%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:13:20 AM UTC 2026
% Result : Unsatisfiable 2.11s 1.89s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 55
% Syntax : Number of formulae : 292 ( 19 unt; 23 def)
% Number of atoms : 839 ( 294 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1006 ( 459 ~; 524 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c2 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c6,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f53,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c10 = inverse(sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c10 = inverse(sk_c3)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c9 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| multiply(X1,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,X5) != sk_c9
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c9
| multiply(sk_c10,X6) != sk_c9
| multiply(X7,sk_c10) != X6
| inverse(X7) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c9 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c9 != multiply(X5,sk_c10)
| sk_c9 != multiply(sk_c10,X6)
| multiply(X7,sk_c10) != X6
| sk_c10 != inverse(X7) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c9 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c9 != multiply(X5,sk_c10)
| sk_c9 != multiply(sk_c10,X6)
| multiply(X7,sk_c10) != X6
| sk_c10 != inverse(X7) ),
inference(equality_resolution,[],[f86]) ).
fof(f88,plain,
! [X2,X3,X0,X6,X7,X4] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c9 != multiply(X4,inverse(X4))
| sk_c9 != multiply(inverse(X4),sk_c10)
| sk_c9 != multiply(sk_c10,X6)
| multiply(X7,sk_c10) != X6
| sk_c10 != inverse(X7) ),
inference(equality_resolution,[],[f87]) ).
fof(f89,plain,
! [X2,X3,X0,X7,X4] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c9 != multiply(X4,inverse(X4))
| sk_c9 != multiply(inverse(X4),sk_c10)
| sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) ),
inference(equality_resolution,[],[f88]) ).
fof(f91,definition,
( spl0_1
<=> ! [X7] :
( sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f92,plain,
( ! [X7] :
( sk_c10 != inverse(X7)
| sk_c9 != multiply(sk_c10,multiply(X7,sk_c10)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,inverse(X4))
| sk_c9 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f95,plain,
( ! [X4] :
( sk_c9 != multiply(inverse(X4),sk_c10)
| sk_c9 != multiply(X4,inverse(X4)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_3
<=> ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f98,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,definition,
( spl0_4
<=> ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f101,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f89,f100,f97,f97,f94,f91]) ).
fof(f104,definition,
( spl0_5
<=> sk_c10 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( sk_c10 = inverse(sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl0_6
<=> sk_c10 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f110,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f84,f108,f104]) ).
fof(f113,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c7,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f115,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f82,f108,f113]) ).
fof(f118,definition,
( spl0_8
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f80,f108,f118]) ).
fof(f123,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c6,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c9 = multiply(sk_c6,sk_c10)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f78,f108,f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f130,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f76,f108,f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = multiply(sk_c5,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f74,f108,f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f141,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f72,f108,f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f70,f108,f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f148,f104]) ).
fof(f152,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f148,f113]) ).
fof(f153,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f148,f118]) ).
fof(f154,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f148,f123]) ).
fof(f155,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f60,f148,f128]) ).
fof(f156,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f58,f148,f133]) ).
fof(f157,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f56,f148,f138]) ).
fof(f158,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f54,f148,f143]) ).
fof(f172,definition,
( spl0_16
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f174,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f36,f172,f104]) ).
fof(f176,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f34,f172,f113]) ).
fof(f177,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f32,f172,f118]) ).
fof(f178,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f172,f123]) ).
fof(f179,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f172,f128]) ).
fof(f180,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f172,f133]) ).
fof(f184,definition,
( spl0_17
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f186,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_5
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f184,f104]) ).
fof(f188,plain,
( spl0_7
| spl0_17 ),
inference(avatar_split_clause,[],[f18,f184,f113]) ).
fof(f189,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f16,f184,f118]) ).
fof(f190,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f14,f184,f123]) ).
fof(f191,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f12,f184,f128]) ).
fof(f192,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f10,f184,f133]) ).
fof(f196,plain,
( sk_c9 != multiply(sk_c6,sk_c10)
| sk_c9 != multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f95,f130]) ).
fof(f203,definition,
( spl0_19
<=> sk_c9 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f204,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| spl0_19 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f216,plain,
( sk_c9 != multiply(sk_c6,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f196,f135]) ).
fof(f217,plain,
( ~ spl0_9
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f216,f133,f128,f94,f123]) ).
fof(f218,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| sk_c9 != multiply(sk_c3,sk_c10)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f95,f150]) ).
fof(f220,definition,
( spl0_21
<=> sk_c9 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f222,plain,
( sk_c9 != multiply(sk_c3,sk_c10)
| spl0_21 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,plain,
( ~ spl0_21
| ~ spl0_19
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f218,f148,f94,f203,f220]) ).
fof(f226,definition,
( spl0_22
<=> multiply(sk_c1,sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f227,plain,
( multiply(sk_c1,sk_c2) = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( multiply(sk_c1,sk_c2) != sk_c9
| spl0_22 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f234,plain,
( sk_c10 != sk_c9
| ~ spl0_17
| spl0_22 ),
inference(forward_demodulation,[],[f228,f186]) ).
fof(f235,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f174]) ).
fof(f237,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f130]) ).
fof(f252,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f253,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c10,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f186]) ).
fof(f255,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c1,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f235]) ).
fof(f258,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f135]) ).
fof(f260,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c9,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f110]) ).
fof(f261,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f255,f1]) ).
fof(f262,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f252,f1]) ).
fof(f267,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f237]) ).
fof(f268,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f267,f1]) ).
fof(f278,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f261,f186]) ).
fof(f287,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f253,f278]) ).
fof(f289,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f287,f186]) ).
fof(f304,plain,
( sk_c6 = multiply(sk_c6,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f268,f135]) ).
fof(f313,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f258,f304]) ).
fof(f315,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f313,f135]) ).
fof(f330,plain,
( multiply(sk_c3,sk_c9) = multiply(sk_c10,sk_c9)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f260,f315]) ).
fof(f333,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f330,f110]) ).
fof(f367,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_7 ),
inference(superposition,[],[f262,f115]) ).
fof(f369,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c10)
| ~ spl0_6 ),
inference(superposition,[],[f262,f110]) ).
fof(f374,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f369,f150]) ).
fof(f376,plain,
( sk_c10 = multiply(sk_c10,sk_c8)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f367,f106]) ).
fof(f386,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f374,f205]) ).
fof(f387,plain,
( ~ spl0_6
| ~ spl0_14
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f389,plain,
( sk_c10 = sk_c9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f204,f289]) ).
fof(f390,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f374,f289]) ).
fof(f393,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f390,f234]) ).
fof(f394,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f395,plain,
( sk_c10 = sk_c9
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f227,f186]) ).
fof(f397,plain,
( sk_c10 = multiply(sk_c3,sk_c10)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f110,f389]) ).
fof(f406,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_21 ),
inference(forward_demodulation,[],[f222,f389]) ).
fof(f409,plain,
( $false
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f397,f406]) ).
fof(f410,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f411,plain,
( ! [X7] :
( sk_c10 != inverse(X7)
| sk_c10 != multiply(sk_c10,multiply(X7,sk_c10)) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f92,f389]) ).
fof(f427,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c10,multiply(sk_c3,sk_c10))
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f411,f150]) ).
fof(f428,plain,
( sk_c10 != multiply(sk_c10,multiply(sk_c3,sk_c10))
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f427]) ).
fof(f437,definition,
( spl0_27
<=> sk_c10 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f509,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f204,f395]) ).
fof(f534,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c10,multiply(sk_c7,sk_c10))
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f92,f106]) ).
fof(f537,plain,
( sk_c9 != multiply(sk_c10,multiply(sk_c7,sk_c10))
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f534]) ).
fof(f539,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f537,f115]) ).
fof(f545,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f539,f120]) ).
fof(f546,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f548,plain,
( sk_c10 != multiply(sk_c6,sk_c9)
| sk_c10 != multiply(sk_c5,sk_c6)
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f101,f130]) ).
fof(f550,plain,
( sk_c10 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f101,f150]) ).
fof(f554,definition,
( spl0_30
<=> sk_c10 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f555,plain,
( sk_c10 = multiply(sk_c3,sk_c10)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f558,definition,
( spl0_31
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f561,plain,
( ~ spl0_30
| ~ spl0_31
| ~ spl0_4
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f550,f148,f100,f558,f554]) ).
fof(f563,plain,
( sk_c10 != sk_c6
| sk_c10 != multiply(sk_c5,sk_c6)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f548,f304]) ).
fof(f574,plain,
( sk_c10 != sk_c9
| sk_c10 != sk_c6
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f563,f135]) ).
fof(f580,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f120,f376]) ).
fof(f603,definition,
( spl0_35
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f604,plain,
( sk_c10 = sk_c9
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f607,plain,
( ~ spl0_27
| ~ spl0_35
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f574,f133,f128,f100,f603,f437]) ).
fof(f608,plain,
( spl0_35
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f580,f118,f113,f104,f603]) ).
fof(f623,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f98,f145]) ).
fof(f626,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f98,f150]) ).
fof(f627,plain,
( sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f626]) ).
fof(f629,plain,
( sk_c10 != multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f623]) ).
fof(f640,plain,
( spl0_30
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f397,f203,f184,f172,f108,f554]) ).
fof(f641,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f333,f133,f128,f108,f558]) ).
fof(f642,plain,
( spl0_35
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f390,f184,f172,f148,f108,f603]) ).
fof(f663,plain,
( ~ spl0_12
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f629,f143,f97,f138]) ).
fof(f664,plain,
( ~ spl0_6
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f627,f148,f97,f108]) ).
fof(f722,plain,
( sk_c10 = multiply(sk_c3,sk_c10)
| ~ spl0_6
| ~ spl0_35 ),
inference(superposition,[],[f110,f604]) ).
fof(f723,plain,
( sk_c6 = multiply(sk_c6,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35 ),
inference(superposition,[],[f304,f604]) ).
fof(f725,plain,
( sk_c9 = sk_c6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35 ),
inference(forward_demodulation,[],[f723,f125]) ).
fof(f726,plain,
( spl0_30
| ~ spl0_6
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f722,f603,f108,f554]) ).
fof(f727,plain,
( sk_c10 = sk_c6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35 ),
inference(forward_demodulation,[],[f725,f604]) ).
fof(f731,plain,
( spl0_27
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f727,f603,f133,f128,f123,f437]) ).
fof(f801,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| ~ spl0_30 ),
inference(forward_demodulation,[],[f428,f555]) ).
fof(f802,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f801,f509]) ).
fof(f803,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f802]) ).
fof(f809,plain,
( sk_c10 != multiply(sk_c10,sk_c9)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f550,f555]) ).
fof(f818,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_30
| ~ spl0_35 ),
inference(forward_demodulation,[],[f809,f604]) ).
fof(f825,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22
| ~ spl0_30
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f818,f509]) ).
fof(f826,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22
| ~ spl0_30
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f825]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f102]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f111]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f116]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f121]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f141]) ).
cnf(s10,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s11,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s12,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s13,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s14,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s16,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s17,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s18,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s27,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f175]) ).
cnf(s28,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s29,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s30,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f178]) ).
cnf(s31,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f179]) ).
cnf(s32,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f180]) ).
cnf(s35,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s36,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s37,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s38,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s39,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s40,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f192]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f217]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_19
| ~ spl0_21 ),
inference(sat_conversion,[],[f223]) ).
cnf(s51,plain,
( ~ spl0_6
| ~ spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f387]) ).
cnf(s55,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f394]) ).
cnf(s56,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f410]) ).
cnf(s69,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f546]) ).
cnf(s70,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_30
| ~ spl0_31 ),
inference(sat_conversion,[],[f561]) ).
cnf(s80,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_27
| ~ spl0_35 ),
inference(sat_conversion,[],[f607]) ).
cnf(s81,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_35 ),
inference(sat_conversion,[],[f608]) ).
cnf(s92,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_30 ),
inference(sat_conversion,[],[f640]) ).
cnf(s93,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| spl0_31 ),
inference(sat_conversion,[],[f641]) ).
cnf(s94,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_35 ),
inference(sat_conversion,[],[f642]) ).
cnf(s104,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f663]) ).
cnf(s105,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(sat_conversion,[],[f664]) ).
cnf(s125,plain,
( ~ spl0_6
| spl0_30
| ~ spl0_35 ),
inference(sat_conversion,[],[f726]) ).
cnf(s127,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_27
| ~ spl0_35 ),
inference(sat_conversion,[],[f731]) ).
cnf(s139,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22
| ~ spl0_30 ),
inference(sat_conversion,[],[f803]) ).
cnf(s143,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22
| ~ spl0_30
| ~ spl0_35 ),
inference(sat_conversion,[],[f826]) ).
cnf(s144,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s143,s125,s51,s55,s94,s3,s11,s27,s35]) ).
cnf(s145,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_14
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s143,s92,s55,s94,s51]) ).
cnf(s146,plain,
( spl0_17
| ~ spl0_14
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s125,s70,s81,s93,s36,s37,s39,s40,s144]) ).
cnf(s147,plain,
( ~ spl0_14
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s125,s70,s81,s93,s28,s29,s31,s32,s145,s146,s144]) ).
cnf(s148,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s127,s80,s81,s12,s13,s14,s15,s16,s144]) ).
cnf(s149,plain,
~ spl0_4,
inference(rat,[],[s127,s80,s81,s4,s5,s6,s7,s8,s147,s148,s144]) ).
cnf(s150,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s104,s17,s18]) ).
cnf(s151,plain,
( ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s104,s9,s10,s105]) ).
cnf(s152,plain,
~ spl0_3,
inference(rat,[],[s151,s150]) ).
cnf(s153,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s46,s38,s39,s40]) ).
cnf(s154,plain,
( spl0_16
| ~ spl0_2 ),
inference(rat,[],[s46,s30,s31,s32]) ).
cnf(s155,plain,
( ~ spl0_14
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s56,s47,s51,s153,s154]) ).
cnf(s156,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s46,s14,s15,s16]) ).
cnf(s157,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s46,s6,s7,s8,s155]) ).
cnf(s158,plain,
~ spl0_2,
inference(rat,[],[s157,s156]) ).
cnf(s159,plain,
spl0_1,
inference(rat,[],[s2,s149,s152,s158]) ).
cnf(s160,plain,
spl0_17,
inference(rat,[],[s69,s35,s36,s37,s159]) ).
cnf(s161,plain,
( ~ spl0_16
| ~ spl0_14
| ~ spl0_6 ),
inference(rat,[],[s139,s92,s55,s51,s159,s160]) ).
cnf(s162,plain,
spl0_16,
inference(rat,[],[s69,s27,s28,s29,s159]) ).
cnf(s163,plain,
spl0_14,
inference(rat,[],[s69,s11,s12,s13,s159]) ).
cnf(s164,plain,
~ spl0_6,
inference(rat,[],[s161,s162,s163]) ).
cnf(s170,plain,
spl0_8,
inference(rat,[],[s5,s164]) ).
cnf(s171,plain,
spl0_7,
inference(rat,[],[s4,s164]) ).
cnf(s172,plain,
spl0_5,
inference(rat,[],[s3,s164]) ).
cnf(s176,plain,
$false,
inference(rat,[],[s69,s172,s159,s170,s171]) ).
fof(f827,plain,
$false,
inference(avatar_sat_refutation,[],[s176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:37:36 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.11/1.89 % (3254717)Input is clausal, will run a generic CNF schedule.
% 2.11/1.89 % (3254724)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=1901960477:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.11/1.89 % (3254730)dis-21_1_sil=8000:lcm=predicate:random_seed=308060805: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)
% 2.11/1.89 % (3254730)Refutation not found, incomplete strategy
% 2.11/1.89 % (3254730)------------------------------
% 2.11/1.89 % (3254730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.89 % (3254730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.89 % (3254730)CaDiCaL version: 2.1.3
% 2.11/1.89 % (3254730)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.89 % (3254730)Time elapsed: 0.003 s
% 2.11/1.89 % (3254730)Peak memory usage: 88 MB
% 2.11/1.89 % (3254730)Instructions burned: 2 (million)
% 2.11/1.89 % (3254728)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3177732134:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.11/1.89 % (3254725)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3121323135:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.11/1.89 % (3254729)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2998711579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.11/1.89 % (3254727)lrs+10_1_sil=8000:sp=occurrence:random_seed=741758821:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.11/1.89 % (3254726)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1089359393:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.11/1.89 % (3254729)First to succeed.
% 2.11/1.89 % (3254729)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3254717"
% 2.11/1.89 % (3254727)Instruction limit reached!
% 2.11/1.89 % (3254727)------------------------------
% 2.11/1.89 % (3254727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.89 % (3254727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.89 % (3254727)CaDiCaL version: 2.1.3
% 2.11/1.89 % (3254727)Termination reason: Instruction limit
% 2.11/1.89 % (3254727)Termination phase: Saturation
% 2.11/1.89 % (3254727)Time elapsed: 0.089 s
% 2.11/1.89 % (3254727)Peak memory usage: 89 MB
% 2.11/1.89 % (3254727)Instructions burned: 108 (million)
% 2.11/1.89 % (3254728)Instruction limit reached!
% 2.11/1.89 % (3254728)------------------------------
% 2.11/1.89 % (3254728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.89 % (3254728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.89 % (3254728)CaDiCaL version: 2.1.3
% 2.11/1.89 % (3254728)Termination reason: Instruction limit
% 2.11/1.89 % (3254728)Termination phase: Saturation
% 2.11/1.89 % (3254728)Time elapsed: 0.107 s
% 2.11/1.89 % (3254728)Peak memory usage: 89 MB
% 2.11/1.89 % (3254728)Instructions burned: 114 (million)
% 2.11/1.89 % (3254730)------------------------------
% 2.11/1.89 % (3254730)------------------------------
% 2.11/1.89 % (3254738)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=2514034066:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 2.11/1.89 % (3254739)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2239790261:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 2.11/1.89 % (3254729)Refutation found. Thanks to Tanya!
% 2.11/1.89 % SZS status Unsatisfiable for theBenchmark
% 2.11/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 5.94/2.13 % (3254729)------------------------------
% 5.94/2.13 % (3254729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/2.13 % (3254729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/2.13 % (3254729)CaDiCaL version: 2.1.3
% 5.94/2.13 % (3254729)Termination reason: Refutation
% 5.94/2.13 % (3254729)Time elapsed: 0.031 s
% 5.94/2.13 % (3254729)Peak memory usage: 89 MB
% 5.94/2.13 % (3254729)Instructions burned: 29 (million)
% 5.94/2.13 % (3254729)------------------------------
% 5.94/2.13 % (3254729)------------------------------
% 5.94/2.13 % (3254717)Success in time 0.707 s
% 5.94/2.13 % Vampire exiting
%------------------------------------------------------------------------------