%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP252-1 : 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 : n026.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 10:17:17 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 57
% Syntax : Number of formulae : 330 ( 21 unt; 19 def)
% Number of atoms : 986 ( 326 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1223 ( 567 ~; 637 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 68 ( 0 sgn 68 !; 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_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f79,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(sk_c8,X5) != sk_c9
| multiply(X6,sk_c8) != X5
| inverse(X6) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(sk_c8,X5)
| multiply(X6,sk_c8) != X5
| sk_c8 != inverse(X6) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X6] :
( sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X6] :
( sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f97,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_5
<=> ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f91,f99,f105,f102,f99,f96,f93]) ).
fof(f109,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f115,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f113,f109]) ).
fof(f118,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f113,f118]) ).
fof(f123,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f124,plain,
( sk_c9 != multiply(sk_c8,sk_c7)
| spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f113,f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f130,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f113,f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f80,f113,f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f140,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f148,f109]) ).
fof(f152,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f72,f148,f118]) ).
fof(f153,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f70,f148,f123]) ).
fof(f154,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f148,f128]) ).
fof(f155,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f148,f133]) ).
fof(f159,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f161,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f159,f109]) ).
fof(f163,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f159,f118]) ).
fof(f164,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f159,f123]) ).
fof(f165,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f159,f128]) ).
fof(f166,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f159,f133]) ).
fof(f170,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f172,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f170,f109]) ).
fof(f174,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f170,f118]) ).
fof(f175,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f170,f123]) ).
fof(f176,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f170,f128]) ).
fof(f177,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f38,f170,f133]) ).
fof(f181,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f183,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_6
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f181,f109]) ).
fof(f185,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f181,f118]) ).
fof(f186,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f181,f123]) ).
fof(f187,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f181,f128]) ).
fof(f188,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f181,f133]) ).
fof(f189,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f181,f138]) ).
fof(f190,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f181,f143]) ).
fof(f192,definition,
( spl0_18
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f194,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f192,f109]) ).
fof(f196,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f192,f118]) ).
fof(f197,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f192,f123]) ).
fof(f198,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f192,f128]) ).
fof(f199,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f192,f133]) ).
fof(f200,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f192,f138]) ).
fof(f201,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f192,f143]) ).
fof(f202,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f97,f135]) ).
fof(f204,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f202]) ).
fof(f206,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f204,f130]) ).
fof(f207,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f206]) ).
fof(f208,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f97,f115]) ).
fof(f209,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f208]) ).
fof(f210,plain,
( sk_c9 != sk_c8
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f209,f150]) ).
fof(f212,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f183]) ).
fof(f214,plain,
( identity = multiply(sk_c8,sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f3,f111]) ).
fof(f223,definition,
( spl0_20
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f224,plain,
( identity = sk_c9
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f225,plain,
( identity != sk_c9
| spl0_20 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f229,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f230,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_18 ),
inference(superposition,[],[f4,f194]) ).
fof(f234,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f120]) ).
fof(f236,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f115]) ).
fof(f238,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f229,f1]) ).
fof(f241,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f212]) ).
fof(f242,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f241,f1]) ).
fof(f245,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f214]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c6,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f245,f1]) ).
fof(f251,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f242,f194]) ).
fof(f261,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f230,f251]) ).
fof(f263,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f261,f194]) ).
fof(f273,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c9,multiply(sk_c9,X0))
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f4,f263]) ).
fof(f291,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f246,f120]) ).
fof(f295,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f291,f125]) ).
fof(f298,plain,
( sk_c9 != sk_c8
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(superposition,[],[f124,f291]) ).
fof(f304,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f234,f291]) ).
fof(f308,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f304,f120]) ).
fof(f372,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f238,f3]) ).
fof(f373,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f238,f238]) ).
fof(f379,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f238,f251]) ).
fof(f393,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f238,f308]) ).
fof(f398,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_7 ),
inference(superposition,[],[f238,f115]) ).
fof(f399,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c3),multiply(sk_c9,X0))
| ~ spl0_7 ),
inference(superposition,[],[f238,f236]) ).
fof(f403,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c9,X0))
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f399,f150]) ).
fof(f404,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f398,f150]) ).
fof(f409,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f393,f3]) ).
fof(f416,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f379,f3]) ).
fof(f420,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f372,f373]) ).
fof(f421,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c8,X0)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f403,f273]) ).
fof(f422,plain,
( sk_c9 = sk_c8
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f404,f263]) ).
fof(f427,plain,
( $false
| ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f416,f225]) ).
fof(f428,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f429,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f420,f409]) ).
fof(f430,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f422,f210]) ).
fof(f431,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f433,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f422,f298]) ).
fof(f434,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f436,plain,
( ! [X0] : multiply(X0,sk_c9) = X0
| ~ spl0_20 ),
inference(forward_demodulation,[],[f420,f224]) ).
fof(f437,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_20 ),
inference(superposition,[],[f1,f224]) ).
fof(f438,plain,
( sk_c9 = multiply(sk_c3,sk_c9)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f115,f422]) ).
fof(f449,plain,
( sk_c9 = sk_c3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f438,f436]) ).
fof(f456,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_16 ),
inference(superposition,[],[f106,f172]) ).
fof(f477,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f103,f422]) ).
fof(f478,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != X2 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f477,f436]) ).
fof(f482,plain,
( sk_c9 != sk_c9
| sk_c9 != sk_c3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f478,f150]) ).
fof(f483,plain,
( sk_c9 != sk_c3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f482]) ).
fof(f485,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f483,f449]) ).
fof(f486,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f497,plain,
( ! [X6] :
( sk_c9 != multiply(sk_c9,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f94,f421]) ).
fof(f498,plain,
( ! [X6] :
( sk_c9 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f497,f437]) ).
fof(f499,plain,
( ! [X6] :
( sk_c9 != multiply(X6,sk_c9)
| sk_c8 != inverse(X6) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f498,f422]) ).
fof(f500,plain,
( ! [X6] :
( sk_c9 != X6
| sk_c8 != inverse(X6) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f499,f436]) ).
fof(f501,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != X6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f500,f422]) ).
fof(f511,plain,
( sk_c9 != sk_c9
| sk_c9 != sk_c3
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f501,f150]) ).
fof(f512,plain,
( sk_c9 != sk_c3
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f511]) ).
fof(f514,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f512,f449]) ).
fof(f515,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f514]) ).
fof(f526,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f100,f194]) ).
fof(f527,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f100,f145]) ).
fof(f528,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f527]) ).
fof(f529,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f526]) ).
fof(f530,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f528,f140]) ).
fof(f531,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f532,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f529,f183]) ).
fof(f533,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f532]) ).
fof(f540,plain,
( sk_c9 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f456]) ).
fof(f547,plain,
( ~ spl0_15
| ~ spl0_5
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f540,f170,f105,f159]) ).
fof(f592,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f130,f295]) ).
fof(f593,plain,
( sk_c9 = multiply(sk_c5,sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f135,f295]) ).
fof(f637,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f161]) ).
fof(f638,plain,
( identity = sk_c2
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f637,f437]) ).
fof(f640,plain,
( sk_c9 = sk_c2
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f638,f224]) ).
fof(f657,plain,
( sk_c9 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f94,f120]) ).
fof(f658,plain,
( sk_c9 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f657,f111]) ).
fof(f662,plain,
( sk_c9 != sk_c8
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f658,f429]) ).
fof(f666,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f662,f295]) ).
fof(f667,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f666]) ).
fof(f674,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f103,f295]) ).
fof(f675,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f674,f436]) ).
fof(f685,plain,
( sk_c9 != sk_c9
| sk_c9 != sk_c2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f675,f161]) ).
fof(f686,plain,
( sk_c9 != sk_c2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f685]) ).
fof(f691,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f686,f640]) ).
fof(f692,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f691]) ).
fof(f720,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f106,f295]) ).
fof(f738,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c5)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f720,f593]) ).
fof(f739,plain,
( sk_c9 != inverse(sk_c5)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f738]) ).
fof(f741,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f739,f592]) ).
fof(f742,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f751,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f674,f593]) ).
fof(f752,plain,
( sk_c9 != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f751]) ).
fof(f754,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f752,f592]) ).
fof(f755,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f754]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f107]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s11,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s12,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s17,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
cnf(s18,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s19,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s24,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s25,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s26,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f175]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s31,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f184]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f185]) ).
cnf(s33,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
cnf(s34,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s35,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s38,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s39,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s40,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f197]) ).
cnf(s41,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f198]) ).
cnf(s42,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f199]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f207]) ).
cnf(s51,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f428]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f431]) ).
cnf(s53,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f434]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f486]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f515]) ).
cnf(s62,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f531]) ).
cnf(s63,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f533]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f547]) ).
cnf(s79,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f667]) ).
cnf(s82,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f692]) ).
cnf(s90,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f742]) ).
cnf(s91,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f755]) ).
cnf(s92,plain,
( spl0_6
| ~ spl0_5 ),
inference(rat,[],[s65,s17,s24]) ).
cnf(s93,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s90,s25,s26,s27,s28,s92]) ).
cnf(s94,plain,
~ spl0_5,
inference(rat,[],[s90,s18,s19,s20,s21,s65,s93,s92]) ).
cnf(s96,plain,
( spl0_11
| spl0_20 ),
inference(rat,[],[s51,s35,s42]) ).
cnf(s97,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_15
| ~ spl0_4
| ~ spl0_6 ),
inference(rat,[],[s51,s34,s41,s91,s96,s82]) ).
cnf(s98,plain,
( ~ spl0_8
| ~ spl0_15
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s53,s5,s12,s33,s40,s97]) ).
cnf(s99,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s56,s51,s4,s11,s32,s39]) ).
cnf(s100,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s91,s19,s20,s21,s98]) ).
cnf(s101,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s56,s51,s3,s10,s31,s38,s100]) ).
cnf(s102,plain,
~ spl0_4,
inference(rat,[],[s101,s99]) ).
cnf(s103,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s62,s43,s44]) ).
cnf(s104,plain,
( ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s62,s36,s37,s63]) ).
cnf(s105,plain,
~ spl0_3,
inference(rat,[],[s104,s103]) ).
cnf(s106,plain,
( spl0_11
| ~ spl0_18
| ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s52,s7,s14]) ).
cnf(s107,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s52,s6,s13,s45,s106]) ).
cnf(s108,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s45,s41,s42]) ).
cnf(s109,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s45,s34,s35,s107]) ).
cnf(s110,plain,
~ spl0_2,
inference(rat,[],[s109,s108]) ).
cnf(s111,plain,
spl0_1,
inference(rat,[],[s2,s102,s94,s105,s110]) ).
cnf(s113,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s53,s5,s12,s79,s111]) ).
cnf(s114,plain,
( spl0_8
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s59,s4,s11,s51,s111]) ).
cnf(s115,plain,
( ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s59,s3,s10,s113,s114,s51,s111]) ).
cnf(s116,plain,
spl0_18,
inference(rat,[],[s79,s38,s39,s40,s111]) ).
cnf(s117,plain,
~ spl0_17,
inference(rat,[],[s115,s116]) ).
cnf(s122,plain,
spl0_9,
inference(rat,[],[s33,s117]) ).
cnf(s123,plain,
spl0_8,
inference(rat,[],[s32,s117]) ).
cnf(s124,plain,
spl0_6,
inference(rat,[],[s31,s117]) ).
cnf(s125,plain,
$false,
inference(rat,[],[s79,s111,s123,s124,s122]) ).
fof(f757,plain,
$false,
inference(avatar_sat_refutation,[],[s125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:45:41 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % (2583186)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (2583195)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1689495499:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (2583192)% WARNING: option uhcvi not known.
% 0.17/0.49 % (2583193)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3222529615:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (2583191)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3895019706_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (2583192)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1970810520:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (2583194)dis+10_1_sil=32000:sp=arity:random_seed=3916351161:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (2583195) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2583186-2583195"...
% 0.17/0.49 % (2583196)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1465209453:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (2583197)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1963775456:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % (2583195)...printing done.
% 0.17/0.49 % (2583195)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (2583195)------------------------------
% 0.17/0.50 % (2583195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (2583195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (2583195)CaDiCaL version: 2.1.3
% 0.17/0.50 % (2583195)Termination reason: Refutation
% 0.17/0.50 % (2583195)Time elapsed: 0.010 s
% 0.17/0.50 % (2583195)Peak memory usage: 12 MB
% 0.17/0.50 % (2583195)Instructions burned: 26 (million)
% 0.17/0.50 % (2583186)Success in time 0.032 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------