%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP329-1 : 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 : 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 10:13:39 AM UTC 2026
% Result : Unsatisfiable 3.19s 1.33s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 46
% Syntax : Number of formulae : 288 ( 18 unt; 16 def)
% Number of atoms : 928 ( 283 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1215 ( 575 ~; 624 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 49 !; 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_c8,sk_c9) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f47,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c8
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(X5,sk_c9) != sk_c7
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f97,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( sk_c7 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,definition,
( spl0_5
<=> ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f107,plain,
( ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,definition,
( spl0_6
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f110,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( multiply(sk_c8,sk_c9) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f91,f109,f96,f106,f102,f99,f96,f93]) ).
fof(f114,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f116,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl0_8
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f88,f118,f114]) ).
fof(f123,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f86,f118,f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f130,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f84,f118,f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f82,f118,f133]) ).
fof(f147,plain,
( spl0_4
| spl0_8 ),
inference(avatar_split_clause,[],[f76,f118,f102]) ).
fof(f149,definition,
( spl0_14
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f151,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f149,f114]) ).
fof(f153,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f72,f149,f123]) ).
fof(f154,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f70,f149,f128]) ).
fof(f155,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f149,f133]) ).
fof(f158,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f149,f102]) ).
fof(f160,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f160,f114]) ).
fof(f164,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f160,f123]) ).
fof(f165,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f160,f128]) ).
fof(f166,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f160,f133]) ).
fof(f169,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f160,f102]) ).
fof(f171,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f173,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f176,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f171,f128]) ).
fof(f177,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f171,f133]) ).
fof(f180,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f34,f171,f102]) ).
fof(f182,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f184,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f187,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f182,f128]) ).
fof(f188,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f182,f133]) ).
fof(f191,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f182,f102]) ).
fof(f192,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f109,f114]) ).
fof(f193,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f109,f123]) ).
fof(f194,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f109,f128]) ).
fof(f195,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f109,f133]) ).
fof(f198,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f109,f102]) ).
fof(f199,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f103]) ).
fof(f205,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f211,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f205,f1]) ).
fof(f252,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_4 ),
inference(superposition,[],[f211,f199]) ).
fof(f257,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_11 ),
inference(superposition,[],[f211,f135]) ).
fof(f259,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f211,f125]) ).
fof(f264,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f259,f116]) ).
fof(f266,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f257,f130]) ).
fof(f277,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f211,f264]) ).
fof(f279,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f277,f3]) ).
fof(f281,plain,
( sk_c8 != sk_c7
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f111,f266]) ).
fof(f285,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f211,f266]) ).
fof(f287,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f285,f3]) ).
fof(f305,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f252,f279]) ).
fof(f306,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f305,f3]) ).
fof(f307,plain,
( sk_c8 = sk_c9
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f306,f287]) ).
fof(f308,plain,
( sk_c8 = sk_c7
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f306,f279]) ).
fof(f315,plain,
( $false
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f308,f281]) ).
fof(f316,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f317,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f110,f266]) ).
fof(f328,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f100,f317]) ).
fof(f332,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f328,f130]) ).
fof(f334,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f332]) ).
fof(f341,definition,
( spl0_19
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f342,plain,
( sk_c8 = sk_c9
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f343,plain,
( sk_c8 != sk_c9
| spl0_19 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f345,plain,
( sk_c8 != sk_c9
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f334,f135]) ).
fof(f348,plain,
( ~ spl0_19
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f345,f133,f128,f109,f99,f341]) ).
fof(f359,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f120]) ).
fof(f364,plain,
( spl0_19
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f307,f133,f128,f123,f114,f102,f341]) ).
fof(f380,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_14
| ~ spl0_19 ),
inference(forward_demodulation,[],[f151,f342]) ).
fof(f381,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f162,f342]) ).
fof(f382,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f184,f342]) ).
fof(f390,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f211,f381]) ).
fof(f392,plain,
( identity = sk_c3
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f390,f3]) ).
fof(f401,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f211,f382]) ).
fof(f403,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f401,f173]) ).
fof(f408,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_2
| ~ spl0_19 ),
inference(forward_demodulation,[],[f97,f342]) ).
fof(f411,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f408,f130]) ).
fof(f413,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f408,f173]) ).
fof(f415,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f413]) ).
fof(f416,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f411]) ).
fof(f418,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f415,f382]) ).
fof(f419,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f418]) ).
fof(f421,plain,
( sk_c8 != sk_c9
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f416,f135]) ).
fof(f426,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f421,f342]) ).
fof(f427,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f426]) ).
fof(f430,plain,
( ! [X2] :
( sk_c8 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c9 != inverse(X2) )
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f107,f342]) ).
fof(f431,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c8,multiply(X2,sk_c8)) )
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f430,f342]) ).
fof(f446,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f431,f130]) ).
fof(f449,plain,
( sk_c8 != sk_c9
| sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_19 ),
inference(superposition,[],[f431,f120]) ).
fof(f451,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f446]) ).
fof(f452,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f449,f342]) ).
fof(f455,plain,
( sk_c8 != multiply(sk_c8,sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f451,f135]) ).
fof(f457,plain,
( sk_c8 != multiply(sk_c8,sk_c3)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_19 ),
inference(forward_demodulation,[],[f452,f380]) ).
fof(f459,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f455,f266]) ).
fof(f460,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f461,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f457,f381]) ).
fof(f462,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f463,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_19 ),
inference(forward_demodulation,[],[f94,f342]) ).
fof(f464,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f463,f317]) ).
fof(f465,plain,
( ! [X5] :
( sk_c8 != inverse(X5)
| sk_c8 != multiply(X5,sk_c8) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f464,f342]) ).
fof(f470,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(superposition,[],[f465,f130]) ).
fof(f475,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f470]) ).
fof(f480,plain,
( sk_c8 != sk_c9
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f475,f135]) ).
fof(f485,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f480,f342]) ).
fof(f486,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f510,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f211,f151]) ).
fof(f512,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f510,f120]) ).
fof(f611,plain,
( sk_c8 = sk_c9
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f512,f162]) ).
fof(f612,plain,
( $false
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f611,f343]) ).
fof(f613,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f612]) ).
fof(f617,plain,
( spl0_19
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f611,f160,f149,f118,f341]) ).
fof(f633,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_19 ),
inference(forward_demodulation,[],[f110,f342]) ).
fof(f634,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_demodulation,[],[f359,f342]) ).
fof(f658,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_19 ),
inference(superposition,[],[f4,f633]) ).
fof(f662,plain,
( sk_c3 = multiply(sk_c8,sk_c2)
| ~ spl0_8
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f634,f392]) ).
fof(f692,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f403,f633]) ).
fof(f698,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f211,f403]) ).
fof(f700,plain,
( identity = sk_c8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f698,f3]) ).
fof(f731,plain,
( sk_c8 = sk_c3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f700,f392]) ).
fof(f734,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f658,f692]) ).
fof(f753,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f211,f734]) ).
fof(f756,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f753,f211]) ).
fof(f796,plain,
( sk_c3 = sk_c2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f662,f756]) ).
fof(f797,plain,
( sk_c8 = sk_c2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f796,f731]) ).
fof(f811,plain,
( sk_c9 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f120,f797]) ).
fof(f812,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f811,f342]) ).
fof(f834,plain,
( sk_c8 != sk_c7
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f104,f812]) ).
fof(f839,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f834,f692]) ).
fof(f840,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f839]) ).
fof(f843,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f463,f692]) ).
fof(f848,plain,
( ! [X5] :
( sk_c8 != inverse(X5)
| sk_c8 != multiply(X5,sk_c8) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f843,f342]) ).
fof(f853,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f848,f173]) ).
fof(f855,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f853]) ).
fof(f858,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f855,f382]) ).
fof(f859,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f858]) ).
fof(f865,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f100,f692]) ).
fof(f868,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f865,f173]) ).
fof(f870,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f868]) ).
fof(f873,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f870,f382]) ).
fof(f874,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f873]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f112]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f121]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s5,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s9,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f147]) ).
cnf(s10,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s11,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s12,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s13,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s16,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s17,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s18,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s19,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s20,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s23,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f169]) ).
cnf(s26,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s27,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s30,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f180]) ).
cnf(s33,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s34,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s37,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s38,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f192]) ).
cnf(s39,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f193]) ).
cnf(s40,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f194]) ).
cnf(s41,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f195]) ).
cnf(s44,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f198]) ).
cnf(s46,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f316]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f348]) ).
cnf(s51,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f364]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f419]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f427]) ).
cnf(s57,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f460]) ).
cnf(s58,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f462]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f486]) ).
cnf(s63,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f613]) ).
cnf(s64,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f617]) ).
cnf(s66,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f840]) ).
cnf(s67,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f859]) ).
cnf(s70,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f874]) ).
cnf(s73,plain,
spl0_4,
inference(rat,[],[s64,s66,s9,s16,s23,s30,s37,s44]) ).
cnf(s74,plain,
spl0_6,
inference(rat,[],[s46,s38,s39,s40,s41,s73]) ).
cnf(s75,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s57,s51,s73]) ).
cnf(s76,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s58,s64,s13,s20]) ).
cnf(s77,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s58,s64,s12,s19]) ).
cnf(s78,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s64,s11,s18,s57,s75,s77,s76]) ).
cnf(s79,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s75,s4,s5,s6,s78]) ).
cnf(s80,plain,
~ spl0_5,
inference(rat,[],[s58,s64,s3,s10,s17,s79]) ).
cnf(s82,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s64,s70,s6,s13,s20,s27,s34,s74]) ).
cnf(s83,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s64,s70,s5,s12,s19,s26,s33,s74]) ).
cnf(s84,plain,
( spl0_9
| spl0_19 ),
inference(rat,[],[s64,s4,s11,s18]) ).
cnf(s85,plain,
( spl0_19
| ~ spl0_11
| ~ spl0_10
| ~ spl0_9 ),
inference(rat,[],[s63,s3,s10,s17,s51,s73]) ).
cnf(s86,plain,
( ~ spl0_10
| ~ spl0_3
| ~ spl0_11 ),
inference(rat,[],[s85,s84,s48,s74]) ).
cnf(s87,plain,
~ spl0_3,
inference(rat,[],[s86,s83,s82]) ).
cnf(s88,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s85,s55]) ).
cnf(s89,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s63,s53,s6,s13,s20,s27,s34]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s63,s53,s5,s12,s19,s26,s33]) ).
cnf(s91,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(rat,[],[s84,s55,s88]) ).
cnf(s92,plain,
~ spl0_2,
inference(rat,[],[s91,s90,s89]) ).
cnf(s93,plain,
spl0_1,
inference(rat,[],[s2,s73,s80,s74,s87,s92]) ).
cnf(s94,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9 ),
inference(rat,[],[s61,s85,s93,s74]) ).
cnf(s95,plain,
spl0_11,
inference(rat,[],[s63,s67,s6,s13,s20,s27,s34,s74,s93]) ).
cnf(s96,plain,
spl0_10,
inference(rat,[],[s63,s67,s5,s12,s19,s26,s33,s74,s93]) ).
cnf(s97,plain,
~ spl0_19,
inference(rat,[],[s61,s93,s74,s96,s95]) ).
cnf(s98,plain,
~ spl0_9,
inference(rat,[],[s94,s95,s96]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s84,s97,s98]) ).
fof(f880,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP329-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:49:35 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.19/1.33 % (2295375)Input is clausal, will run a generic CNF schedule.
% 3.19/1.33 % (2295469)dis-21_1_sil=8000:lcm=predicate:random_seed=3771807596: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)
% 3.19/1.33 % (2295469)Refutation not found, incomplete strategy
% 3.19/1.33 % (2295469)------------------------------
% 3.19/1.33 % (2295469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (2295469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (2295469)CaDiCaL version: 2.1.3
% 3.19/1.33 % (2295469)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.33 % (2295469)Time elapsed: 0.001 s
% 3.19/1.33 % (2295469)Peak memory usage: 88 MB
% 3.19/1.33 % (2295469)Instructions burned: 2 (million)
% 3.19/1.33 % (2295465)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3861128479:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.19/1.33 % (2295460)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=422005344:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.19/1.33 % (2295464)lrs+10_1_sil=8000:sp=occurrence:random_seed=502518243:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.19/1.33 % (2295461)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=52598258:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.19/1.33 % (2295462)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=954381002:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.19/1.33 % (2295464)Refutation not found, incomplete strategy
% 3.19/1.33 % (2295464)------------------------------
% 3.19/1.33 % (2295464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (2295464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (2295464)CaDiCaL version: 2.1.3
% 3.19/1.33 % (2295464)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.33 % (2295464)Time elapsed: 0.003 s
% 3.19/1.33 % (2295464)Peak memory usage: 88 MB
% 3.19/1.33 % (2295464)Instructions burned: 3 (million)
% 3.19/1.33 % (2295467)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3049797124:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.19/1.33 % (2295467)First to succeed.
% 3.19/1.33 % (2295467)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2295375"
% 3.19/1.33 % (2295465)Instruction limit reached!
% 3.19/1.33 % (2295465)------------------------------
% 3.19/1.33 % (2295465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (2295465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (2295465)CaDiCaL version: 2.1.3
% 3.19/1.33 % (2295465)Termination reason: Instruction limit
% 3.19/1.33 % (2295465)Termination phase: Saturation
% 3.19/1.33 % (2295465)Time elapsed: 0.067 s
% 3.19/1.33 % (2295465)Peak memory usage: 89 MB
% 3.19/1.33 % (2295465)Instructions burned: 115 (million)
% 3.19/1.33 % (2295469)------------------------------
% 3.19/1.33 % (2295469)------------------------------
% 3.19/1.33 % (2295515)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=4049254678:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.19/1.33 % (2295515)Refutation not found, incomplete strategy
% 3.19/1.33 % (2295515)------------------------------
% 3.19/1.33 % (2295515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (2295515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (2295515)CaDiCaL version: 2.1.3
% 3.19/1.33 % (2295515)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.33 % (2295515)Time elapsed: 0.003 s
% 3.19/1.33 % (2295515)Peak memory usage: 88 MB
% 3.19/1.33 % (2295515)Instructions burned: 3 (million)
% 3.19/1.33 % (2295527)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3838796951: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)
% 3.19/1.33 % (2295527)Refutation not found, incomplete strategy
% 3.19/1.33 % (2295527)------------------------------
% 3.19/1.33 % (2295527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (2295527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (2295527)CaDiCaL version: 2.1.3
% 3.19/1.33 % (2295527)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.33 % (2295527)Time elapsed: 0.002 s
% 3.19/1.33 % (2295527)Peak memory usage: 88 MB
% 3.19/1.33 % (2295527)Instructions burned: 4 (million)
% 3.19/1.33 % (2295464)------------------------------
% 3.19/1.33 % (2295464)------------------------------
% 3.19/1.33 % (2295467)Refutation found. Thanks to Tanya!
% 3.19/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.19/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.53 % (2295467)------------------------------
% 3.95/1.53 % (2295467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.53 % (2295467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.53 % (2295467)CaDiCaL version: 2.1.3
% 3.95/1.53 % (2295467)Termination reason: Refutation
% 3.95/1.53 % (2295467)Time elapsed: 0.020 s
% 3.95/1.53 % (2295467)Peak memory usage: 90 MB
% 3.95/1.53 % (2295467)Instructions burned: 29 (million)
% 3.95/1.53 % (2295467)------------------------------
% 3.95/1.53 % (2295467)------------------------------
% 3.95/1.53 % (2295375)Success in time 0.464 s
% 3.95/1.53 % Vampire exiting
%------------------------------------------------------------------------------