%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP238-1 : 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 : n005.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 10:17:15 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 41
% Syntax : Number of formulae : 307 ( 25 unt; 19 def)
% Number of atoms : 1091 ( 347 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1564 ( 780 ~; 765 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 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_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c11) = sk_c10
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f13]) ).
fof(f21,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = inverse(sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c11 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f29]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f65,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f67]) ).
fof(f85,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f87]) ).
fof(f105,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f106,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f105]) ).
fof(f107,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f108,plain,
( sk_c11 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f107]) ).
fof(f109,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
fof(f110,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f109]) ).
fof(f125,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| multiply(sk_c11,X1) != sk_c10
| multiply(X2,sk_c11) != X1
| inverse(X2) != sk_c11
| multiply(X3,X4) != sk_c11
| inverse(X3) != X4
| multiply(X4,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,X7) != sk_c10
| inverse(X6) != X7
| multiply(X7,sk_c11) != sk_c10
| inverse(X8) != sk_c10
| multiply(X8,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f126,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,X1)
| multiply(X2,sk_c11) != X1
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c11 != multiply(X4,sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(reorient_equations,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X0,X8,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c11 != multiply(X4,sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(equality_resolution,[],[f126]) ).
fof(f128,plain,
! [X2,X3,X0,X8,X6,X7,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(equality_resolution,[],[f127]) ).
fof(f129,plain,
! [X2,X3,X0,X8,X6,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(equality_resolution,[],[f128]) ).
fof(f131,definition,
( spl0_1
<=> ! [X8] :
( sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f132,plain,
( ! [X8] :
( sk_c10 != multiply(X8,sk_c11)
| sk_c10 != inverse(X8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl0_2
<=> ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f135,plain,
( ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl0_3
<=> ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f138,plain,
( ! [X5] :
( sk_c11 != multiply(X5,sk_c10)
| sk_c11 != inverse(X5) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl0_4
<=> ! [X3] :
( sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f141,plain,
( ! [X3] :
( sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,definition,
( spl0_5
<=> ! [X2] :
( sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f144,plain,
( ! [X2] :
( sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,definition,
( spl0_6
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f147,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( inverse(sk_c11) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f129,f146,f137,f143,f140,f137,f134,f131]) ).
fof(f151,definition,
( spl0_7
<=> sk_c10 = multiply(sk_c9,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f153,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl0_8
<=> sk_c11 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f157,plain,
( sk_c11 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f160,definition,
( spl0_9
<=> sk_c10 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f162,plain,
( sk_c10 = inverse(sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f180,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c6,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f182,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f185,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f187,plain,
( sk_c11 = inverse(sk_c6)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f190,definition,
( spl0_15
<=> sk_c11 = multiply(sk_c5,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f192,plain,
( sk_c11 = multiply(sk_c5,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f110,f155,f190]) ).
fof(f195,definition,
( spl0_16
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f197,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f108,f155,f195]) ).
fof(f200,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f202,plain,
( sk_c11 = multiply(sk_c4,sk_c5)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f106,f155,f200]) ).
fof(f205,definition,
( spl0_18
<=> sk_c3 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f207,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f216,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f88,f205,f195]) ).
fof(f217,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f86,f205,f200]) ).
fof(f219,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c11,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f221,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f230,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f68,f219,f195]) ).
fof(f231,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f66,f219,f200]) ).
fof(f233,definition,
( spl0_20
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f235,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f244,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f48,f233,f195]) ).
fof(f245,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f46,f233,f200]) ).
fof(f247,definition,
( spl0_21
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f249,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f257,plain,
( spl0_15
| spl0_21 ),
inference(avatar_split_clause,[],[f30,f247,f190]) ).
fof(f258,plain,
( spl0_16
| spl0_21 ),
inference(avatar_split_clause,[],[f28,f247,f195]) ).
fof(f259,plain,
( spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f26,f247,f200]) ).
fof(f260,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f146,f151]) ).
fof(f261,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f22,f146,f160]) ).
fof(f265,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f146,f180]) ).
fof(f266,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f146,f185]) ).
fof(f268,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f146,f195]) ).
fof(f269,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f146,f200]) ).
fof(f270,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_16 ),
inference(superposition,[],[f3,f197]) ).
fof(f271,plain,
( identity = multiply(sk_c11,sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f3,f187]) ).
fof(f275,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f281,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f202]) ).
fof(f284,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f275,f1]) ).
fof(f286,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f270]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c4,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f286,f1]) ).
fof(f288,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c6,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f271]) ).
fof(f289,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c6,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f288,f1]) ).
fof(f294,plain,
( sk_c5 = multiply(sk_c5,sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f287,f202]) ).
fof(f306,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f289,f182]) ).
fof(f328,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c11,sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f281,f294]) ).
fof(f334,plain,
( sk_c10 = multiply(sk_c4,sk_c5)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f328,f306]) ).
fof(f336,plain,
( sk_c11 = sk_c10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f334,f202]) ).
fof(f369,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f284,f3]) ).
fof(f373,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c5),X0)
| ~ spl0_16 ),
inference(superposition,[],[f284,f287]) ).
fof(f380,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f284,f284]) ).
fof(f382,plain,
( sk_c11 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f284,f294]) ).
fof(f387,plain,
( sk_c10 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_15 ),
inference(superposition,[],[f284,f192]) ).
fof(f404,plain,
( identity = sk_c11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f382,f3]) ).
fof(f412,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f369,f380]) ).
fof(f424,plain,
( ! [X0] : multiply(X0,sk_c11) = X0
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f412,f404]) ).
fof(f448,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1,f404]) ).
fof(f472,plain,
( sk_c10 = sk_c9
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f153,f424]) ).
fof(f474,plain,
( identity = inverse(sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f424]) ).
fof(f496,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f474,f404]) ).
fof(f497,plain,
( sk_c11 = sk_c9
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f472,f336]) ).
fof(f550,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f162,f497]) ).
fof(f551,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f550,f148]) ).
fof(f552,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f551]) ).
fof(f587,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f387,f373]) ).
fof(f599,plain,
( sk_c11 = sk_c10
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f147,f496]) ).
fof(f602,plain,
( sk_c10 = sk_c4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f587,f424]) ).
fof(f607,plain,
( sk_c11 = sk_c4
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f602,f599]) ).
fof(f616,plain,
( sk_c11 = multiply(sk_c5,sk_c11)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f192,f599]) ).
fof(f619,plain,
( sk_c11 = sk_c5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f616,f424]) ).
fof(f629,plain,
( identity = multiply(sk_c11,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f157]) ).
fof(f650,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_21 ),
inference(superposition,[],[f3,f249]) ).
fof(f651,plain,
( identity = sk_c1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f650,f448]) ).
fof(f653,plain,
( sk_c11 = sk_c1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f651,f404]) ).
fof(f685,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20 ),
inference(superposition,[],[f138,f235]) ).
fof(f687,plain,
( identity != sk_c11
| sk_c11 != inverse(inverse(sk_c10))
| ~ spl0_3 ),
inference(superposition,[],[f138,f3]) ).
fof(f689,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f685]) ).
fof(f692,plain,
( sk_c11 != inverse(inverse(sk_c10))
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f687,f404]) ).
fof(f694,plain,
( $false
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f689,f249]) ).
fof(f695,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f699,plain,
( sk_c11 != inverse(inverse(sk_c11))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f692,f599]) ).
fof(f703,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f699,f496]) ).
fof(f706,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f703,f496]) ).
fof(f707,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f708,plain,
( ! [X8] :
( sk_c11 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f132,f599]) ).
fof(f724,plain,
( ! [X8] :
( sk_c10 != X8
| sk_c11 != inverse(X8) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f708,f424]) ).
fof(f729,plain,
( ! [X8] :
( sk_c11 != inverse(X8)
| sk_c11 != X8 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f724,f599]) ).
fof(f731,plain,
( sk_c11 != sk_c5
| sk_c11 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f729,f197]) ).
fof(f734,plain,
( sk_c11 != sk_c11
| sk_c11 != sk_c1
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f729,f249]) ).
fof(f737,plain,
( sk_c11 != sk_c1
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f734]) ).
fof(f739,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f737,f653]) ).
fof(f740,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f739]) ).
fof(f743,plain,
( sk_c11 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f731,f619]) ).
fof(f749,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f743,f607]) ).
fof(f750,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f749]) ).
fof(f753,plain,
( ! [X6] :
( sk_c11 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f135,f599]) ).
fof(f754,plain,
( ! [X6] :
( sk_c10 != inverse(X6)
| sk_c11 != multiply(X6,inverse(X6)) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f753,f424]) ).
fof(f755,plain,
( ! [X6] :
( sk_c11 != multiply(X6,inverse(X6))
| sk_c11 != inverse(X6) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f754,f599]) ).
fof(f777,plain,
( sk_c11 != inverse(identity)
| sk_c11 != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f755,f1]) ).
fof(f779,plain,
( sk_c11 != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f777]) ).
fof(f782,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f779,f404]) ).
fof(f789,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f782,f496]) ).
fof(f790,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f804,plain,
( ! [X3] :
( sk_c11 != multiply(inverse(X3),sk_c11)
| sk_c11 != multiply(X3,inverse(X3)) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f141,f599]) ).
fof(f805,plain,
( ! [X3] :
( sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != inverse(X3) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f804,f424]) ).
fof(f823,plain,
( sk_c11 != inverse(identity)
| sk_c11 != inverse(identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f805,f1]) ).
fof(f825,plain,
( sk_c11 != inverse(identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f823]) ).
fof(f828,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f825,f404]) ).
fof(f835,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f828,f496]) ).
fof(f836,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f835]) ).
fof(f850,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f144,f448]) ).
fof(f851,plain,
( ! [X2] :
( sk_c10 != X2
| sk_c11 != inverse(X2) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f850,f424]) ).
fof(f852,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != X2 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f851,f599]) ).
fof(f867,plain,
( sk_c11 != sk_c5
| sk_c11 != sk_c4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f852,f197]) ).
fof(f870,plain,
( sk_c11 != sk_c11
| sk_c11 != sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f852,f249]) ).
fof(f873,plain,
( sk_c11 != sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f870]) ).
fof(f875,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f873,f653]) ).
fof(f876,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f879,plain,
( sk_c11 != sk_c4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f867,f619]) ).
fof(f885,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f879,f607]) ).
fof(f886,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f885]) ).
fof(f893,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6 ),
inference(superposition,[],[f3,f147]) ).
fof(f906,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_18 ),
inference(superposition,[],[f284,f207]) ).
fof(f909,plain,
( sk_c11 = multiply(sk_c11,sk_c3)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f906,f157]) ).
fof(f913,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_19 ),
inference(superposition,[],[f284,f221]) ).
fof(f914,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_19 ),
inference(superposition,[],[f4,f221]) ).
fof(f916,plain,
( sk_c3 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_19 ),
inference(forward_demodulation,[],[f913,f147]) ).
fof(f948,plain,
( identity != sk_c10
| sk_c10 != inverse(inverse(sk_c11))
| ~ spl0_1 ),
inference(superposition,[],[f132,f3]) ).
fof(f987,plain,
( ! [X0,X1] :
( sk_c11 != multiply(X0,multiply(X1,inverse(multiply(X0,X1))))
| sk_c11 != multiply(inverse(multiply(X0,X1)),sk_c10) )
| ~ spl0_4 ),
inference(superposition,[],[f141,f4]) ).
fof(f1095,definition,
( spl0_26
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f1096,plain,
( sk_c11 = sk_c10
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1097,plain,
( sk_c11 != sk_c10
| spl0_26 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1102,plain,
( sk_c2 = multiply(inverse(sk_c11),identity)
| ~ spl0_8 ),
inference(superposition,[],[f284,f629]) ).
fof(f1105,plain,
( inverse(sk_c11) = sk_c2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1102,f412]) ).
fof(f1107,plain,
( sk_c10 = sk_c2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1105,f147]) ).
fof(f1110,plain,
( sk_c1 = multiply(inverse(sk_c11),identity)
| ~ spl0_21 ),
inference(superposition,[],[f284,f650]) ).
fof(f1113,plain,
( inverse(sk_c11) = sk_c1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1110,f412]) ).
fof(f1115,plain,
( sk_c10 = sk_c1
| ~ spl0_6
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1113,f147]) ).
fof(f1118,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f157,f1107]) ).
fof(f1128,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f235,f1115]) ).
fof(f1388,plain,
( sk_c11 = sk_c10
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f909,f221]) ).
fof(f1392,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c3,inverse(sk_c11)))
| sk_c11 != multiply(inverse(sk_c11),sk_c10)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f987,f909]) ).
fof(f1393,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f284,f909]) ).
fof(f1396,plain,
( identity = sk_c3
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1393,f3]) ).
fof(f1397,plain,
( sk_c11 != multiply(sk_c10,inverse(sk_c11))
| sk_c11 != multiply(inverse(sk_c11),sk_c10)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1392,f914]) ).
fof(f1402,plain,
( $false
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f1388,f1097]) ).
fof(f1403,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f1402]) ).
fof(f1443,plain,
( ! [X6] :
( sk_c11 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11) )
| ~ spl0_2
| ~ spl0_26 ),
inference(forward_demodulation,[],[f135,f1096]) ).
fof(f1444,plain,
( ! [X6] :
( sk_c11 != multiply(inverse(X6),sk_c11)
| sk_c11 != multiply(X6,inverse(X6)) )
| ~ spl0_2
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1443,f1096]) ).
fof(f1453,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f893,f1096]) ).
fof(f1490,plain,
( sk_c11 != multiply(sk_c1,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_2
| ~ spl0_21
| ~ spl0_26 ),
inference(superposition,[],[f1444,f249]) ).
fof(f1557,plain,
( ! [X2] :
( sk_c11 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2) )
| ~ spl0_5
| ~ spl0_26 ),
inference(forward_demodulation,[],[f144,f1096]) ).
fof(f1561,plain,
( sk_c3 = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_19
| ~ spl0_26 ),
inference(forward_demodulation,[],[f916,f1096]) ).
fof(f1564,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1128,f1096]) ).
fof(f1632,plain,
( sk_c11 != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(sk_c11))
| ~ spl0_5
| ~ spl0_26 ),
inference(superposition,[],[f1557,f3]) ).
fof(f1637,plain,
( sk_c11 != inverse(inverse(sk_c11))
| ~ spl0_5
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1632,f412]) ).
fof(f1642,plain,
( sk_c11 != inverse(sk_c10)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1637,f147]) ).
fof(f1649,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1642,f1118]) ).
fof(f1650,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1649]) ).
fof(f1844,plain,
( identity != sk_c11
| sk_c10 != inverse(inverse(sk_c11))
| ~ spl0_1
| ~ spl0_26 ),
inference(forward_demodulation,[],[f948,f1096]) ).
fof(f1869,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1453,f1564]) ).
fof(f1871,plain,
( sk_c11 = sk_c3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1561,f1564]) ).
fof(f1878,plain,
( sk_c11 != sk_c3
| sk_c10 != inverse(inverse(sk_c11))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1844,f1396]) ).
fof(f1885,plain,
( sk_c10 != inverse(inverse(sk_c11))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1878,f1871]) ).
fof(f1889,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1885,f147]) ).
fof(f1896,plain,
( sk_c11 != sk_c10
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1889,f1118]) ).
fof(f1897,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1896,f1096]) ).
fof(f1898,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1897]) ).
fof(f1914,plain,
( sk_c11 != multiply(sk_c10,sk_c10)
| sk_c11 != multiply(inverse(sk_c11),sk_c10)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1397,f147]) ).
fof(f1967,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(inverse(sk_c11),sk_c10)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1914,f1096]) ).
fof(f2021,plain,
( sk_c11 != multiply(inverse(sk_c11),sk_c10)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1967,f1564]) ).
fof(f2080,plain,
( sk_c11 != multiply(inverse(sk_c11),sk_c11)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f2021,f1096]) ).
fof(f2096,plain,
( identity != sk_c11
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f2080,f3]) ).
fof(f2099,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f2096,f1869]) ).
fof(f2100,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f2099]) ).
fof(f2112,plain,
( sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1490,f1564]) ).
fof(f2137,plain,
( sk_c11 != multiply(sk_c10,sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f2112,f1115]) ).
fof(f2156,plain,
( identity != sk_c11
| ~ spl0_2
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_demodulation,[],[f2137,f893]) ).
fof(f2167,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f2156,f1869]) ).
fof(f2168,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f2167]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f149]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s10,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f193]) ).
cnf(s11,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s12,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s21,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f216]) ).
cnf(s22,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f217]) ).
cnf(s31,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s32,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f231]) ).
cnf(s41,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f244]) ).
cnf(s42,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f245]) ).
cnf(s50,plain,
( spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s51,plain,
( spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f258]) ).
cnf(s52,plain,
( spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f259]) ).
cnf(s53,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f260]) ).
cnf(s54,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f261]) ).
cnf(s58,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f265]) ).
cnf(s59,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f266]) ).
cnf(s61,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f268]) ).
cnf(s62,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f269]) ).
cnf(s63,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f552]) ).
cnf(s70,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f695]) ).
cnf(s73,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f707]) ).
cnf(s74,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f740]) ).
cnf(s77,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f750]) ).
cnf(s80,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f790]) ).
cnf(s86,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f836]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f876]) ).
cnf(s94,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f886]) ).
cnf(s121,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_26 ),
inference(sat_conversion,[],[f1403]) ).
cnf(s147,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_26 ),
inference(sat_conversion,[],[f1650]) ).
cnf(s191,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(sat_conversion,[],[f1898]) ).
cnf(s238,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(sat_conversion,[],[f2100]) ).
cnf(s256,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_26 ),
inference(sat_conversion,[],[f2168]) ).
cnf(s257,plain,
spl0_6,
inference(rat,[],[s63,s53,s54,s58,s59,s61,s62]) ).
cnf(s258,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s94,s10,s11,s12,s257]) ).
cnf(s259,plain,
( spl0_17
| ~ spl0_5 ),
inference(rat,[],[s121,s22,s32,s147,s258,s257]) ).
cnf(s260,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s121,s21,s31,s147,s258,s257]) ).
cnf(s261,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_5 ),
inference(rat,[],[s50,s91,s94,s257]) ).
cnf(s262,plain,
~ spl0_5,
inference(rat,[],[s261,s260,s259]) ).
cnf(s263,plain,
( spl0_17
| ~ spl0_4 ),
inference(rat,[],[s238,s121,s12,s22,s32,s42,s52,s257]) ).
cnf(s264,plain,
( ~ spl0_17
| ~ spl0_4 ),
inference(rat,[],[s238,s121,s11,s21,s31,s41,s51,s86,s257]) ).
cnf(s265,plain,
~ spl0_4,
inference(rat,[],[s264,s263]) ).
cnf(s266,plain,
( spl0_17
| ~ spl0_3 ),
inference(rat,[],[s70,s42,s52]) ).
cnf(s267,plain,
( ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s70,s41,s51,s73,s257]) ).
cnf(s268,plain,
~ spl0_3,
inference(rat,[],[s267,s266]) ).
cnf(s269,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s121,s256,s12,s22,s32,s42,s52,s257]) ).
cnf(s270,plain,
( ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s121,s256,s11,s21,s31,s41,s51,s80,s257]) ).
cnf(s271,plain,
~ spl0_2,
inference(rat,[],[s270,s269]) ).
cnf(s272,plain,
spl0_1,
inference(rat,[],[s2,s262,s265,s257,s268,s271]) ).
cnf(s273,plain,
spl0_17,
inference(rat,[],[s191,s121,s12,s22,s32,s42,s52,s257,s272]) ).
cnf(s274,plain,
~ spl0_16,
inference(rat,[],[s50,s77,s74,s273,s257,s272]) ).
cnf(s275,plain,
spl0_21,
inference(rat,[],[s51,s274]) ).
cnf(s276,plain,
spl0_20,
inference(rat,[],[s41,s274]) ).
cnf(s277,plain,
spl0_19,
inference(rat,[],[s31,s274]) ).
cnf(s278,plain,
spl0_18,
inference(rat,[],[s21,s274]) ).
cnf(s279,plain,
spl0_8,
inference(rat,[],[s11,s274]) ).
cnf(s280,plain,
spl0_26,
inference(rat,[],[s121,s279,s277,s278]) ).
cnf(s281,plain,
$false,
inference(rat,[],[s191,s280,s275,s276,s277,s272,s257,s278,s279]) ).
fof(f2169,plain,
$false,
inference(avatar_sat_refutation,[],[s281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP238-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:37:48 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.48 % (3742814)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3742823)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=214103063:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3742820)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3742822)dis+10_1_sil=32000:sp=arity:random_seed=105510748:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3742819)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1327685574_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3742820)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3381797546:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3742824)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3676971658:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3742821)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=946630753:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3742825)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=215296413:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % (3742823) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3742814-3742823"...
% 0.17/0.48 % (3742823)...printing done.
% 0.17/0.48 % (3742823)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (3742823)------------------------------
% 0.17/0.49 % (3742823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3742823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3742823)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3742823)Termination reason: Refutation
% 0.17/0.49 % (3742823)Time elapsed: 0.017 s
% 0.17/0.49 % (3742823)Peak memory usage: 13 MB
% 0.17/0.49 % (3742823)Instructions burned: 53 (million)
% 0.17/0.49 % (3742814)Success in time 0.054 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------