%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP271-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 10:17:20 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 52
% Syntax : Number of formulae : 327 ( 21 unt; 20 def)
% Number of atoms : 1116 ( 368 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1513 ( 724 ~; 769 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = inverse(sk_c1)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c10 = inverse(sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f105]) ).
fof(f108,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f109,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| sk_c11 != multiply(X4,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_2
| ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f106,f114,f117,f111,f114,f111,f108]) ).
fof(f126,definition,
( spl0_6
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f128,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f146,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f148,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f94,f126,f146]) ).
fof(f151,definition,
( spl0_11
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f153,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f92,f126,f151]) ).
fof(f156,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f158,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f90,f126,f156]) ).
fof(f161,definition,
( spl0_13
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f163,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f88,f126,f161]) ).
fof(f166,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f168,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f86,f126,f166]) ).
fof(f171,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f172,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| spl0_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f173,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f176,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f178,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f183,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f74,f176,f146]) ).
fof(f184,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f72,f176,f151]) ).
fof(f185,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f70,f176,f156]) ).
fof(f186,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f68,f176,f161]) ).
fof(f187,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f66,f176,f166]) ).
fof(f193,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f54,f117,f146]) ).
fof(f194,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f52,f117,f151]) ).
fof(f195,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f50,f117,f156]) ).
fof(f196,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f48,f117,f161]) ).
fof(f197,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f46,f117,f166]) ).
fof(f198,plain,
( spl0_15
| spl0_4 ),
inference(avatar_split_clause,[],[f44,f117,f171]) ).
fof(f200,definition,
( spl0_17
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f202,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f207,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f200,f146]) ).
fof(f208,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f200,f151]) ).
fof(f209,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f200,f156]) ).
fof(f210,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f200,f161]) ).
fof(f211,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f200,f166]) ).
fof(f212,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f200,f171]) ).
fof(f214,definition,
( spl0_18
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f216,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f221,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f15,f214,f146]) ).
fof(f222,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f13,f214,f151]) ).
fof(f223,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f11,f214,f156]) ).
fof(f224,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f9,f214,f161]) ).
fof(f225,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f214,f166]) ).
fof(f226,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f214,f171]) ).
fof(f227,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f168]) ).
fof(f234,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f240,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f234,f1]) ).
fof(f243,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f227]) ).
fof(f244,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f243,f1]) ).
fof(f257,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f244,f173]) ).
fof(f306,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f240,f257]) ).
fof(f311,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f240,f163]) ).
fof(f314,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_11 ),
inference(superposition,[],[f240,f153]) ).
fof(f331,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f314,f148]) ).
fof(f334,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f311,f158]) ).
fof(f338,plain,
( identity = sk_c10
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f306,f3]) ).
fof(f371,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f240,f331]) ).
fof(f373,plain,
( identity = sk_c11
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f371,f3]) ).
fof(f378,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f227,f373]) ).
fof(f387,plain,
( identity = sk_c3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f378,f1]) ).
fof(f393,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f334,f338]) ).
fof(f394,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f393,f1]) ).
fof(f396,plain,
( sk_c10 != multiply(sk_c11,identity)
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f119,f394]) ).
fof(f397,plain,
( sk_c10 != multiply(identity,identity)
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f396,f373]) ).
fof(f399,plain,
( identity != sk_c10
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f397,f1]) ).
fof(f400,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f399,f338]) ).
fof(f401,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f402,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f115,f373]) ).
fof(f404,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f402,f338]) ).
fof(f406,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f404,f373]) ).
fof(f408,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f406,f1]) ).
fof(f413,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f408]) ).
fof(f427,plain,
( sk_c11 = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f168,f387]) ).
fof(f428,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f427,f373]) ).
fof(f476,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f428,f413]) ).
fof(f477,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f476]) ).
fof(f478,plain,
( ! [X6,X4] :
( identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f109,f373]) ).
fof(f479,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),identity)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f478,f338]) ).
fof(f480,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| identity != multiply(X4,inverse(X4))
| identity != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f479,f373]) ).
fof(f482,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| identity != multiply(sk_c4,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f480,f158]) ).
fof(f503,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c4,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f482,f338]) ).
fof(f514,plain,
( ! [X0] :
( identity != sk_c9
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f503,f163]) ).
fof(f517,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f514,f394]) ).
fof(f520,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f517,f338]) ).
fof(f522,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f520,f1]) ).
fof(f524,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f522,f338]) ).
fof(f534,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f524,f3]) ).
fof(f545,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f534,f428]) ).
fof(f547,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f545,f428]) ).
fof(f549,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f547,f428]) ).
fof(f552,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f549,f428]) ).
fof(f553,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f552,f428]) ).
fof(f554,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f553]) ).
fof(f555,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f112,f338]) ).
fof(f556,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f555,f394]) ).
fof(f557,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f556,f338]) ).
fof(f560,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f557,f3]) ).
fof(f562,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f560]) ).
fof(f564,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f562,f428]) ).
fof(f567,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f564,f428]) ).
fof(f568,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f571,plain,
( sk_c10 != multiply(sk_c3,identity)
| ~ spl0_10
| ~ spl0_11
| spl0_15 ),
inference(forward_demodulation,[],[f172,f373]) ).
fof(f572,plain,
( identity = inverse(sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f202,f373]) ).
fof(f573,plain,
( sk_c10 = multiply(sk_c1,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f216,f373]) ).
fof(f577,plain,
( sk_c10 != multiply(identity,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f571,f387]) ).
fof(f580,plain,
( identity != sk_c10
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f577,f1]) ).
fof(f582,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_6 ),
inference(superposition,[],[f3,f128]) ).
fof(f584,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f3,f572]) ).
fof(f585,plain,
( identity = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f584,f1]) ).
fof(f589,plain,
( sk_c10 = multiply(identity,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f573,f585]) ).
fof(f590,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f589,f1]) ).
fof(f591,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f590,f580]) ).
fof(f592,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f591]) ).
fof(f594,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f202]) ).
fof(f596,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c9,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f118]) ).
fof(f600,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f240,f216]) ).
fof(f602,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f600,f202]) ).
fof(f606,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f115,f216]) ).
fof(f607,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f606]) ).
fof(f608,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f607,f202]) ).
fof(f609,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f615,definition,
( spl0_29
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f616,plain,
( identity = sk_c10
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f617,plain,
( identity != sk_c10
| spl0_29 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f643,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_29 ),
inference(forward_demodulation,[],[f112,f616]) ).
fof(f644,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_29 ),
inference(forward_demodulation,[],[f643,f616]) ).
fof(f645,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_6
| ~ spl0_29 ),
inference(forward_demodulation,[],[f582,f616]) ).
fof(f646,plain,
( identity = sk_c2
| ~ spl0_6
| ~ spl0_29 ),
inference(forward_demodulation,[],[f645,f1]) ).
fof(f648,plain,
( sk_c9 = multiply(identity,sk_c10)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_29 ),
inference(superposition,[],[f178,f646]) ).
fof(f649,plain,
( sk_c10 = inverse(identity)
| ~ spl0_6
| ~ spl0_29 ),
inference(superposition,[],[f128,f646]) ).
fof(f650,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_29 ),
inference(forward_demodulation,[],[f649,f616]) ).
fof(f651,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_16
| ~ spl0_29 ),
inference(forward_demodulation,[],[f648,f1]) ).
fof(f652,plain,
( identity = sk_c9
| ~ spl0_6
| ~ spl0_16
| ~ spl0_29 ),
inference(forward_demodulation,[],[f651,f616]) ).
fof(f653,plain,
( identity != sk_c9
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_29 ),
inference(superposition,[],[f644,f1]) ).
fof(f662,definition,
( spl0_33
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f663,plain,
( identity = sk_c9
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f667,definition,
( spl0_34
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f668,plain,
( identity = inverse(identity)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f670,plain,
( ~ spl0_34
| ~ spl0_33
| ~ spl0_2
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f653,f615,f111,f662,f667]) ).
fof(f673,plain,
( spl0_33
| ~ spl0_6
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f652,f615,f176,f126,f662]) ).
fof(f681,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_29 ),
inference(forward_demodulation,[],[f109,f616]) ).
fof(f682,plain,
( spl0_34
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f650,f615,f126,f667]) ).
fof(f722,definition,
( spl0_41
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f734,definition,
( spl0_42
<=> ! [X0] :
( identity != inverse(inverse(X0))
| inverse(X0) != multiply(X0,identity) ) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f735,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f737,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c11 != multiply(identity,identity)
| sk_c11 != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_29
| ~ spl0_34 ),
inference(superposition,[],[f681,f668]) ).
fof(f740,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c11 != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_29
| ~ spl0_34 ),
inference(duplicate_literal_removal,[],[f737]) ).
fof(f742,plain,
( ! [X0] :
( identity != sk_c11
| inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_29
| ~ spl0_34 ),
inference(forward_demodulation,[],[f740,f1]) ).
fof(f757,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c11,multiply(identity,X0))
| ~ spl0_4
| ~ spl0_33 ),
inference(forward_demodulation,[],[f596,f663]) ).
fof(f758,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c10,X0)
| ~ spl0_4
| ~ spl0_33 ),
inference(forward_demodulation,[],[f757,f1]) ).
fof(f759,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,X0)
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_demodulation,[],[f758,f616]) ).
fof(f760,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_demodulation,[],[f759,f1]) ).
fof(f762,plain,
( identity = sk_c1
| ~ spl0_4
| ~ spl0_17
| ~ spl0_29
| ~ spl0_33 ),
inference(superposition,[],[f760,f594]) ).
fof(f780,plain,
( sk_c11 = inverse(identity)
| ~ spl0_4
| ~ spl0_17
| ~ spl0_29
| ~ spl0_33 ),
inference(superposition,[],[f202,f762]) ).
fof(f781,plain,
( identity = sk_c11
| ~ spl0_4
| ~ spl0_17
| ~ spl0_29
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_demodulation,[],[f780,f668]) ).
fof(f789,plain,
( spl0_42
| ~ spl0_41
| ~ spl0_1
| ~ spl0_29
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f742,f667,f615,f108,f722,f734]) ).
fof(f790,plain,
( spl0_41
| ~ spl0_4
| ~ spl0_17
| ~ spl0_29
| ~ spl0_33
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f781,f667,f662,f615,f200,f117,f722]) ).
fof(f828,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_42 ),
inference(superposition,[],[f735,f3]) ).
fof(f833,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_demodulation,[],[f828,f668]) ).
fof(f836,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f833,f668]) ).
fof(f839,plain,
( identity != inverse(inverse(identity))
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_demodulation,[],[f836,f668]) ).
fof(f843,plain,
( identity != inverse(identity)
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_demodulation,[],[f839,f668]) ).
fof(f846,plain,
( $false
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f843,f668]) ).
fof(f847,plain,
( ~ spl0_34
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f846]) ).
fof(f876,definition,
( spl0_43
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f877,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f898,plain,
( spl0_43
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f602,f214,f200,f876]) ).
fof(f899,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_43 ),
inference(superposition,[],[f240,f877]) ).
fof(f902,plain,
( identity = sk_c10
| ~ spl0_43 ),
inference(forward_demodulation,[],[f899,f3]) ).
fof(f903,plain,
( $false
| spl0_29
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f902,f617]) ).
fof(f904,plain,
( spl0_29
| ~ spl0_43 ),
inference(avatar_contradiction_clause,[],[f903]) ).
cnf(s1,plain,
( spl0_2
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f120]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f159]) ).
cnf(s10,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f164]) ).
cnf(s11,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f169]) ).
cnf(s17,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f183]) ).
cnf(s18,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f184]) ).
cnf(s19,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f185]) ).
cnf(s20,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f186]) ).
cnf(s21,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s27,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f193]) ).
cnf(s28,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f194]) ).
cnf(s29,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f195]) ).
cnf(s30,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f196]) ).
cnf(s31,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f197]) ).
cnf(s32,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f198]) ).
cnf(s37,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s38,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s39,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f209]) ).
cnf(s40,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f210]) ).
cnf(s41,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f211]) ).
cnf(s42,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f212]) ).
cnf(s47,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s48,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s49,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f223]) ).
cnf(s50,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f224]) ).
cnf(s51,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f225]) ).
cnf(s52,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f226]) ).
cnf(s53,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f401]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f477]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f554]) ).
cnf(s63,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f568]) ).
cnf(s64,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f592]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f609]) ).
cnf(s70,plain,
( ~ spl0_2
| ~ spl0_29
| ~ spl0_33
| ~ spl0_34 ),
inference(sat_conversion,[],[f670]) ).
cnf(s72,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_29
| spl0_33 ),
inference(sat_conversion,[],[f673]) ).
cnf(s74,plain,
( ~ spl0_6
| ~ spl0_29
| spl0_34 ),
inference(sat_conversion,[],[f682]) ).
cnf(s83,plain,
( ~ spl0_1
| ~ spl0_29
| ~ spl0_34
| ~ spl0_41
| spl0_42 ),
inference(sat_conversion,[],[f789]) ).
cnf(s84,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_29
| ~ spl0_33
| ~ spl0_34
| spl0_41 ),
inference(sat_conversion,[],[f790]) ).
cnf(s92,plain,
( ~ spl0_34
| ~ spl0_42 ),
inference(sat_conversion,[],[f847]) ).
cnf(s96,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_43 ),
inference(sat_conversion,[],[f898]) ).
cnf(s97,plain,
( spl0_29
| ~ spl0_43 ),
inference(sat_conversion,[],[f904]) ).
cnf(s98,plain,
spl0_4,
inference(rat,[],[s53,s27,s28,s29,s30,s31,s32]) ).
cnf(s100,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_3
| ~ spl0_10 ),
inference(rat,[],[s64,s42,s52,s55]) ).
cnf(s101,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s65,s41,s51]) ).
cnf(s102,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s65,s38,s48]) ).
cnf(s103,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s65,s37,s47,s100]) ).
cnf(s104,plain,
~ spl0_3,
inference(rat,[],[s103,s102,s101]) ).
cnf(s105,plain,
( spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s63,s19,s20]) ).
cnf(s106,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_29
| ~ spl0_2 ),
inference(rat,[],[s70,s72,s74]) ).
cnf(s107,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s63,s9,s10,s106,s105,s97,s64,s96]) ).
cnf(s108,plain,
( spl0_18
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s63,s49,s50,s52]) ).
cnf(s109,plain,
( ~ spl0_18
| ~ spl0_14
| ~ spl0_2
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s63,s39,s40,s42,s107]) ).
cnf(s110,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_2
| ~ spl0_10 ),
inference(rat,[],[s109,s108]) ).
cnf(s111,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s97,s106,s96,s11,s21,s41,s51]) ).
cnf(s112,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s97,s106,s96,s8,s18,s38,s48]) ).
cnf(s113,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s97,s106,s96,s7,s17,s37,s47,s110]) ).
cnf(s114,plain,
~ spl0_2,
inference(rat,[],[s113,s112,s111]) ).
cnf(s115,plain,
spl0_1,
inference(rat,[],[s2,s98,s104,s114]) ).
cnf(s116,plain,
( spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s61,s19,s20,s115]) ).
cnf(s117,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_29
| ~ spl0_17 ),
inference(rat,[],[s84,s83,s92,s72,s74,s98,s115]) ).
cnf(s118,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s61,s9,s10,s117,s116,s97,s64,s96,s115]) ).
cnf(s119,plain,
( spl0_17
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s61,s39,s40,s42,s115]) ).
cnf(s120,plain,
( ~ spl0_17
| ~ spl0_14
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s61,s49,s50,s52,s118,s115]) ).
cnf(s121,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s120,s119]) ).
cnf(s122,plain,
spl0_14,
inference(rat,[],[s97,s117,s96,s11,s21,s41,s51]) ).
cnf(s123,plain,
spl0_11,
inference(rat,[],[s97,s117,s96,s8,s18,s38,s48]) ).
cnf(s124,plain,
~ spl0_10,
inference(rat,[],[s121,s122,s123]) ).
cnf(s125,plain,
spl0_18,
inference(rat,[],[s47,s124]) ).
cnf(s126,plain,
spl0_17,
inference(rat,[],[s37,s124]) ).
cnf(s127,plain,
spl0_16,
inference(rat,[],[s17,s124]) ).
cnf(s128,plain,
spl0_6,
inference(rat,[],[s7,s124]) ).
cnf(s129,plain,
spl0_43,
inference(rat,[],[s96,s126,s125]) ).
cnf(s130,plain,
~ spl0_29,
inference(rat,[],[s117,s126,s127,s128]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s97,s129,s130]) ).
fof(f905,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP271-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:46:26 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.49 % (2584414)Will run a generic schedule for satisfiability detection.
% 0.15/0.49 % (2584419)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3457795914_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.49 % TRYING [1]
% 0.15/0.49 % TRYING [2]
% 0.15/0.49 % (2584420)% WARNING: option uhcvi not known.
% 0.15/0.49 % TRYING [3]
% 0.15/0.49 % TRYING [4]
% 0.15/0.49 % (2584420)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3219925322:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.49 % (2584421)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1494428170:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.49 % (2584422)dis+10_1_sil=32000:sp=arity:random_seed=2677792620:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.49 % (2584424)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3084623663:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.49 % (2584423)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2504544430:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.49 % (2584425)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2092256646:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.49 % TRYING [5]
% 0.15/0.49 % (2584422) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2584414-2584422"...
% 0.15/0.49 % (2584422)...printing done.
% 0.15/0.49 % (2584422)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (2584422)------------------------------
% 0.15/0.49 % (2584422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (2584422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (2584422)CaDiCaL version: 2.1.3
% 0.15/0.49 % (2584422)Termination reason: Refutation
% 0.15/0.49 % (2584422)Time elapsed: 0.020 s
% 0.15/0.49 % (2584422)Peak memory usage: 12 MB
% 0.15/0.49 % (2584422)Instructions burned: 32 (million)
% 0.15/0.49 % (2584414)Success in time 0.06 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------