%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP217-1 : 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 : n007.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 10:13:21 AM UTC 2026
% Result : Unsatisfiable 2.37s 1.15s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 57
% Syntax : Number of formulae : 292 ( 17 unt; 26 def)
% Number of atoms : 819 ( 307 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 971 ( 444 ~; 501 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 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_c1) = sk_c11
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c1) = sk_c11
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c1) = sk_c11
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c1) = sk_c11
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c1) = sk_c11
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c1) = sk_c11
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c1) = sk_c11
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = inverse(sk_c2)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f71,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f83,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f87]) ).
fof(f95,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c11 = inverse(sk_c4)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c11 = inverse(sk_c4)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c11 = inverse(sk_c4)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c11) != sk_c10
| multiply(sk_c11,X3) != sk_c10
| multiply(X4,sk_c11) != X3
| inverse(X4) != sk_c11
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| multiply(sk_c11,X7) != sk_c10
| multiply(X8,sk_c11) != X7
| inverse(X8) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| sk_c10 != multiply(X2,sk_c11)
| sk_c10 != multiply(sk_c11,X3)
| multiply(X4,sk_c11) != X3
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c11 != multiply(X6,sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,X3)
| multiply(X4,sk_c11) != X3
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c11 != multiply(X6,sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,multiply(X4,sk_c11))
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c11 != multiply(X6,sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f103]) ).
fof(f105,plain,
! [X0,X1,X8,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,multiply(X4,sk_c11))
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,inverse(X5))
| sk_c11 != multiply(inverse(X5),sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X8,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,multiply(X4,sk_c11))
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,inverse(X5))
| sk_c11 != multiply(inverse(X5),sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f105]) ).
fof(f108,definition,
( spl0_1
<=> ! [X8] :
( sk_c10 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f109,plain,
( ! [X8] :
( sk_c11 != inverse(X8)
| sk_c10 != multiply(sk_c11,multiply(X8,sk_c11)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X5] :
( sk_c11 != multiply(X5,inverse(X5))
| sk_c11 != multiply(inverse(X5),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X5] :
( sk_c11 != multiply(inverse(X5),sk_c10)
| sk_c11 != multiply(X5,inverse(X5)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X1] :
( sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X1] :
( sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(X1,inverse(X1)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f106,f117,f114,f108,f111,f108]) ).
fof(f121,definition,
( spl0_5
<=> sk_c11 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f123,plain,
( sk_c11 = inverse(sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl0_6
<=> sk_c11 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f127,plain,
( sk_c11 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f100,f125,f121]) ).
fof(f130,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c8,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 = multiply(sk_c8,sk_c11)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f98,f125,f130]) ).
fof(f135,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f137,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f96,f125,f135]) ).
fof(f140,definition,
( spl0_9
<=> sk_c11 = multiply(sk_c7,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f145,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f147,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f150,definition,
( spl0_11
<=> sk_c11 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f152,plain,
( sk_c11 = multiply(sk_c6,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f155,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c4,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f157,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f88,f155,f121]) ).
fof(f159,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f86,f155,f130]) ).
fof(f160,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f84,f155,f135]) ).
fof(f165,definition,
( spl0_13
<=> sk_c10 = multiply(sk_c11,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f167,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f76,f165,f121]) ).
fof(f169,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f74,f165,f130]) ).
fof(f170,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f72,f165,f135]) ).
fof(f175,definition,
( spl0_14
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f177,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f175,f121]) ).
fof(f185,definition,
( spl0_15
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f187,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f185,f121]) ).
fof(f195,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f197,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f195,f121]) ).
fof(f201,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f34,f195,f140]) ).
fof(f202,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f32,f195,f145]) ).
fof(f203,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f195,f150]) ).
fof(f205,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f207,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl0_5
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f205,f121]) ).
fof(f209,plain,
( spl0_7
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f205,f130]) ).
fof(f210,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f205,f135]) ).
fof(f211,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f205,f140]) ).
fof(f212,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f205,f145]) ).
fof(f213,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f18,f205,f150]) ).
fof(f215,definition,
( spl0_18
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f217,plain,
( inverse(sk_c1) = sk_c11
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( spl0_5
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f215,f121]) ).
fof(f219,plain,
( spl0_7
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f215,f130]) ).
fof(f220,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f215,f135]) ).
fof(f221,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f215,f140]) ).
fof(f222,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f215,f145]) ).
fof(f223,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f215,f150]) ).
fof(f225,plain,
( sk_c11 != multiply(sk_c7,sk_c10)
| sk_c11 != multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f112,f147]) ).
fof(f231,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f233,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| spl0_19 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,definition,
( spl0_20
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f236,plain,
( sk_c11 = sk_c9
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f239,plain,
( sk_c11 != multiply(sk_c7,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f225,f152]) ).
fof(f240,plain,
( ~ spl0_9
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f239,f150,f145,f111,f140]) ).
fof(f249,definition,
( spl0_22
<=> sk_c11 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f250,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( sk_c11 != multiply(sk_c2,sk_c3)
| spl0_22 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f257,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f112,f217]) ).
fof(f259,definition,
( spl0_24
<=> sk_c11 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f260,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( ~ spl0_24
| ~ spl0_19
| ~ spl0_2
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f257,f215,f111,f231,f259]) ).
fof(f263,plain,
( sk_c11 != sk_c10
| ~ spl0_16
| spl0_22 ),
inference(forward_demodulation,[],[f251,f197]) ).
fof(f264,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f217]) ).
fof(f265,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f3,f147]) ).
fof(f275,definition,
( spl0_26
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f276,plain,
( identity = sk_c11
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f281,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f285,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c1,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f264]) ).
fof(f291,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c1,X0)) = X0
| ~ spl0_18 ),
inference(forward_demodulation,[],[f285,f1]) ).
fof(f292,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f281,f1]) ).
fof(f295,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f265]) ).
fof(f296,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f295,f1]) ).
fof(f306,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f291,f207]) ).
fof(f317,plain,
( sk_c7 = multiply(sk_c7,sk_c11)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f296,f152]) ).
fof(f332,plain,
( sk_c11 = sk_c10
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f250,f197]) ).
fof(f338,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_16
| spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f233,f332]) ).
fof(f341,plain,
( sk_c11 != sk_c10
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f338,f306]) ).
fof(f344,plain,
( $false
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f341,f332]) ).
fof(f345,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f344]) ).
fof(f437,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| sk_c10 != multiply(sk_c1,sk_c11)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f115,f217]) ).
fof(f438,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| sk_c10 != multiply(sk_c8,sk_c11)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f115,f123]) ).
fof(f439,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| sk_c10 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f115,f187]) ).
fof(f452,plain,
( sk_c10 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f439,f177]) ).
fof(f454,plain,
( sk_c10 != multiply(sk_c1,sk_c11)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f437,f306]) ).
fof(f456,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f452,f197]) ).
fof(f457,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f467,definition,
( spl0_37
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f468,plain,
( sk_c11 = sk_c10
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f475,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_17
| ~ spl0_37 ),
inference(superposition,[],[f207,f468]) ).
fof(f479,plain,
( spl0_24
| ~ spl0_17
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f475,f467,f205,f259]) ).
fof(f488,plain,
( sk_c11 != sk_c10
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f454,f260]) ).
fof(f489,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_24
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f488,f468]) ).
fof(f490,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_24
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f491,plain,
( ! [X8] :
( sk_c11 != inverse(X8)
| sk_c11 != multiply(sk_c11,multiply(X8,sk_c11)) )
| ~ spl0_1
| ~ spl0_37 ),
inference(forward_demodulation,[],[f109,f468]) ).
fof(f492,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c11,multiply(sk_c1,sk_c11))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_37 ),
inference(superposition,[],[f491,f217]) ).
fof(f498,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c1,sk_c11))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f492]) ).
fof(f501,plain,
( $false
| ~ spl0_1
| ~ spl0_18
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f498,f291]) ).
fof(f502,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f501]) ).
fof(f509,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c11) )
| ~ spl0_4
| ~ spl0_37 ),
inference(forward_demodulation,[],[f118,f468]) ).
fof(f511,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_37 ),
inference(superposition,[],[f509,f217]) ).
fof(f513,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c8,sk_c11)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_37 ),
inference(superposition,[],[f509,f123]) ).
fof(f516,plain,
( sk_c11 != multiply(sk_c8,sk_c11)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f513]) ).
fof(f517,plain,
( sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f511]) ).
fof(f519,plain,
( sk_c11 != sk_c9
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_37 ),
inference(forward_demodulation,[],[f516,f132]) ).
fof(f525,plain,
( sk_c11 != sk_c11
| sk_c10 != multiply(sk_c11,multiply(sk_c8,sk_c11))
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f109,f123]) ).
fof(f528,plain,
( sk_c10 != multiply(sk_c11,multiply(sk_c8,sk_c11))
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f525]) ).
fof(f531,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f528,f132]) ).
fof(f535,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f531,f137]) ).
fof(f536,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f732,plain,
( sk_c11 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f292,f317]) ).
fof(f739,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c9)
| ~ spl0_7 ),
inference(superposition,[],[f292,f132]) ).
fof(f745,plain,
( sk_c11 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f292,f157]) ).
fof(f750,plain,
( sk_c11 = multiply(sk_c11,sk_c5)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f745,f127]) ).
fof(f752,plain,
( sk_c11 = multiply(sk_c11,sk_c9)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f739,f123]) ).
fof(f757,plain,
( identity = sk_c11
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f732,f3]) ).
fof(f768,plain,
( spl0_26
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f757,f150,f145,f275]) ).
fof(f780,plain,
( sk_c11 = sk_c10
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f750,f167]) ).
fof(f803,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f137,f752]) ).
fof(f809,plain,
( sk_c9 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f292,f752]) ).
fof(f811,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f809,f3]) ).
fof(f820,plain,
( sk_c11 = sk_c9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f811,f276]) ).
fof(f830,plain,
( ~ spl0_24
| ~ spl0_4
| ~ spl0_18
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f517,f467,f215,f117,f259]) ).
fof(f831,plain,
( ~ spl0_20
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f519,f467,f130,f121,f117,f235]) ).
fof(f835,plain,
( spl0_37
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f803,f135,f130,f121,f467]) ).
fof(f837,plain,
( spl0_20
| ~ spl0_5
| ~ spl0_7
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f820,f275,f130,f121,f235]) ).
fof(f843,definition,
( spl0_39
<=> sk_c10 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f847,plain,
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c11,sk_c11)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f438,f132]) ).
fof(f856,definition,
( spl0_40
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f858,plain,
( sk_c10 != sk_c9
| spl0_40 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f859,plain,
( ~ spl0_39
| ~ spl0_40
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f847,f130,f121,f114,f856,f843]) ).
fof(f872,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_8
| ~ spl0_20 ),
inference(superposition,[],[f137,f236]) ).
fof(f873,plain,
( spl0_39
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f872,f235,f135,f843]) ).
fof(f874,plain,
( sk_c11 != sk_c10
| ~ spl0_20
| spl0_40 ),
inference(forward_demodulation,[],[f858,f236]) ).
fof(f875,plain,
( ~ spl0_37
| ~ spl0_20
| spl0_40 ),
inference(avatar_split_clause,[],[f874,f856,f235,f467]) ).
fof(f876,plain,
( spl0_37
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f780,f165,f155,f125,f467]) ).
fof(f881,plain,
( ~ spl0_37
| ~ spl0_16
| spl0_22 ),
inference(avatar_split_clause,[],[f263,f249,f195,f467]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f119]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f128]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f138]) ).
cnf(s9,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f158]) ).
cnf(s10,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f159]) ).
cnf(s11,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f160]) ).
cnf(s15,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f168]) ).
cnf(s16,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s17,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f170]) ).
cnf(s21,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f178]) ).
cnf(s27,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f188]) ).
cnf(s33,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s36,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f201]) ).
cnf(s37,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f202]) ).
cnf(s38,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f203]) ).
cnf(s39,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s40,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f209]) ).
cnf(s41,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f210]) ).
cnf(s42,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f211]) ).
cnf(s43,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f212]) ).
cnf(s44,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f213]) ).
cnf(s45,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f218]) ).
cnf(s46,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f219]) ).
cnf(s47,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f220]) ).
cnf(s48,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s49,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s50,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f223]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f240]) ).
cnf(s56,plain,
( ~ spl0_2
| ~ spl0_18
| ~ spl0_19
| ~ spl0_24 ),
inference(sat_conversion,[],[f262]) ).
cnf(s60,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f345]) ).
cnf(s75,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f457]) ).
cnf(s79,plain,
( ~ spl0_17
| spl0_24
| ~ spl0_37 ),
inference(sat_conversion,[],[f479]) ).
cnf(s81,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_24
| ~ spl0_37 ),
inference(sat_conversion,[],[f490]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_37 ),
inference(sat_conversion,[],[f502]) ).
cnf(s87,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f536]) ).
cnf(s92,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_26 ),
inference(sat_conversion,[],[f768]) ).
cnf(s101,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_24
| ~ spl0_37 ),
inference(sat_conversion,[],[f830]) ).
cnf(s102,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_20
| ~ spl0_37 ),
inference(sat_conversion,[],[f831]) ).
cnf(s106,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_37 ),
inference(sat_conversion,[],[f835]) ).
cnf(s109,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_20
| ~ spl0_26 ),
inference(sat_conversion,[],[f837]) ).
cnf(s113,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_39
| ~ spl0_40 ),
inference(sat_conversion,[],[f859]) ).
cnf(s119,plain,
( ~ spl0_8
| ~ spl0_20
| spl0_39 ),
inference(sat_conversion,[],[f873]) ).
cnf(s120,plain,
( ~ spl0_20
| ~ spl0_37
| spl0_40 ),
inference(sat_conversion,[],[f875]) ).
cnf(s121,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_37 ),
inference(sat_conversion,[],[f876]) ).
cnf(s123,plain,
( ~ spl0_16
| spl0_22
| ~ spl0_37 ),
inference(sat_conversion,[],[f881]) ).
cnf(s128,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s79,s101,s121,s3,s9,s15,s39,s45]) ).
cnf(s129,plain,
( spl0_18
| ~ spl0_37
| ~ spl0_4 ),
inference(rat,[],[s109,s102,s92,s46,s49,s50,s128]) ).
cnf(s130,plain,
( ~ spl0_37
| ~ spl0_4 ),
inference(rat,[],[s109,s102,s92,s40,s43,s44,s79,s101,s129,s128]) ).
cnf(s131,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s106,s16,s17,s128,s130]) ).
cnf(s132,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s106,s10,s11,s128,s130]) ).
cnf(s133,plain,
~ spl0_4,
inference(rat,[],[s106,s4,s5,s121,s132,s131,s130,s128]) ).
cnf(s134,plain,
( spl0_18
| ~ spl0_7
| ~ spl0_37
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s113,s119,s120,s109,s92,s47,s49,s50]) ).
cnf(s135,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_37
| ~ spl0_3 ),
inference(rat,[],[s81,s79]) ).
cnf(s136,plain,
( ~ spl0_7
| ~ spl0_37
| ~ spl0_3
| ~ spl0_5 ),
inference(rat,[],[s113,s119,s120,s109,s92,s41,s43,s44,s135,s134]) ).
cnf(s137,plain,
( ~ spl0_37
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s135,s40,s46,s136]) ).
cnf(s138,plain,
( spl0_13
| spl0_37
| ~ spl0_5 ),
inference(rat,[],[s106,s16,s17]) ).
cnf(s139,plain,
( spl0_12
| spl0_37
| ~ spl0_5 ),
inference(rat,[],[s106,s10,s11]) ).
cnf(s140,plain,
( spl0_37
| ~ spl0_5 ),
inference(rat,[],[s106,s4,s5,s121,s139,s138]) ).
cnf(s141,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s140,s137]) ).
cnf(s142,plain,
~ spl0_3,
inference(rat,[],[s75,s21,s27,s33,s141]) ).
cnf(s143,plain,
( ~ spl0_16
| spl0_19
| ~ spl0_18
| ~ spl0_17
| ~ spl0_37 ),
inference(rat,[],[s60,s123]) ).
cnf(s144,plain,
( spl0_16
| ~ spl0_2 ),
inference(rat,[],[s37,s53,s36,s38]) ).
cnf(s145,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_37
| ~ spl0_2 ),
inference(rat,[],[s143,s56,s144,s79]) ).
cnf(s146,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s53,s48,s49,s50]) ).
cnf(s147,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s53,s42,s43,s44]) ).
cnf(s148,plain,
spl0_37,
inference(rat,[],[s121,s3,s9,s15,s140]) ).
cnf(s149,plain,
~ spl0_2,
inference(rat,[],[s145,s147,s146,s148]) ).
cnf(s150,plain,
spl0_1,
inference(rat,[],[s2,s133,s142,s149]) ).
cnf(s151,plain,
~ spl0_18,
inference(rat,[],[s82,s148,s150]) ).
cnf(s155,plain,
spl0_8,
inference(rat,[],[s47,s151]) ).
cnf(s156,plain,
spl0_7,
inference(rat,[],[s46,s151]) ).
cnf(s158,plain,
~ spl0_5,
inference(rat,[],[s87,s156,s150,s155]) ).
cnf(s159,plain,
$false,
inference(rat,[],[s45,s151,s158]) ).
fof(f889,plain,
$false,
inference(avatar_sat_refutation,[],[s159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP217-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:35:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.37/1.15 % (1160031)Input is clausal, will run a generic CNF schedule.
% 2.37/1.15 % (1160041)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2675067380:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.37/1.15 % (1160041)First to succeed.
% 2.37/1.15 % (1160041)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1160031"
% 2.37/1.15 % (1160039)lrs+10_1_sil=8000:sp=occurrence:random_seed=1404786239:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.37/1.15 % (1160038)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3271178524:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.37/1.15 % (1160037)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3783983867:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.37/1.15 % (1160036)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=2755816189:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.37/1.15 % (1160040)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3091184769:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.37/1.15 % (1160039)Refutation not found, incomplete strategy
% 2.37/1.15 % (1160039)------------------------------
% 2.37/1.15 % (1160039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.15 % (1160039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.15 % (1160039)CaDiCaL version: 2.1.3
% 2.37/1.15 % (1160039)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.15 % (1160039)Time elapsed: 0.008 s
% 2.37/1.15 % (1160039)Peak memory usage: 88 MB
% 2.37/1.15 % (1160039)Instructions burned: 11 (million)
% 2.37/1.15 % (1160042)dis-21_1_sil=8000:lcm=predicate:random_seed=1783475201: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)
% 2.37/1.15 % (1160042)Refutation not found, incomplete strategy
% 2.37/1.15 % (1160042)------------------------------
% 2.37/1.15 % (1160042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.15 % (1160042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.15 % (1160042)CaDiCaL version: 2.1.3
% 2.37/1.15 % (1160042)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.15 % (1160042)Time elapsed: 0.002 s
% 2.37/1.15 % (1160042)Peak memory usage: 88 MB
% 2.37/1.15 % (1160042)Instructions burned: 3 (million)
% 2.37/1.15 % (1160040)Instruction limit reached!
% 2.37/1.15 % (1160040)------------------------------
% 2.37/1.15 % (1160040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.15 % (1160040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.15 % (1160040)CaDiCaL version: 2.1.3
% 2.37/1.15 % (1160040)Termination reason: Instruction limit
% 2.37/1.15 % (1160040)Termination phase: Saturation
% 2.37/1.15 % (1160040)Time elapsed: 0.064 s
% 2.37/1.15 % (1160040)Peak memory usage: 89 MB
% 2.37/1.15 % (1160040)Instructions burned: 115 (million)
% 2.37/1.15 % (1160041)Refutation found. Thanks to Tanya!
% 2.37/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.37/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.25 % (1160041)------------------------------
% 2.62/1.25 % (1160041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.25 % (1160041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.25 % (1160041)CaDiCaL version: 2.1.3
% 2.62/1.25 % (1160041)Termination reason: Refutation
% 2.62/1.25 % (1160041)Time elapsed: 0.011 s
% 2.62/1.25 % (1160041)Peak memory usage: 90 MB
% 2.62/1.25 % (1160041)Instructions burned: 30 (million)
% 2.62/1.25 % (1160041)------------------------------
% 2.62/1.25 % (1160041)------------------------------
% 2.62/1.25 % (1160031)Success in time 0.306 s
% 2.62/1.25 % Vampire exiting
%------------------------------------------------------------------------------