%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP373-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 10:17:37 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 43
% Syntax : Number of formulae : 312 ( 23 unt; 21 def)
% Number of atoms : 1142 ( 370 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1642 ( 812 ~; 809 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c10 = multiply(sk_c1,sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c10 = multiply(sk_c1,sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f63,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f103,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
( sk_c9 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f106,plain,
( sk_c9 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f105]) ).
fof(f123,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c9
| 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/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f124,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c10 != multiply(X1,sk_c9)
| sk_c9 != 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,[],[f123]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( inverse(sk_c11) != sk_c10
| sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c10 != multiply(X1,sk_c9)
| sk_c9 != 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,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X0,X1,X6,X4] :
( inverse(sk_c11) != sk_c10
| sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c10 != multiply(X1,sk_c9)
| sk_c9 != 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,[],[f125]) ).
fof(f128,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(f129,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,[],[f128]) ).
fof(f131,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f132,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f135,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl0_4
<=> ! [X1] :
( sk_c10 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f138,plain,
( ! [X1] :
( sk_c10 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl0_5
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f141,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f142,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl0_6
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f145,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f146,plain,
( inverse(sk_c11) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f126,f144,f134,f140,f137,f134,f131,f128]) ).
fof(f153,definition,
( spl0_8
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f155,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f173,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f175,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f178,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f180,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f183,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f185,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f188,definition,
( spl0_15
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f190,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f193,definition,
( spl0_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f195,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f106,f153,f193]) ).
fof(f198,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f199,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| spl0_17 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f104,f153,f198]) ).
fof(f203,definition,
( spl0_18
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f214,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f86,f203,f193]) ).
fof(f215,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f84,f203,f198]) ).
fof(f220,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f74,f140,f173]) ).
fof(f221,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f72,f140,f178]) ).
fof(f222,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f70,f140,f183]) ).
fof(f223,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f68,f140,f188]) ).
fof(f224,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f66,f140,f193]) ).
fof(f225,plain,
( spl0_17
| spl0_5 ),
inference(avatar_split_clause,[],[f64,f140,f198]) ).
fof(f227,definition,
( spl0_19
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f229,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f238,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f46,f227,f193]) ).
fof(f239,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f44,f227,f198]) ).
fof(f241,definition,
( spl0_20
<=> sk_c10 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f243,plain,
( sk_c10 = multiply(sk_c1,sk_c11)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f252,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f26,f241,f193]) ).
fof(f253,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f24,f241,f198]) ).
fof(f258,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f144,f173]) ).
fof(f259,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f144,f178]) ).
fof(f262,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f144,f193]) ).
fof(f263,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f144,f198]) ).
fof(f264,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_16 ),
inference(superposition,[],[f3,f195]) ).
fof(f271,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f277,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f271,f1]) ).
fof(f280,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f264]) ).
fof(f281,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f280,f1]) ).
fof(f294,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f281,f200]) ).
fof(f343,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f277,f294]) ).
fof(f348,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f277,f190]) ).
fof(f351,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_13 ),
inference(superposition,[],[f277,f180]) ).
fof(f368,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f351,f175]) ).
fof(f371,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f348,f185]) ).
fof(f375,plain,
( identity = sk_c10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f343,f3]) ).
fof(f408,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f277,f368]) ).
fof(f410,plain,
( identity = sk_c11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f408,f3]) ).
fof(f415,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f264,f410]) ).
fof(f424,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f415,f1]) ).
fof(f430,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f371,f375]) ).
fof(f431,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f430,f1]) ).
fof(f433,plain,
( sk_c10 != multiply(sk_c11,identity)
| spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f142,f431]) ).
fof(f434,plain,
( sk_c10 != multiply(identity,identity)
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f433,f410]) ).
fof(f436,plain,
( identity != sk_c10
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f434,f1]) ).
fof(f437,plain,
( $false
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f436,f375]) ).
fof(f438,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f437]) ).
fof(f440,plain,
( identity != inverse(sk_c11)
| spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f146,f375]) ).
fof(f442,plain,
( identity != inverse(identity)
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f440,f410]) ).
fof(f448,plain,
( sk_c11 = inverse(identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f195,f424]) ).
fof(f449,plain,
( identity = inverse(identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f448,f410]) ).
fof(f454,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f449,f442]) ).
fof(f455,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f460,plain,
( identity = inverse(sk_c11)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f145,f375]) ).
fof(f565,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f132,f375]) ).
fof(f598,plain,
( ! [X2] :
( identity != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f135,f375]) ).
fof(f603,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f460]) ).
fof(f604,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f603,f1]) ).
fof(f611,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f460,f604]) ).
fof(f651,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f598,f604]) ).
fof(f652,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f651,f604]) ).
fof(f658,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f652,f3]) ).
fof(f662,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f658]) ).
fof(f665,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f662,f611]) ).
fof(f670,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f665,f611]) ).
fof(f671,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f672,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_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f129,f604]) ).
fof(f673,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_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f672,f375]) ).
fof(f674,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_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f673,f604]) ).
fof(f677,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f674,f460]) ).
fof(f695,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f677,f1]) ).
fof(f702,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f695,f604]) ).
fof(f709,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f702,f1]) ).
fof(f759,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f141,f604]) ).
fof(f761,plain,
( ! [X1] :
( identity != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f138,f375]) ).
fof(f763,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f759,f1]) ).
fof(f764,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f763,f375]) ).
fof(f776,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f761,f764]) ).
fof(f777,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f776,f764]) ).
fof(f781,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f777,f3]) ).
fof(f785,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f781]) ).
fof(f788,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f785,f611]) ).
fof(f793,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f788,f611]) ).
fof(f794,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f793]) ).
fof(f849,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f709,f3]) ).
fof(f854,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f849,f611]) ).
fof(f857,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f854,f611]) ).
fof(f860,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f857,f611]) ).
fof(f865,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f860,f611]) ).
fof(f866,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f865,f611]) ).
fof(f867,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f866]) ).
fof(f869,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f565,f764]) ).
fof(f871,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f869,f375]) ).
fof(f876,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f871,f3]) ).
fof(f880,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f876]) ).
fof(f883,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f880,f611]) ).
fof(f888,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f883,f611]) ).
fof(f889,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f888]) ).
fof(f891,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6 ),
inference(superposition,[],[f3,f145]) ).
fof(f894,plain,
( sk_c9 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f277,f141]) ).
fof(f895,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c9,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f141]) ).
fof(f896,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f894,f145]) ).
fof(f897,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f277,f205]) ).
fof(f899,plain,
( sk_c9 = multiply(sk_c9,sk_c10)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f897,f155]) ).
fof(f909,plain,
( identity != sk_c9
| sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_2 ),
inference(superposition,[],[f132,f3]) ).
fof(f918,definition,
( spl0_31
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f919,plain,
( sk_c11 = sk_c9
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f920,plain,
( sk_c11 != sk_c9
| spl0_31 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f928,definition,
( spl0_33
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f929,plain,
( identity = sk_c9
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f937,definition,
( spl0_35
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f938,plain,
( sk_c10 = sk_c9
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f951,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20 ),
inference(superposition,[],[f135,f243]) ).
fof(f952,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f951]) ).
fof(f953,plain,
( $false
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f952,f229]) ).
fof(f954,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f953]) ).
fof(f960,definition,
( spl0_37
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f961,plain,
( identity = sk_c10
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f985,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| sk_c11 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity))
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1 ),
inference(superposition,[],[f129,f1]) ).
fof(f1048,plain,
( multiply(sk_c11,sk_c9) = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f895,f899]) ).
fof(f1049,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f277,f899]) ).
fof(f1051,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1049,f3]) ).
fof(f1052,plain,
( sk_c9 = multiply(sk_c11,sk_c9)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1048,f896]) ).
fof(f1054,plain,
( spl0_37
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1051,f203,f153,f960]) ).
fof(f1055,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1052,f141]) ).
fof(f1056,plain,
( spl0_35
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1055,f203,f153,f144,f140,f937]) ).
fof(f1069,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_6
| ~ spl0_37 ),
inference(superposition,[],[f891,f961]) ).
fof(f1070,plain,
( sk_c9 = multiply(identity,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_37 ),
inference(superposition,[],[f896,f961]) ).
fof(f1077,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1070,f1]) ).
fof(f1078,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1069,f1]) ).
fof(f1084,plain,
( spl0_33
| ~ spl0_5
| ~ spl0_6
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1077,f960,f144,f140,f928]) ).
fof(f1096,plain,
( identity != sk_c11
| spl0_31
| ~ spl0_33 ),
inference(superposition,[],[f920,f929]) ).
fof(f1121,plain,
( $false
| ~ spl0_6
| spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1078,f1096]) ).
fof(f1122,plain,
( ~ spl0_6
| spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1121]) ).
fof(f1123,plain,
( identity = sk_c11
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_demodulation,[],[f919,f929]) ).
fof(f1129,plain,
( sk_c10 = inverse(identity)
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33 ),
inference(superposition,[],[f145,f1123]) ).
fof(f1132,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_16
| ~ spl0_31
| ~ spl0_33 ),
inference(superposition,[],[f264,f1123]) ).
fof(f1143,plain,
( identity = sk_c3
| ~ spl0_16
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1132,f1]) ).
fof(f1146,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1129,f961]) ).
fof(f1182,plain,
( sk_c10 != multiply(identity,sk_c11)
| ~ spl0_16
| spl0_17
| ~ spl0_31
| ~ spl0_33 ),
inference(superposition,[],[f199,f1143]) ).
fof(f1189,plain,
( sk_c11 != sk_c10
| ~ spl0_16
| spl0_17
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1182,f1]) ).
fof(f1193,plain,
( identity != sk_c11
| ~ spl0_16
| spl0_17
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1189,f961]) ).
fof(f1194,plain,
( $false
| ~ spl0_16
| spl0_17
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1193,f1123]) ).
fof(f1195,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1194]) ).
fof(f1212,definition,
( spl0_52
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1213,plain,
( identity = inverse(identity)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f1217,plain,
( spl0_52
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1146,f960,f928,f918,f144,f1212]) ).
fof(f1222,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c11 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity))
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1
| ~ spl0_52 ),
inference(forward_demodulation,[],[f985,f1213]) ).
fof(f1223,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| identity != inverse(X0)
| inverse(X0) != inverse(inverse(identity))
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_33
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1222,f1123]) ).
fof(f1224,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| identity != multiply(X0,inverse(X0))
| identity != inverse(X0)
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_33
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1223,f1213]) ).
fof(f1225,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != multiply(X0,inverse(X0))
| identity != inverse(X0)
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_33
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1224,f1213]) ).
fof(f1226,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != multiply(X0,inverse(X0))
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_33
| ~ spl0_52 ),
inference(duplicate_literal_removal,[],[f1225]) ).
fof(f1227,plain,
( ! [X0] :
( sk_c11 != multiply(inverse(X0),identity)
| identity != inverse(X0)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1226,f961]) ).
fof(f1228,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != inverse(X0)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1227,f1123]) ).
fof(f1234,plain,
( identity != multiply(sk_c11,identity)
| identity != sk_c11
| identity != multiply(sk_c1,sk_c11)
| ~ spl0_1
| ~ spl0_19
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(superposition,[],[f1228,f229]) ).
fof(f1242,plain,
( identity != multiply(sk_c11,identity)
| identity != multiply(sk_c1,sk_c11)
| ~ spl0_1
| ~ spl0_19
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1234,f1123]) ).
fof(f1250,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c1,sk_c11)
| ~ spl0_1
| ~ spl0_19
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1242,f1123]) ).
fof(f1255,plain,
( identity != multiply(sk_c1,sk_c11)
| ~ spl0_1
| ~ spl0_19
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1250,f1]) ).
fof(f1258,plain,
( identity != sk_c10
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1255,f243]) ).
fof(f1261,plain,
( $false
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1258,f961]) ).
fof(f1262,plain,
( ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f1261]) ).
fof(f1268,plain,
( ! [X1] :
( sk_c10 != multiply(X1,sk_c10)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_35 ),
inference(forward_demodulation,[],[f138,f938]) ).
fof(f1269,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1268,f961]) ).
fof(f1270,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| identity != multiply(X1,identity) )
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1269,f938]) ).
fof(f1271,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1270,f961]) ).
fof(f1274,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37 ),
inference(superposition,[],[f1271,f3]) ).
fof(f1276,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f1274]) ).
fof(f1278,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1276,f1213]) ).
fof(f1281,plain,
( $false
| ~ spl0_4
| ~ spl0_35
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1278,f1213]) ).
fof(f1282,plain,
( ~ spl0_4
| ~ spl0_35
| ~ spl0_37
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f1281]) ).
fof(f1287,plain,
( sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_2
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f909,f929]) ).
fof(f1294,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_33
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1287,f961]) ).
fof(f1301,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1294,f1213]) ).
fof(f1305,plain,
( $false
| ~ spl0_2
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1301,f1213]) ).
fof(f1306,plain,
( ~ spl0_2
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f1305]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f147]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s11,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f196]) ).
cnf(s12,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s21,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s22,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s27,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f220]) ).
cnf(s28,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f221]) ).
cnf(s29,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f222]) ).
cnf(s30,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f223]) ).
cnf(s31,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f224]) ).
cnf(s32,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f225]) ).
cnf(s41,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f238]) ).
cnf(s42,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f239]) ).
cnf(s51,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f252]) ).
cnf(s52,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f253]) ).
cnf(s57,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f258]) ).
cnf(s58,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f259]) ).
cnf(s61,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f262]) ).
cnf(s62,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f263]) ).
cnf(s63,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f438]) ).
cnf(s64,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f455]) ).
cnf(s80,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f671]) ).
cnf(s91,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f794]) ).
cnf(s95,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f867]) ).
cnf(s98,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f889]) ).
cnf(s103,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f954]) ).
cnf(s117,plain,
( ~ spl0_8
| ~ spl0_18
| spl0_37 ),
inference(sat_conversion,[],[f1054]) ).
cnf(s118,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| spl0_35 ),
inference(sat_conversion,[],[f1056]) ).
cnf(s120,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_33
| ~ spl0_37 ),
inference(sat_conversion,[],[f1084]) ).
cnf(s121,plain,
( ~ spl0_6
| spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(sat_conversion,[],[f1122]) ).
cnf(s126,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37 ),
inference(sat_conversion,[],[f1195]) ).
cnf(s130,plain,
( ~ spl0_6
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| spl0_52 ),
inference(sat_conversion,[],[f1217]) ).
cnf(s133,plain,
( ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(sat_conversion,[],[f1262]) ).
cnf(s137,plain,
( ~ spl0_4
| ~ spl0_35
| ~ spl0_37
| ~ spl0_52 ),
inference(sat_conversion,[],[f1282]) ).
cnf(s141,plain,
( ~ spl0_2
| ~ spl0_33
| ~ spl0_37
| ~ spl0_52 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s142,plain,
spl0_5,
inference(rat,[],[s63,s27,s28,s29,s30,s31,s32]) ).
cnf(s143,plain,
spl0_6,
inference(rat,[],[s64,s57,s58,s61,s62]) ).
cnf(s144,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s91,s11,s12,s143,s142]) ).
cnf(s145,plain,
( ~ spl0_33
| spl0_52
| ~ spl0_37 ),
inference(rat,[],[s121,s130,s143]) ).
cnf(s146,plain,
( ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s145,s137,s120,s118,s117,s144,s142,s143]) ).
cnf(s147,plain,
~ spl0_4,
inference(rat,[],[s91,s21,s22,s146,s143,s142]) ).
cnf(s148,plain,
( ~ spl0_16
| ~ spl0_3
| ~ spl0_37
| ~ spl0_33 ),
inference(rat,[],[s126,s80,s121,s143]) ).
cnf(s149,plain,
( ~ spl0_3
| ~ spl0_37
| ~ spl0_33 ),
inference(rat,[],[s103,s41,s51,s148]) ).
cnf(s150,plain,
( ~ spl0_37
| ~ spl0_33
| spl0_1 ),
inference(rat,[],[s149,s2,s141,s145,s143,s147,s142]) ).
cnf(s151,plain,
( spl0_17
| ~ spl0_3 ),
inference(rat,[],[s103,s42,s52]) ).
cnf(s152,plain,
( ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s103,s41,s51,s80,s143]) ).
cnf(s153,plain,
~ spl0_3,
inference(rat,[],[s152,s151]) ).
cnf(s154,plain,
( spl0_17
| spl0_37 ),
inference(rat,[],[s117,s12,s22]) ).
cnf(s155,plain,
( spl0_37
| ~ spl0_2 ),
inference(rat,[],[s117,s11,s21,s98,s154,s143,s142]) ).
cnf(s156,plain,
spl0_1,
inference(rat,[],[s150,s120,s155,s2,s142,s143,s153,s147]) ).
cnf(s157,plain,
spl0_17,
inference(rat,[],[s133,s121,s145,s120,s154,s42,s52,s156,s143,s142]) ).
cnf(s158,plain,
~ spl0_16,
inference(rat,[],[s95,s156,s143,s157]) ).
cnf(s159,plain,
spl0_20,
inference(rat,[],[s51,s158]) ).
cnf(s160,plain,
spl0_19,
inference(rat,[],[s41,s158]) ).
cnf(s161,plain,
spl0_18,
inference(rat,[],[s21,s158]) ).
cnf(s162,plain,
spl0_8,
inference(rat,[],[s11,s158]) ).
cnf(s164,plain,
spl0_37,
inference(rat,[],[s117,s161,s162]) ).
cnf(s165,plain,
spl0_33,
inference(rat,[],[s120,s143,s142,s164]) ).
cnf(s166,plain,
spl0_52,
inference(rat,[],[s145,s165,s164]) ).
cnf(s167,plain,
spl0_31,
inference(rat,[],[s121,s165,s143,s164]) ).
cnf(s168,plain,
$false,
inference(rat,[],[s133,s165,s160,s159,s167,s156,s164,s166]) ).
fof(f1307,plain,
$false,
inference(avatar_sat_refutation,[],[s168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP373-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 10:01:38 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % (2093383)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (2093393)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=910801843:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (2093389)% WARNING: option uhcvi not known.
% 0.17/0.49 % (2093390)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1898459879:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (2093388)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=985503665_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (2093389)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1111569558:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (2093391)dis+10_1_sil=32000:sp=arity:random_seed=4078563709:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (2093392)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1954470635:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (2093394)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=463320167:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (2093391) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2093383-2093391"...
% 0.17/0.49 % TRYING [5]
% 0.17/0.49 % (2093391)...printing done.
% 0.17/0.49 % (2093391)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (2093391)------------------------------
% 0.17/0.49 % (2093391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2093391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2093391)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2093391)Termination reason: Refutation
% 0.17/0.49 % (2093391)Time elapsed: 0.025 s
% 0.17/0.49 % (2093391)Peak memory usage: 12 MB
% 0.17/0.49 % (2093391)Instructions burned: 40 (million)
% 0.17/0.49 % (2093383)Success in time 0.063 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------