%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP380-1 : 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 : n002.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 10:17:39 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 34
% Syntax : Number of formulae : 272 ( 19 unt; 16 def)
% Number of atoms : 1067 ( 372 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1617 ( 822 ~; 779 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 106 !; 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_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| multiply(X1,sk_c9) != 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/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| sk_c10 != multiply(X1,sk_c9)
| 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,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| 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(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X6,X7,X4] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| 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,[],[f105]) ).
fof(f107,plain,
! [X2,X3,X0,X6,X4] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| 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,[],[f106]) ).
fof(f109,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(f110,plain,
( ! [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) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f113,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f116,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl0_4
<=> ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f119,plain,
( ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_5
<=> sk_c11 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f122,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( sk_c11 != multiply(sk_c10,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl0_6
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f126,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( inverse(sk_c11) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f107,f125,f121,f118,f115,f112,f109]) ).
fof(f154,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f159,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f161,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f164,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f166,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f169,definition,
( spl0_15
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f171,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f174,definition,
( spl0_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f176,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f179,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f184,definition,
( spl0_18
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f186,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f195,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f66,f184,f174]) ).
fof(f196,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f64,f184,f179]) ).
fof(f198,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f200,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f209,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f46,f198,f174]) ).
fof(f210,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f44,f198,f179]) ).
fof(f215,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f34,f121,f154]) ).
fof(f216,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f32,f121,f159]) ).
fof(f217,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f30,f121,f164]) ).
fof(f218,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f121,f169]) ).
fof(f219,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f121,f174]) ).
fof(f220,plain,
( spl0_17
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f121,f179]) ).
fof(f225,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f125,f154]) ).
fof(f226,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f125,f159]) ).
fof(f229,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f125,f174]) ).
fof(f230,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f125,f179]) ).
fof(f231,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_16 ),
inference(superposition,[],[f3,f176]) ).
fof(f238,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f244,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f238,f1]) ).
fof(f247,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f231]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f247,f1]) ).
fof(f261,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f248,f181]) ).
fof(f310,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f244,f261]) ).
fof(f315,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f244,f171]) ).
fof(f318,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_13 ),
inference(superposition,[],[f244,f161]) ).
fof(f335,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f318,f156]) ).
fof(f338,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f315,f166]) ).
fof(f342,plain,
( identity = sk_c10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f310,f3]) ).
fof(f377,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f244,f335]) ).
fof(f379,plain,
( identity = sk_c11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f377,f3]) ).
fof(f383,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f231,f379]) ).
fof(f392,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f383,f1]) ).
fof(f396,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f338,f342]) ).
fof(f397,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f396,f1]) ).
fof(f399,plain,
( sk_c11 != multiply(sk_c10,identity)
| spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f123,f397]) ).
fof(f400,plain,
( sk_c11 != multiply(identity,identity)
| spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f399,f342]) ).
fof(f402,plain,
( identity != sk_c11
| spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f400,f1]) ).
fof(f403,plain,
( $false
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f402,f379]) ).
fof(f404,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f406,plain,
( identity != inverse(sk_c11)
| spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f127,f342]) ).
fof(f408,plain,
( identity != inverse(identity)
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f406,f379]) ).
fof(f414,plain,
( sk_c11 = inverse(identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f176,f392]) ).
fof(f415,plain,
( identity = inverse(identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f414,f379]) ).
fof(f420,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f415,f408]) ).
fof(f421,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f425,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f119,f342]) ).
fof(f426,plain,
( identity = inverse(sk_c11)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f126,f342]) ).
fof(f546,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f113,f342]) ).
fof(f565,plain,
( sk_c11 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f122,f342]) ).
fof(f566,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c9 != multiply(X3,identity) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f546,f342]) ).
fof(f568,plain,
( sk_c11 = sk_c9
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f565,f1]) ).
fof(f607,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f426]) ).
fof(f608,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f607,f1]) ).
fof(f617,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f426,f608]) ).
fof(f645,plain,
( ! [X3] :
( sk_c11 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f566,f568]) ).
fof(f646,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f645,f608]) ).
fof(f649,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f646,f3]) ).
fof(f653,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f649]) ).
fof(f655,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f653,f617]) ).
fof(f658,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f655,f617]) ).
fof(f659,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f661,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c11)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f425,f568]) ).
fof(f663,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f661,f608]) ).
fof(f665,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f663,f342]) ).
fof(f673,plain,
( identity != multiply(sk_c11,identity)
| identity != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f665,f176]) ).
fof(f683,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f673,f608]) ).
fof(f691,plain,
( identity != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f683,f1]) ).
fof(f693,plain,
( identity != sk_c10
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f691,f181]) ).
fof(f696,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f693,f342]) ).
fof(f697,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f696]) ).
fof(f698,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,[],[f110,f608]) ).
fof(f699,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,[],[f698,f342]) ).
fof(f700,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,[],[f699,f608]) ).
fof(f707,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,[],[f700,f426]) ).
fof(f721,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,[],[f707,f1]) ).
fof(f726,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,[],[f721,f608]) ).
fof(f730,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f726,f1]) ).
fof(f746,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f730,f3]) ).
fof(f753,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f746,f617]) ).
fof(f757,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f753,f617]) ).
fof(f761,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f757,f617]) ).
fof(f766,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f761,f617]) ).
fof(f771,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f766,f617]) ).
fof(f772,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f771]) ).
fof(f773,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f116,f608]) ).
fof(f774,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f773,f342]) ).
fof(f775,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f774,f608]) ).
fof(f779,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f775,f3]) ).
fof(f785,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f779]) ).
fof(f789,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f785,f617]) ).
fof(f796,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f789,f617]) ).
fof(f797,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f796]) ).
fof(f799,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6 ),
inference(superposition,[],[f3,f126]) ).
fof(f803,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c10,multiply(sk_c9,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f122]) ).
fof(f806,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_19 ),
inference(superposition,[],[f244,f200]) ).
fof(f808,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f806,f186]) ).
fof(f816,plain,
( ! [X0,X1] :
( sk_c10 != multiply(X0,multiply(X1,sk_c11))
| sk_c11 != inverse(multiply(X0,X1)) )
| ~ spl0_3 ),
inference(superposition,[],[f116,f4]) ).
fof(f824,definition,
( spl0_29
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f825,plain,
( identity = sk_c10
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f824]) ).
fof(f834,definition,
( spl0_31
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f835,plain,
( sk_c11 = sk_c10
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f834]) ).
fof(f836,plain,
( sk_c11 != sk_c10
| spl0_31 ),
inference(avatar_component_clause,[],[f834]) ).
fof(f849,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f244,f808]) ).
fof(f851,plain,
( identity = sk_c10
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f849,f3]) ).
fof(f852,plain,
( spl0_29
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f851,f198,f184,f824]) ).
fof(f865,plain,
( sk_c11 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_29 ),
inference(superposition,[],[f122,f825]) ).
fof(f870,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_6
| ~ spl0_29 ),
inference(superposition,[],[f799,f825]) ).
fof(f874,plain,
( identity != sk_c11
| ~ spl0_29
| spl0_31 ),
inference(superposition,[],[f836,f825]) ).
fof(f877,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_29 ),
inference(forward_demodulation,[],[f870,f1]) ).
fof(f880,plain,
( sk_c11 = sk_c9
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f865,f1]) ).
fof(f881,plain,
( ! [X0,X1] :
( identity != multiply(X0,multiply(X1,sk_c11))
| sk_c11 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_29 ),
inference(forward_demodulation,[],[f816,f825]) ).
fof(f882,plain,
( $false
| ~ spl0_6
| ~ spl0_29
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f877,f874]) ).
fof(f883,plain,
( ~ spl0_6
| ~ spl0_29
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f882]) ).
fof(f884,plain,
( identity = sk_c11
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f835,f825]) ).
fof(f886,plain,
( sk_c10 = inverse(identity)
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(superposition,[],[f126,f884]) ).
fof(f895,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f886,f825]) ).
fof(f911,plain,
( ! [X0,X1] :
( identity != multiply(X0,multiply(X1,identity))
| sk_c11 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f881,f884]) ).
fof(f912,plain,
( ! [X0,X1] :
( identity != multiply(X0,multiply(X1,identity))
| identity != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f911,f884]) ).
fof(f913,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f880,f884]) ).
fof(f922,plain,
( identity != multiply(sk_c11,identity)
| identity != inverse(multiply(sk_c10,sk_c9))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(superposition,[],[f912,f803]) ).
fof(f936,plain,
( identity != multiply(identity,identity)
| identity != inverse(multiply(sk_c10,sk_c9))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f922,f884]) ).
fof(f953,plain,
( identity != inverse(multiply(sk_c10,sk_c9))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f936,f1]) ).
fof(f958,plain,
( identity != inverse(sk_c11)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f953,f122]) ).
fof(f963,plain,
( identity != sk_c10
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f958,f126]) ).
fof(f968,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f963,f825]) ).
fof(f969,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f968]) ).
fof(f970,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_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f110,f884]) ).
fof(f971,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_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f970,f825]) ).
fof(f972,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_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f971,f884]) ).
fof(f985,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| identity != multiply(sk_c11,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(superposition,[],[f972,f126]) ).
fof(f994,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f985,f825]) ).
fof(f996,plain,
( ! [X0] :
( identity != multiply(sk_c11,identity)
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f994,f825]) ).
fof(f1005,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f996,f884]) ).
fof(f1006,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1005,f1]) ).
fof(f1007,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1006,f825]) ).
fof(f1008,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1007,f1]) ).
fof(f1009,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1008,f825]) ).
fof(f1045,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(superposition,[],[f1009,f3]) ).
fof(f1048,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1045,f895]) ).
fof(f1050,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1048,f895]) ).
fof(f1052,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1050,f895]) ).
fof(f1055,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1052,f895]) ).
fof(f1056,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1055,f895]) ).
fof(f1057,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f1056]) ).
fof(f1058,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_4
| ~ spl0_29 ),
inference(forward_demodulation,[],[f119,f825]) ).
fof(f1059,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1058,f913]) ).
fof(f1060,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1059,f825]) ).
fof(f1062,plain,
( identity != multiply(sk_c10,identity)
| identity != multiply(sk_c11,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(superposition,[],[f1060,f126]) ).
fof(f1070,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c11,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1062,f825]) ).
fof(f1075,plain,
( identity != multiply(sk_c11,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1070,f1]) ).
fof(f1076,plain,
( identity != multiply(sk_c11,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1075,f825]) ).
fof(f1077,plain,
( identity != multiply(identity,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1076,f884]) ).
fof(f1078,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1077,f1]) ).
fof(f1079,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f1078]) ).
fof(f1080,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_29 ),
inference(forward_demodulation,[],[f113,f825]) ).
fof(f1081,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1080,f913]) ).
fof(f1082,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1081,f825]) ).
fof(f1085,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(superposition,[],[f1082,f3]) ).
fof(f1086,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_29
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f1085]) ).
fof(f1088,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1086,f895]) ).
fof(f1091,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1088,f895]) ).
fof(f1092,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f1091]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f128]) ).
cnf(s20,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s21,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s30,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f209]) ).
cnf(s31,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f210]) ).
cnf(s36,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f215]) ).
cnf(s37,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f216]) ).
cnf(s38,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f217]) ).
cnf(s39,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f218]) ).
cnf(s40,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f219]) ).
cnf(s41,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f220]) ).
cnf(s46,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f225]) ).
cnf(s47,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f226]) ).
cnf(s50,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f229]) ).
cnf(s51,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f230]) ).
cnf(s52,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f404]) ).
cnf(s53,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f421]) ).
cnf(s72,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f659]) ).
cnf(s77,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f697]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f772]) ).
cnf(s86,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f797]) ).
cnf(s90,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_29 ),
inference(sat_conversion,[],[f852]) ).
cnf(s92,plain,
( ~ spl0_6
| ~ spl0_29
| spl0_31 ),
inference(sat_conversion,[],[f883]) ).
cnf(s98,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(sat_conversion,[],[f969]) ).
cnf(s108,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s111,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(sat_conversion,[],[f1079]) ).
cnf(s113,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_29
| ~ spl0_31 ),
inference(sat_conversion,[],[f1092]) ).
cnf(s114,plain,
spl0_5,
inference(rat,[],[s52,s36,s37,s38,s39,s40,s41]) ).
cnf(s115,plain,
spl0_6,
inference(rat,[],[s53,s46,s47,s50,s51]) ).
cnf(s117,plain,
( ~ spl0_29
| ~ spl0_4 ),
inference(rat,[],[s111,s92,s115,s114]) ).
cnf(s118,plain,
( spl0_17
| spl0_29 ),
inference(rat,[],[s90,s21,s31]) ).
cnf(s119,plain,
~ spl0_4,
inference(rat,[],[s90,s20,s30,s77,s118,s117,s115,s114]) ).
cnf(s120,plain,
( ~ spl0_29
| ~ spl0_3 ),
inference(rat,[],[s98,s92,s115,s114]) ).
cnf(s121,plain,
~ spl0_3,
inference(rat,[],[s90,s20,s30,s86,s118,s120,s115]) ).
cnf(s122,plain,
( ~ spl0_29
| ~ spl0_2 ),
inference(rat,[],[s113,s92,s115,s114]) ).
cnf(s123,plain,
~ spl0_2,
inference(rat,[],[s90,s20,s30,s72,s118,s122,s115,s114]) ).
cnf(s124,plain,
spl0_1,
inference(rat,[],[s1,s115,s119,s114,s121,s123]) ).
cnf(s125,plain,
~ spl0_29,
inference(rat,[],[s108,s92,s115,s124]) ).
cnf(s126,plain,
spl0_17,
inference(rat,[],[s118,s125]) ).
cnf(s127,plain,
~ spl0_16,
inference(rat,[],[s82,s124,s115,s126]) ).
cnf(s128,plain,
spl0_19,
inference(rat,[],[s30,s127]) ).
cnf(s129,plain,
spl0_18,
inference(rat,[],[s20,s127]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s90,s125,s128,s129]) ).
fof(f1093,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 % Computer : n002.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 10:02:36 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 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
% 0.20/0.51 % (3305650)Will run a generic schedule for satisfiability detection.
% 0.20/0.51 % (3305660)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4196595118_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.51 % TRYING [1]
% 0.20/0.51 % TRYING [2]
% 0.20/0.51 % (3305661)% WARNING: option uhcvi not known.
% 0.20/0.51 % TRYING [3]
% 0.20/0.51 % TRYING [4]
% 0.20/0.51 % (3305661)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1622701662:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.51 % (3305664)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1418889134:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.51 % (3305662)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1906102871:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.51 % (3305663)dis+10_1_sil=32000:sp=arity:random_seed=4019234389:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.51 % TRYING [5]
% 0.20/0.51 % (3305666)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3621144749:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.51 % (3305665)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2237559326:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.51 % TRYING [6]
% 0.20/0.51 % (3305663) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3305650-3305663"...
% 0.20/0.51 % (3305663)...printing done.
% 0.20/0.51 % (3305664) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3305650-3305664"...
% 0.20/0.51 % (3305663)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (3305663)------------------------------
% 0.20/0.52 % (3305663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.52 % (3305663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.52 % (3305663)CaDiCaL version: 2.1.3
% 0.20/0.52 % (3305663)Termination reason: Refutation
% 0.20/0.52 % (3305663)Time elapsed: 0.023 s
% 0.20/0.52 % (3305663)Peak memory usage: 12 MB
% 0.20/0.52 % (3305663)Instructions burned: 36 (million)
% 0.20/0.52 % (3305650)Success in time 0.064 s
% 0.20/0.52 % Vampire exiting
%------------------------------------------------------------------------------