ~ spl0_25
| ~ spl0_4 ),
inference(rat,[],[s105,s78,s42,s49,s124]) ).
cnf(s126,plain,
( ~ spl0_20
| spl0_25 ),
inference(rat,[],[s76,s122]) ).
cnf(s127,plain,
spl0_25,
inference(rat,[],[s74,s53,s54,s126]) ).
cnf(s128,plain,
~ spl0_4,
inference(rat,[],[s125,s127]) ).
cnf(s129,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s85,s29,s36]) ).
cnf(s130,plain,
( ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s85,s30,s37,s87]) ).
cnf(s131,plain,
~ spl0_3,
inference(rat,[],[s130,s129]) ).
cnf(s132,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s83,s41,s48,s66,s127]) ).
cnf(s133,plain,
~ spl0_2,
inference(rat,[],[s101,s78,s79,s42,s49,s132,s68,s127]) ).
cnf(s134,plain,
spl0_1,
inference(rat,[],[s2,s121,s128,s131,s133]) ).
cnf(s135,plain,
~ spl0_11,
inference(rat,[],[s123,s93,s127,s134]) ).
cnf(s136,plain,
spl0_19,
inference(rat,[],[s49,s135]) ).
cnf(s137,plain,
spl0_18,
inference(rat,[],[s42,s135]) ).
cnf(s144,plain,
spl0_23,
inference(rat,[],[s78,s127,s136,s137]) ).
cnf(s145,plain,
$false,
inference(rat,[],[s92,s127,s134,s136,s137,s144]) ).
fof(f1322,plain,
$false,
inference(avatar_sat_refutation,[],[s145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP243-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:37:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.52/0.90 % (1164004)Input is clausal, will run a generic CNF schedule.
% 0.52/0.90 % (1164014)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2387165642:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.52/0.90 % (1164009)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=3959285680:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.52/0.90 % (1164011)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3174332495:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.52/0.90 % (1164010)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2784223386:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.52/0.90 % (1164012)lrs+10_1_sil=8000:sp=occurrence:random_seed=191499995:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.52/0.90 % (1164014)First to succeed.
% 0.52/0.90 % (1164015)dis-21_1_sil=8000:lcm=predicate:random_seed=323334874: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)
% 0.52/0.90 % (1164013)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=73283753:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.52/0.90 % (1164014)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1164004"
% 0.52/0.90 % (1164015)Refutation not found, incomplete strategy
% 0.52/0.90 % (1164015)------------------------------
% 0.52/0.90 % (1164015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.52/0.90 % (1164015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.90 % (1164015)CaDiCaL version: 2.1.3
% 0.52/0.90 % (1164015)Termination reason: Refutation not found, incomplete strategy
% 0.52/0.90 % (1164015)Time elapsed: 0.002 s
% 0.52/0.90 % (1164015)Peak memory usage: 88 MB
% 0.52/0.90 % (1164015)Instructions burned: 3 (million)
% 0.52/0.90 % (1164012)Instruction limit reached!
% 0.52/0.90 % (1164012)------------------------------
% 0.52/0.90 % (1164012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.52/0.90 % (1164012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.90 % (1164012)CaDiCaL version: 2.1.3
% 0.52/0.90 % (1164012)Termination reason: Instruction limit
% 0.52/0.90 % (1164012)Termination phase: Saturation
% 0.52/0.90 % (1164012)Time elapsed: 0.052 s
% 0.52/0.90 % (1164012)Peak memory usage: 89 MB
% 0.52/0.90 % (1164012)Instructions burned: 108 (million)
% 0.52/0.90 % (1164013)Instruction limit reached!
% 0.52/0.90 % (1164013)------------------------------
% 0.52/0.90 % (1164013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.52/0.90 % (1164013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.90 % (1164013)CaDiCaL version: 2.1.3
% 0.52/0.90 % (1164013)Termination reason: Instruction limit
% 0.52/0.90 % (1164013)Termination phase: Saturation
% 0.52/0.90 % (1164013)Time elapsed: 0.064 s
% 0.52/0.90 % (1164013)Peak memory usage: 89 MB
% 0.52/0.90 % (1164013)Instructions burned: 115 (million)
% 0.52/0.90 % (1164014)Refutation found. Thanks to Tanya!
% 0.52/0.90 % SZS status Unsatisfiable for theBenchmark
% 0.52/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/1.09 % (1164014)------------------------------
% 2.41/1.09 % (1164014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.09 % (1164014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.09 % (1164014)CaDiCaL version: 2.1.3
% 2.41/1.09 % (1164014)Termination reason: Refutation
% 2.41/1.09 % (1164014)Time elapsed: 0.014 s
% 2.41/1.09 % (1164014)Peak memory usage: 90 MB
% 2.41/1.09 % (1164014)Instructions burned: 40 (million)
% 2.41/1.09 % (1164014)------------------------------
% 2.41/1.09 % (1164014)------------------------------
% 2.41/1.09 % (1164004)Success in time 0.291 s
% 2.41/1.09 % Vampire exiting
%------------------------------------------------------------------------------