%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP251-1 : 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 : n009.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 10:13:27 AM UTC 2026
% Result : Unsatisfiable 2.63s 1.28s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 57
% Syntax : Number of formulae : 311 ( 21 unt; 19 def)
% Number of atoms : 910 ( 300 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1107 ( 508 ~; 580 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f79,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f97,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != 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_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f91,f99,f105,f102,f99,f96,f93]) ).
fof(f109,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f111,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f115,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f113,f109]) ).
fof(f118,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f113,f118]) ).
fof(f123,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f113,f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f131,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f113,f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f80,f113,f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f140,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f148,f109]) ).
fof(f152,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f72,f148,f118]) ).
fof(f153,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f70,f148,f123]) ).
fof(f154,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f148,f128]) ).
fof(f155,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f148,f133]) ).
fof(f159,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f161,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f159,f109]) ).
fof(f163,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f159,f118]) ).
fof(f164,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f159,f123]) ).
fof(f167,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f50,f159,f138]) ).
fof(f168,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f159,f143]) ).
fof(f170,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f172,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f170,f109]) ).
fof(f174,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f170,f118]) ).
fof(f175,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f170,f123]) ).
fof(f178,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f36,f170,f138]) ).
fof(f179,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f34,f170,f143]) ).
fof(f181,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f183,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_6
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f181,f109]) ).
fof(f185,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f181,f118]) ).
fof(f186,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f181,f123]) ).
fof(f187,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f181,f128]) ).
fof(f188,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f181,f133]) ).
fof(f189,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f181,f138]) ).
fof(f190,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f181,f143]) ).
fof(f192,definition,
( spl0_18
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f194,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f192,f109]) ).
fof(f196,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f192,f118]) ).
fof(f197,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f192,f123]) ).
fof(f198,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f192,f128]) ).
fof(f199,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f192,f133]) ).
fof(f200,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f192,f138]) ).
fof(f201,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f192,f143]) ).
fof(f202,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f97,f135]) ).
fof(f203,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f202]) ).
fof(f206,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f203,f133,f96,f128]) ).
fof(f207,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f97,f115]) ).
fof(f208,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f207]) ).
fof(f209,plain,
( sk_c9 != sk_c8
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f208,f150]) ).
fof(f211,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f183]) ).
fof(f222,definition,
( spl0_20
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f223,plain,
( identity = sk_c9
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( identity != sk_c9
| spl0_20 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f228,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f229,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_18 ),
inference(superposition,[],[f4,f194]) ).
fof(f230,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f211]) ).
fof(f238,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f230,f1]) ).
fof(f239,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f228,f1]) ).
fof(f255,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f238,f194]) ).
fof(f263,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f229,f255]) ).
fof(f265,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f263,f194]) ).
fof(f354,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f239,f265]) ).
fof(f359,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f239,f145]) ).
fof(f365,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f239,f120]) ).
fof(f369,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_7 ),
inference(superposition,[],[f239,f115]) ).
fof(f375,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f369,f150]) ).
fof(f379,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f365,f111]) ).
fof(f383,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f359,f140]) ).
fof(f384,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f354,f3]) ).
fof(f388,plain,
( sk_c9 = sk_c8
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f375,f265]) ).
fof(f397,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f388,f209]) ).
fof(f398,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f401,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f384,f192,f181,f222]) ).
fof(f405,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c6,sk_c9)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f106,f111]) ).
fof(f406,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f106,f161]) ).
fof(f409,plain,
( sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f406]) ).
fof(f410,plain,
( sk_c8 != multiply(sk_c6,sk_c9)
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f405]) ).
fof(f411,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f409,f172]) ).
fof(f412,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f411]) ).
fof(f413,plain,
( sk_c8 != sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f410,f120]) ).
fof(f435,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f100,f194]) ).
fof(f436,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f100,f145]) ).
fof(f437,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f436]) ).
fof(f438,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f435]) ).
fof(f439,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f437,f140]) ).
fof(f440,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f441,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f438,f183]) ).
fof(f442,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f441]) ).
fof(f450,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != multiply(sk_c9,multiply(X6,sk_c9)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f94,f388]) ).
fof(f455,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f450,f161]) ).
fof(f458,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f455]) ).
fof(f460,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f458,f172]) ).
fof(f472,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f460,f388]) ).
fof(f474,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f472,f265]) ).
fof(f475,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f474]) ).
fof(f478,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c9) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f103,f388]) ).
fof(f479,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f379,f125]) ).
fof(f483,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f239,f379]) ).
fof(f485,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f483,f3]) ).
fof(f488,plain,
( sk_c9 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_20 ),
inference(forward_demodulation,[],[f485,f223]) ).
fof(f492,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f478,f111]) ).
fof(f493,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f478,f161]) ).
fof(f496,plain,
( sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f493]) ).
fof(f497,plain,
( sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f492]) ).
fof(f498,plain,
( sk_c9 != sk_c8
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f496,f172]) ).
fof(f499,plain,
( sk_c9 != sk_c7
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f497,f120]) ).
fof(f510,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f498,f388]) ).
fof(f511,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f524,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f488,f499]) ).
fof(f525,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f524]) ).
fof(f563,plain,
( sk_c9 != sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_20 ),
inference(superposition,[],[f413,f488]) ).
fof(f570,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f563,f479]) ).
fof(f571,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f570]) ).
fof(f572,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c9) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f103,f479]) ).
fof(f576,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f572,f111]) ).
fof(f577,plain,
( sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f576]) ).
fof(f578,plain,
( sk_c9 != sk_c7
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f577,f120]) ).
fof(f580,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f578,f488]) ).
fof(f581,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f580]) ).
fof(f582,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != multiply(sk_c9,multiply(X6,sk_c9)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f94,f479]) ).
fof(f587,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f582,f111]) ).
fof(f588,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f587]) ).
fof(f589,plain,
( sk_c9 != multiply(sk_c9,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f588,f120]) ).
fof(f591,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f589,f379]) ).
fof(f592,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f591]) ).
fof(f618,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f239,f383]) ).
fof(f620,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f618,f3]) ).
fof(f623,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f620,f224]) ).
fof(f624,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f623]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f107]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s11,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s12,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s17,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
cnf(s18,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s19,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s22,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s23,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s24,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s25,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s26,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f175]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f178]) ).
cnf(s30,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f179]) ).
cnf(s31,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f184]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f185]) ).
cnf(s33,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
cnf(s34,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s35,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s38,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s39,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s40,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f197]) ).
cnf(s41,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f198]) ).
cnf(s42,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f199]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f206]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f398]) ).
cnf(s56,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f401]) ).
cnf(s58,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f412]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f440]) ).
cnf(s62,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f442]) ).
cnf(s66,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f475]) ).
cnf(s70,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f511]) ).
cnf(s71,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f525]) ).
cnf(s73,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(sat_conversion,[],[f571]) ).
cnf(s74,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(sat_conversion,[],[f581]) ).
cnf(s75,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f592]) ).
cnf(s76,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f624]) ).
cnf(s77,plain,
( spl0_6
| ~ spl0_5 ),
inference(rat,[],[s58,s17,s24]) ).
cnf(s78,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s73,s76,s25,s26,s29,s30,s77]) ).
cnf(s79,plain,
~ spl0_5,
inference(rat,[],[s73,s76,s18,s19,s22,s23,s58,s78,s77]) ).
cnf(s80,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s74,s76,s25,s26,s29,s30]) ).
cnf(s81,plain,
( spl0_13
| spl0_20 ),
inference(rat,[],[s56,s37,s44]) ).
cnf(s82,plain,
( ~ spl0_13
| spl0_20 ),
inference(rat,[],[s56,s36,s43,s76]) ).
cnf(s83,plain,
spl0_20,
inference(rat,[],[s82,s81]) ).
cnf(s84,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s71,s5,s12,s33,s40,s74,s83]) ).
cnf(s85,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s18,s70,s4,s11,s32,s39,s84,s80]) ).
cnf(s86,plain,
~ spl0_4,
inference(rat,[],[s70,s3,s10,s17,s24,s31,s38,s85]) ).
cnf(s87,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s61,s43,s44]) ).
cnf(s88,plain,
( ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s61,s36,s37,s62]) ).
cnf(s89,plain,
~ spl0_3,
inference(rat,[],[s88,s87]) ).
cnf(s91,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s46,s13,s14]) ).
cnf(s92,plain,
( spl0_7
| ~ spl0_2 ),
inference(rat,[],[s46,s6,s7]) ).
cnf(s93,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s46,s41,s42]) ).
cnf(s94,plain,
( ~ spl0_18
| ~ spl0_14
| ~ spl0_2
| ~ spl0_7 ),
inference(rat,[],[s46,s34,s35,s53]) ).
cnf(s95,plain,
~ spl0_2,
inference(rat,[],[s94,s93,s92,s91]) ).
cnf(s96,plain,
spl0_1,
inference(rat,[],[s2,s86,s79,s89,s95]) ).
cnf(s97,plain,
spl0_14,
inference(rat,[],[s75,s10,s11,s12,s96]) ).
cnf(s98,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s66,s19,s26,s96,s97]) ).
cnf(s99,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s66,s18,s25,s96,s97]) ).
cnf(s100,plain,
( ~ spl0_7
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s66,s17,s24,s75,s99,s98,s97,s96]) ).
cnf(s101,plain,
spl0_7,
inference(rat,[],[s75,s3,s4,s5,s96]) ).
cnf(s102,plain,
spl0_18,
inference(rat,[],[s75,s38,s39,s40,s96]) ).
cnf(s103,plain,
~ spl0_17,
inference(rat,[],[s100,s101,s102]) ).
cnf(s108,plain,
spl0_9,
inference(rat,[],[s33,s103]) ).
cnf(s109,plain,
spl0_8,
inference(rat,[],[s32,s103]) ).
cnf(s110,plain,
spl0_6,
inference(rat,[],[s31,s103]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s75,s108,s96,s110,s109]) ).
fof(f625,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.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 09:43:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.63/1.28 % (1781515)Input is clausal, will run a generic CNF schedule.
% 2.63/1.28 % (1781628)lrs+10_1_sil=8000:sp=occurrence:random_seed=3896747100:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.63/1.28 % (1781630)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=187797975:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.63/1.28 % (1781625)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=274744463:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.63/1.28 % (1781631)dis-21_1_sil=8000:lcm=predicate:random_seed=889257461: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)
% 2.63/1.28 % (1781624)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=844984571:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.63/1.28 % (1781627)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3432746859:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.63/1.28 % (1781629)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4251803624:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.63/1.28 % (1781631)Refutation not found, incomplete strategy
% 2.63/1.28 % (1781631)------------------------------
% 2.63/1.28 % (1781631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.28 % (1781631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.28 % (1781631)CaDiCaL version: 2.1.3
% 2.63/1.28 % (1781631)Termination reason: Refutation not found, incomplete strategy
% 2.63/1.28 % (1781631)Time elapsed: 0.002 s
% 2.63/1.28 % (1781631)Peak memory usage: 88 MB
% 2.63/1.28 % (1781631)Instructions burned: 2 (million)
% 2.63/1.28 % (1781630)First to succeed.
% 2.63/1.28 % (1781630)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1781515"
% 2.63/1.28 % (1781628)Instruction limit reached!
% 2.63/1.28 % (1781628)------------------------------
% 2.63/1.28 % (1781628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.28 % (1781628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.28 % (1781628)CaDiCaL version: 2.1.3
% 2.63/1.28 % (1781628)Termination reason: Instruction limit
% 2.63/1.28 % (1781628)Termination phase: Saturation
% 2.63/1.28 % (1781628)Time elapsed: 0.031 s
% 2.63/1.28 % (1781628)Peak memory usage: 89 MB
% 2.63/1.28 % (1781628)Instructions burned: 110 (million)
% 2.63/1.28 % (1781629)Instruction limit reached!
% 2.63/1.28 % (1781629)------------------------------
% 2.63/1.28 % (1781629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.28 % (1781629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.28 % (1781629)CaDiCaL version: 2.1.3
% 2.63/1.28 % (1781629)Termination reason: Instruction limit
% 2.63/1.28 % (1781629)Termination phase: Saturation
% 2.63/1.28 % (1781629)Time elapsed: 0.067 s
% 2.63/1.28 % (1781629)Peak memory usage: 89 MB
% 2.63/1.28 % (1781629)Instructions burned: 114 (million)
% 2.63/1.28 % (1781686)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=1038333722:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.63/1.28 % (1781686)Instruction limit reached!
% 2.63/1.28 % (1781686)------------------------------
% 2.63/1.28 % (1781686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.28 % (1781686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.28 % (1781686)CaDiCaL version: 2.1.3
% 2.63/1.28 % (1781686)Termination reason: Instruction limit
% 2.63/1.28 % (1781686)Termination phase: Saturation
% 2.63/1.28 % (1781686)Time elapsed: 0.039 s
% 2.63/1.28 % (1781686)Peak memory usage: 90 MB
% 2.63/1.28 % (1781686)Instructions burned: 148 (million)
% 2.63/1.28 % (1781687)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3929471944: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)
% 2.63/1.28 % (1781631)------------------------------
% 2.63/1.28 % (1781631)------------------------------
% 2.63/1.28 % (1781630)Refutation found. Thanks to Tanya!
% 2.63/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.63/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.47 % (1781630)------------------------------
% 3.65/1.47 % (1781630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.47 % (1781630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.47 % (1781630)CaDiCaL version: 2.1.3
% 3.65/1.47 % (1781630)Termination reason: Refutation
% 3.65/1.47 % (1781630)Time elapsed: 0.016 s
% 3.65/1.47 % (1781630)Peak memory usage: 90 MB
% 3.65/1.47 % (1781630)Instructions burned: 23 (million)
% 3.65/1.47 % (1781630)------------------------------
% 3.65/1.47 % (1781630)------------------------------
% 3.65/1.47 % (1781515)Success in time 0.44 s
% 3.65/1.47 % Vampire exiting
%------------------------------------------------------------------------------