%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : 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 10:17:11 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.56s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 52
% Syntax : Number of formulae : 324 ( 22 unt; 19 def)
% Number of atoms : 1012 ( 324 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1304 ( 616 ~; 669 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f21,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f67,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f83,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) )
| ~ 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(X4,inverse(X4))
| sk_c9 != multiply(inverse(X4),sk_c10) )
| ~ 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(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ 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(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(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(f140,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
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(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(f160,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f160,f104]) ).
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(f181,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f172,f138]) ).
fof(f182,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f172,f143]) ).
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(f193,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f8,f184,f138]) ).
fof(f194,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f6,f184,f143]) ).
fof(f196,plain,
( sk_c9 != multiply(sk_c5,sk_c6)
| sk_c9 != multiply(sk_c6,sk_c10)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f95,f130]) ).
fof(f206,definition,
( spl0_19
<=> sk_c9 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f207,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| spl0_19 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f213,plain,
( sk_c9 != multiply(sk_c6,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f196,f135]) ).
fof(f222,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f213,f125]) ).
fof(f223,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f226,plain,
( sk_c9 != multiply(sk_c3,sk_c10)
| sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f95,f150]) ).
fof(f236,definition,
( spl0_22
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f237,plain,
( sk_c10 = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( sk_c10 != sk_c9
| spl0_22 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f241,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f174]) ).
fof(f242,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f145]) ).
fof(f243,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f130]) ).
fof(f244,plain,
( identity = multiply(sk_c10,sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f3,f106]) ).
fof(f245,plain,
( identity = multiply(sk_c10,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f150]) ).
fof(f258,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f259,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c10,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f186]) ).
fof(f263,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f135]) ).
fof(f267,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f258,f1]) ).
fof(f270,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c1,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f241]) ).
fof(f271,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f270,f1]) ).
fof(f272,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c4,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f242]) ).
fof(f273,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c4,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f272,f1]) ).
fof(f274,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f243]) ).
fof(f275,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f274,f1]) ).
fof(f280,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f271,f186]) ).
fof(f291,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f259,f280]) ).
fof(f293,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f291,f186]) ).
fof(f304,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f273,f140]) ).
fof(f307,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f304,f208]) ).
fof(f308,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f309,plain,
( sk_c6 = multiply(sk_c6,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f275,f135]) ).
fof(f318,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f263,f309]) ).
fof(f320,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f318,f135]) ).
fof(f471,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f267,f3]) ).
fof(f472,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f267,f267]) ).
fof(f482,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f267,f293]) ).
fof(f486,plain,
( sk_c7 = multiply(inverse(sk_c10),identity)
| ~ spl0_5 ),
inference(superposition,[],[f267,f244]) ).
fof(f487,plain,
( sk_c3 = multiply(inverse(sk_c10),identity)
| ~ spl0_14 ),
inference(superposition,[],[f267,f245]) ).
fof(f488,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f267,f320]) ).
fof(f495,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_7 ),
inference(superposition,[],[f267,f115]) ).
fof(f497,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c10)
| ~ spl0_6 ),
inference(superposition,[],[f267,f110]) ).
fof(f506,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f497,f150]) ).
fof(f508,plain,
( sk_c10 = multiply(sk_c10,sk_c8)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f495,f106]) ).
fof(f514,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f488,f3]) ).
fof(f515,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[],[f486,f487]) ).
fof(f518,plain,
( identity = sk_c10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f482,f3]) ).
fof(f523,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f471,f472]) ).
fof(f543,plain,
( sk_c10 = sk_c9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f207,f293]) ).
fof(f546,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f506,f293]) ).
fof(f554,plain,
( sk_c10 = multiply(sk_c3,sk_c10)
| ~ spl0_6
| ~ spl0_22 ),
inference(superposition,[],[f110,f237]) ).
fof(f556,plain,
( sk_c10 = multiply(sk_c2,sk_c10)
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f162,f237]) ).
fof(f560,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f320,f237]) ).
fof(f574,plain,
( ! [X0] : multiply(X0,sk_c10) = X0
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f523,f518]) ).
fof(f576,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f226,f237]) ).
fof(f583,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f576,f554]) ).
fof(f592,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f583,f293]) ).
fof(f595,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f592,f237]) ).
fof(f596,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f595]) ).
fof(f600,plain,
( $false
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f543,f238]) ).
fof(f601,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f602,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f546,f238]) ).
fof(f603,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f602]) ).
fof(f605,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f514,f518]) ).
fof(f613,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f605,f238]) ).
fof(f614,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f619,plain,
( ! [X7] :
( sk_c9 != multiply(sk_c10,X7)
| sk_c10 != inverse(X7) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f92,f574]) ).
fof(f623,plain,
( sk_c10 = sk_c3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f554,f574]) ).
fof(f624,plain,
( sk_c2 = sk_c10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f556,f574]) ).
fof(f625,plain,
( ! [X7] :
( sk_c10 != multiply(sk_c10,X7)
| sk_c10 != inverse(X7) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f619,f237]) ).
fof(f645,plain,
( identity != sk_c10
| sk_c10 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f625,f245]) ).
fof(f648,plain,
( sk_c10 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f645,f518]) ).
fof(f655,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f648,f150]) ).
fof(f656,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f655]) ).
fof(f663,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c10)
| sk_c10 != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f101,f237]) ).
fof(f664,plain,
( ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| inverse(X0) != sk_c10 )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f663,f574]) ).
fof(f669,plain,
( multiply(sk_c1,sk_c2) != sk_c10
| sk_c2 != sk_c10
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f664,f174]) ).
fof(f672,plain,
( sk_c10 != multiply(sk_c7,sk_c10)
| sk_c10 != sk_c10
| ~ spl0_4
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f664,f106]) ).
fof(f678,plain,
( sk_c10 != multiply(sk_c7,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f672]) ).
fof(f682,plain,
( sk_c10 != sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f678,f574]) ).
fof(f685,plain,
( sk_c2 != sk_c10
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f669,f186]) ).
fof(f690,plain,
( sk_c10 != sk_c3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f682,f515]) ).
fof(f694,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f685,f624]) ).
fof(f695,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f696,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f690,f623]) ).
fof(f697,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f696]) ).
fof(f698,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f98,f237]) ).
fof(f699,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != X3 )
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f698,f574]) ).
fof(f705,plain,
( sk_c10 != sk_c10
| sk_c10 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f699,f106]) ).
fof(f706,plain,
( sk_c10 != sk_c10
| sk_c10 != sk_c3
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f699,f150]) ).
fof(f707,plain,
( sk_c10 != sk_c3
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f706]) ).
fof(f708,plain,
( sk_c10 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f705]) ).
fof(f710,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f707,f623]) ).
fof(f711,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f712,plain,
( sk_c10 != sk_c3
| ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f708,f515]) ).
fof(f725,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f712,f623]) ).
fof(f726,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f725]) ).
fof(f754,plain,
( sk_c10 = multiply(sk_c4,sk_c10)
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f140,f237]) ).
fof(f761,plain,
( ! [X7] :
( sk_c10 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) )
| ~ spl0_1
| ~ spl0_22 ),
inference(forward_demodulation,[],[f92,f237]) ).
fof(f807,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f761,f273]) ).
fof(f808,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_13
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f807]) ).
fof(f809,plain,
( $false
| ~ spl0_1
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f808,f145]) ).
fof(f810,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f809]) ).
fof(f826,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f508,f120]) ).
fof(f833,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f663,f145]) ).
fof(f847,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f833,f560]) ).
fof(f855,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f847,f754]) ).
fof(f856,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f855]) ).
fof(f878,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f698,f754]) ).
fof(f880,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f878]) ).
fof(f883,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f880,f145]) ).
fof(f884,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f883]) ).
fof(f895,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f826,f238]) ).
fof(f896,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f895]) ).
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(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(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(s19,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
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(s33,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f181]) ).
cnf(s34,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f182]) ).
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(s41,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f193]) ).
cnf(s42,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f194]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f223]) ).
cnf(s53,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f308]) ).
cnf(s71,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f596]) ).
cnf(s73,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_19
| spl0_22 ),
inference(sat_conversion,[],[f601]) ).
cnf(s74,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f603]) ).
cnf(s76,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f614]) ).
cnf(s78,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f656]) ).
cnf(s84,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f695]) ).
cnf(s85,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f697]) ).
cnf(s86,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f711]) ).
cnf(s89,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f726]) ).
cnf(s94,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f810]) ).
cnf(s98,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f856]) ).
cnf(s104,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f884]) ).
cnf(s109,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_22 ),
inference(sat_conversion,[],[f896]) ).
cnf(s111,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s74,s84,s3,s11,s19,s27,s35]) ).
cnf(s112,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(rat,[],[s74,s85]) ).
cnf(s113,plain,
( spl0_17
| ~ spl0_4 ),
inference(rat,[],[s109,s98,s36,s37,s39,s40,s41,s42,s111]) ).
cnf(s114,plain,
( spl0_16
| ~ spl0_4 ),
inference(rat,[],[s109,s98,s28,s29,s31,s32,s33,s34,s111]) ).
cnf(s115,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s76,s98,s15,s16,s17,s18,s113,s114]) ).
cnf(s116,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_4
| ~ spl0_5
| ~ spl0_16 ),
inference(rat,[],[s76,s98,s7,s8,s9,s10,s112]) ).
cnf(s117,plain,
~ spl0_4,
inference(rat,[],[s116,s115,s114,s113,s111]) ).
cnf(s118,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_6
| ~ spl0_14
| ~ spl0_3
| ~ spl0_5 ),
inference(rat,[],[s74,s89]) ).
cnf(s119,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s109,s104,s36,s37,s41,s42]) ).
cnf(s120,plain,
( spl0_16
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s109,s104,s28,s29,s33,s34]) ).
cnf(s121,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s76,s104,s15,s16,s17,s18,s119,s120]) ).
cnf(s122,plain,
( ~ spl0_14
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s76,s104,s7,s8,s9,s10,s118]) ).
cnf(s123,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s122,s121,s120,s119]) ).
cnf(s124,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_16
| ~ spl0_3
| ~ spl0_6 ),
inference(rat,[],[s74,s86]) ).
cnf(s125,plain,
~ spl0_3,
inference(rat,[],[s124,s3,s11,s27,s35,s123]) ).
cnf(s126,plain,
( ~ spl0_6
| ~ spl0_17
| ~ spl0_16
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s71,s74]) ).
cnf(s127,plain,
( spl0_6
| ~ spl0_2 ),
inference(rat,[],[s47,s6,s7,s8]) ).
cnf(s128,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s47,s38,s39,s40]) ).
cnf(s129,plain,
( spl0_16
| ~ spl0_2 ),
inference(rat,[],[s47,s30,s31,s32]) ).
cnf(s130,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17 ),
inference(rat,[],[s47,s14,s15,s16,s126]) ).
cnf(s131,plain,
~ spl0_2,
inference(rat,[],[s130,s129,s128,s127]) ).
cnf(s132,plain,
spl0_1,
inference(rat,[],[s2,s117,s125,s131]) ).
cnf(s133,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_14 ),
inference(rat,[],[s53,s9,s10,s74,s73,s78,s132]) ).
cnf(s134,plain,
spl0_17,
inference(rat,[],[s109,s94,s35,s36,s37,s42,s132]) ).
cnf(s135,plain,
spl0_16,
inference(rat,[],[s109,s94,s27,s28,s29,s34,s132]) ).
cnf(s136,plain,
~ spl0_14,
inference(rat,[],[s133,s134,s135]) ).
cnf(s137,plain,
spl0_13,
inference(rat,[],[s18,s136]) ).
cnf(s139,plain,
spl0_11,
inference(rat,[],[s16,s136]) ).
cnf(s140,plain,
spl0_10,
inference(rat,[],[s15,s136]) ).
cnf(s145,plain,
~ spl0_22,
inference(rat,[],[s94,s132,s137]) ).
cnf(s147,plain,
$false,
inference(rat,[],[s76,s145,s134,s135,s139,s140]) ).
fof(f899,plain,
$false,
inference(avatar_sat_refutation,[],[s147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.42 % Computer : n007.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 09:35:40 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.47 Running first-order model finding
% 0.16/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.56 % (1159447)Will run a generic schedule for satisfiability detection.
% 0.23/0.56 % (1159454)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2108510112:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.56 % (1159452)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3393840913_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.56 % (1159453)% WARNING: option uhcvi not known.
% 0.23/0.56 % TRYING [1]
% 0.23/0.56 % TRYING [2]
% 0.23/0.56 % TRYING [3]
% 0.23/0.56 % (1159453)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2587274171:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.56 % TRYING [4]
% 0.23/0.56 % (1159456)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1676840562:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.56 % (1159455)dis+10_1_sil=32000:sp=arity:random_seed=1634735862:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.56 % (1159457)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3464644543:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.56 % (1159458)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3875919657:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.56 % TRYING [5]
% 0.23/0.56 % (1159456) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1159447-1159456"...
% 0.23/0.56 % (1159453) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1159447-1159453"...
% 0.23/0.56 % (1159456)...printing done.
% 0.23/0.56 % (1159453)...printing done.
% 0.23/0.56 % (1159455) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1159447-1159455"...
% 0.23/0.56 % (1159456)Refutation found. Thanks to Tanya!
% 0.23/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.56 % (1159456)------------------------------
% 0.23/0.56 % (1159456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.56 % (1159456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.56 % (1159456)CaDiCaL version: 2.1.3
% 0.23/0.56 % (1159456)Termination reason: Refutation
% 0.23/0.56 % (1159456)Time elapsed: 0.031 s
% 0.23/0.56 % (1159456)Peak memory usage: 13 MB
% 0.23/0.56 % (1159456)Instructions burned: 30 (million)
% 0.23/0.56 % (1159447)Success in time 0.072 s
% 0.23/0.56 % Vampire exiting
%------------------------------------------------------------------------------