%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP390-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:49 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.97s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 283 ( 19 unt; 17 def)
% Number of atoms : 844 ( 279 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1051 ( 490 ~; 544 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c8) = sk_c7
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f69,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f71]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(X5) != sk_c9
| multiply(X5,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c8) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c8) ),
inference(equality_resolution,[],[f78]) ).
fof(f81,definition,
( spl0_1
<=> ! [X5] :
( sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_2
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f85,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl0_3
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f88,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_4
<=> ! [X1] :
( sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X1] :
( sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != multiply(X1,inverse(X1)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( inverse(sk_c8) != sk_c7
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f79,f93,f81,f90,f87,f84,f81]) ).
fof(f98,definition,
( spl0_6
<=> sk_c9 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f100,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f102,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f104,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f107,definition,
( spl0_8
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f109,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f112,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f114,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f72,f102,f112]) ).
fof(f117,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f70,f102,f117]) ).
fof(f122,definition,
( spl0_11
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f124,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f127,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f129,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f132,definition,
( spl0_13
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f137,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f60,f132,f112]) ).
fof(f138,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f58,f132,f117]) ).
fof(f139,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f56,f132,f122]) ).
fof(f140,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f132,f127]) ).
fof(f142,definition,
( spl0_14
<=> sk_c8 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f147,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f142,f112]) ).
fof(f148,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f142,f117]) ).
fof(f149,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f142,f122]) ).
fof(f150,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f142,f127]) ).
fof(f152,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f153,plain,
( sk_c9 != multiply(sk_c1,sk_c8)
| spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f154,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f152,f98]) ).
fof(f156,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f152,f107]) ).
fof(f157,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f152,f112]) ).
fof(f158,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f152,f117]) ).
fof(f159,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f152,f122]) ).
fof(f160,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f152,f127]) ).
fof(f162,definition,
( spl0_16
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f162,f98]) ).
fof(f166,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f162,f107]) ).
fof(f169,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f162,f122]) ).
fof(f170,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f18,f162,f127]) ).
fof(f173,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f93,f112]) ).
fof(f174,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f93,f117]) ).
fof(f175,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f93,f122]) ).
fof(f176,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f93,f127]) ).
fof(f177,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f109]) ).
fof(f178,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f114]) ).
fof(f181,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f181,f1]) ).
fof(f234,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f187,f119]) ).
fof(f236,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_12 ),
inference(superposition,[],[f187,f129]) ).
fof(f238,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_9 ),
inference(superposition,[],[f187,f178]) ).
fof(f239,plain,
( sk_c6 = multiply(inverse(sk_c9),identity)
| ~ spl0_8 ),
inference(superposition,[],[f187,f177]) ).
fof(f242,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f236,f124]) ).
fof(f243,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f234,f114]) ).
fof(f249,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f187,f242]) ).
fof(f251,plain,
( identity = sk_c8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f3]) ).
fof(f255,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f187,f243]) ).
fof(f257,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f255,f3]) ).
fof(f262,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f257,f251]) ).
fof(f263,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f238,f251]) ).
fof(f264,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f263,f3]) ).
fof(f265,plain,
( sk_c8 = sk_c5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f264,f251]) ).
fof(f270,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f114,f265]) ).
fof(f276,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f95,f270]) ).
fof(f280,plain,
( $false
| spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f276,f262]) ).
fof(f281,plain,
( spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f284,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f88,f124]) ).
fof(f288,plain,
( sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f284]) ).
fof(f290,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f288,f129]) ).
fof(f291,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f310,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f94]) ).
fof(f311,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f310,f257]) ).
fof(f319,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f134]) ).
fof(f330,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f88,f164]) ).
fof(f332,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f164]) ).
fof(f333,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_3
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f330]) ).
fof(f334,plain,
( sk_c7 = multiply(sk_c9,sk_c1)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f332,f257]) ).
fof(f335,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_7 ),
inference(superposition,[],[f187,f104]) ).
fof(f336,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f104]) ).
fof(f337,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_14 ),
inference(superposition,[],[f187,f144]) ).
fof(f338,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c3,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f144]) ).
fof(f339,plain,
( sk_c3 = multiply(sk_c3,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f337,f134]) ).
fof(f340,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f187,f154]) ).
fof(f341,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f154]) ).
fof(f342,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f340,f164]) ).
fof(f343,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f187,f311]) ).
fof(f345,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f343,f3]) ).
fof(f348,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f345,f257]) ).
fof(f352,plain,
( sk_c1 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f187,f334]) ).
fof(f367,plain,
( multiply(sk_c2,sk_c3) = multiply(sk_c8,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f338,f339]) ).
fof(f368,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f187,f339]) ).
fof(f370,plain,
( identity = sk_c8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f368,f3]) ).
fof(f371,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f367,f144]) ).
fof(f375,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c1),multiply(sk_c9,X0))
| ~ spl0_15 ),
inference(superposition,[],[f187,f341]) ).
fof(f378,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c9,X0))
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f375,f164]) ).
fof(f428,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f239,f257]) ).
fof(f429,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f428,f348]) ).
fof(f434,plain,
( sk_c1 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f352,f348]) ).
fof(f479,plain,
( sk_c6 = sk_c1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f434,f429]) ).
fof(f556,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1,f370]) ).
fof(f557,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f310,f370]) ).
fof(f558,plain,
( sk_c8 = multiply(sk_c3,sk_c2)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f319,f370]) ).
fof(f559,plain,
( sk_c8 = multiply(sk_c9,sk_c1)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f332,f370]) ).
fof(f563,plain,
( sk_c2 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f187,f558]) ).
fof(f571,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f336,f557]) ).
fof(f576,plain,
( sk_c3 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f571,f339]) ).
fof(f586,plain,
( sk_c8 = sk_c3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f371,f576]) ).
fof(f602,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f335,f586]) ).
fof(f603,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f602,f3]) ).
fof(f604,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f603,f370]) ).
fof(f613,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f563,f586]) ).
fof(f614,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f613,f3]) ).
fof(f615,plain,
( sk_c8 = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f614,f370]) ).
fof(f713,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c9,X0)) = X0
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f378,f556]) ).
fof(f717,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f713,f342]) ).
fof(f720,plain,
( sk_c1 = multiply(sk_c9,sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f713,f559]) ).
fof(f758,plain,
( sk_c9 = sk_c1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f720,f717]) ).
fof(f764,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f333,f758]) ).
fof(f767,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f764,f342]) ).
fof(f768,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f767]) ).
fof(f771,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[],[f82,f164]) ).
fof(f778,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f85,f604]) ).
fof(f788,plain,
( sk_c8 != sk_c3
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f778,f134]) ).
fof(f790,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f788,f586]) ).
fof(f794,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f790,f615]) ).
fof(f797,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f794,f371]) ).
fof(f798,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f797]) ).
fof(f799,plain,
( ! [X1] :
( sk_c8 != multiply(inverse(X1),sk_c8)
| sk_c8 != multiply(X1,inverse(X1)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f91,f604]) ).
fof(f801,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f799,f94]) ).
fof(f813,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f801,f557]) ).
fof(f819,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f813,f556]) ).
fof(f824,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f819,f604]) ).
fof(f825,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f824]) ).
fof(f926,plain,
( sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f771]) ).
fof(f928,plain,
( ~ spl0_15
| ~ spl0_1
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f926,f162,f81,f152]) ).
fof(f934,plain,
( sk_c9 != multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f153,f479]) ).
fof(f938,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f934,f100]) ).
fof(f939,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f938]) ).
fof(f943,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c6,sk_c8)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f82,f109]) ).
fof(f945,plain,
( sk_c9 != multiply(sk_c6,sk_c8)
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f943]) ).
fof(f947,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f945,f100]) ).
fof(f948,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f947]) ).
fof(f961,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f85,f114]) ).
fof(f963,plain,
( sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f961]) ).
fof(f964,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f963,f119]) ).
fof(f965,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f964]) ).
fof(f971,definition,
( spl0_25
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f973,plain,
( sk_c8 != sk_c7
| spl0_25 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f979,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,inverse(sk_c5))
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f91,f234]) ).
fof(f981,plain,
( sk_c8 != multiply(sk_c5,inverse(sk_c5))
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f979]) ).
fof(f983,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f981,f114]) ).
fof(f1004,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f983,f119]) ).
fof(f1007,plain,
( ~ spl0_25
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1004,f117,f112,f90,f971]) ).
fof(f1008,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f257,f345]) ).
fof(f1009,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f1008,f973]) ).
fof(f1010,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f1009]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f96]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f115]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s11,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s12,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s13,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s14,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s17,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s18,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s19,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s20,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s21,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s22,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s23,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s24,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s25,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s26,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s27,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s28,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s31,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f169]) ).
cnf(s32,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f173]) ).
cnf(s36,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f174]) ).
cnf(s37,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f175]) ).
cnf(s38,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f176]) ).
cnf(s39,plain,
( spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f281]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f291]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f768]) ).
cnf(s56,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f798]) ).
cnf(s60,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f825]) ).
cnf(s68,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f928]) ).
cnf(s71,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f939]) ).
cnf(s72,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f948]) ).
cnf(s73,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f965]) ).
cnf(s79,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_25 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s80,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_25 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s81,plain,
spl0_5,
inference(rat,[],[s39,s35,s36,s37,s38]) ).
cnf(s82,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s79,s80,s5,s6,s81]) ).
cnf(s83,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s79,s80,s81]) ).
cnf(s84,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s60,s12,s18,s82,s81]) ).
cnf(s85,plain,
~ spl0_4,
inference(rat,[],[s60,s11,s17,s83,s84,s82,s81]) ).
cnf(s86,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s40,s13,s14]) ).
cnf(s87,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s52,s20,s26,s32,s86]) ).
cnf(s88,plain,
~ spl0_3,
inference(rat,[],[s52,s19,s25,s31,s40,s87,s86]) ).
cnf(s89,plain,
( spl0_10
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s56,s6,s18,s81]) ).
cnf(s90,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s56,s5,s17,s73,s89,s81]) ).
cnf(s91,plain,
~ spl0_2,
inference(rat,[],[s73,s11,s12,s90]) ).
cnf(s92,plain,
spl0_1,
inference(rat,[],[s2,s85,s81,s88,s91]) ).
cnf(s94,plain,
spl0_16,
inference(rat,[],[s72,s27,s28,s92]) ).
cnf(s95,plain,
~ spl0_15,
inference(rat,[],[s68,s92,s94]) ).
cnf(s97,plain,
spl0_10,
inference(rat,[],[s24,s95]) ).
cnf(s98,plain,
spl0_9,
inference(rat,[],[s23,s95]) ).
cnf(s99,plain,
spl0_8,
inference(rat,[],[s22,s95]) ).
cnf(s100,plain,
spl0_6,
inference(rat,[],[s21,s95]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s71,s94,s97,s98,s100,s81,s95,s99]) ).
fof(f1011,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP390-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:00:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.97 % (2164760)Input is clausal, will run a generic CNF schedule.
% 0.54/0.97 % (2164771)dis-21_1_sil=8000:lcm=predicate:random_seed=2460238895:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.54/0.97 % (2164770)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1318166988:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.54/0.97 % (2164765)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=602405489:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.54/0.97 % (2164766)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=81446817:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.54/0.97 % (2164767)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1174660570:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.54/0.97 % (2164769)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3527198503:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.54/0.97 % (2164768)lrs+10_1_sil=8000:sp=occurrence:random_seed=162137483:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.54/0.97 % (2164771)Refutation not found, incomplete strategy
% 0.54/0.97 % (2164771)------------------------------
% 0.54/0.97 % (2164771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.97 % (2164771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.97 % (2164771)CaDiCaL version: 2.1.3
% 0.54/0.97 % (2164771)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.97 % (2164771)Time elapsed: 0.002 s
% 0.54/0.97 % (2164771)Peak memory usage: 88 MB
% 0.54/0.97 % (2164771)Instructions burned: 2 (million)
% 0.54/0.97 % (2164768)Refutation not found, incomplete strategy
% 0.54/0.97 % (2164768)------------------------------
% 0.54/0.97 % (2164768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.97 % (2164768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.97 % (2164768)CaDiCaL version: 2.1.3
% 0.54/0.97 % (2164768)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.97 % (2164768)Time elapsed: 0.003 s
% 0.54/0.97 % (2164768)Peak memory usage: 88 MB
% 0.54/0.97 % (2164768)Instructions burned: 3 (million)
% 0.54/0.97 % (2164770)First to succeed.
% 0.54/0.97 % (2164770)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2164760"
% 0.54/0.97 % (2164769)Instruction limit reached!
% 0.54/0.97 % (2164769)------------------------------
% 0.54/0.97 % (2164769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.97 % (2164769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.97 % (2164769)CaDiCaL version: 2.1.3
% 0.54/0.97 % (2164769)Termination reason: Instruction limit
% 0.54/0.97 % (2164769)Termination phase: Saturation
% 0.54/0.97 % (2164769)Time elapsed: 0.065 s
% 0.54/0.97 % (2164769)Peak memory usage: 89 MB
% 0.54/0.97 % (2164769)Instructions burned: 114 (million)
% 0.54/0.97 % (2164779)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2090501014:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.54/0.97 % (2164779)Refutation not found, incomplete strategy
% 0.54/0.97 % (2164779)------------------------------
% 0.54/0.97 % (2164779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.97 % (2164779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.97 % (2164779)CaDiCaL version: 2.1.3
% 0.54/0.97 % (2164779)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.97 % (2164779)Time elapsed: 0.003 s
% 0.54/0.97 % (2164779)Peak memory usage: 88 MB
% 0.54/0.97 % (2164779)Instructions burned: 3 (million)
% 0.54/0.97 % (2164770)Refutation found. Thanks to Tanya!
% 0.54/0.97 % SZS status Unsatisfiable for theBenchmark
% 0.54/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 3.02/1.17 % (2164770)------------------------------
% 3.02/1.17 % (2164770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.17 % (2164770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.17 % (2164770)CaDiCaL version: 2.1.3
% 3.02/1.17 % (2164770)Termination reason: Refutation
% 3.02/1.17 % (2164770)Time elapsed: 0.023 s
% 3.02/1.17 % (2164770)Peak memory usage: 90 MB
% 3.02/1.17 % (2164770)Instructions burned: 36 (million)
% 3.02/1.17 % (2164770)------------------------------
% 3.02/1.17 % (2164770)------------------------------
% 3.02/1.17 % (2164760)Success in time 0.373 s
% 3.02/1.17 % Vampire exiting
%------------------------------------------------------------------------------