%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP369-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 10:17:37 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 56
% Syntax : Number of formulae : 397 ( 24 unt; 21 def)
% Number of atoms : 1512 ( 408 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 2190 (1075 ~;1094 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c9,sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c2) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c2) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c2
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c2
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c2
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f57,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c7 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c7 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| multiply(sk_c9,X0) != sk_c8
| multiply(X1,sk_c9) != X0
| inverse(X1) != sk_c9
| multiply(X2,sk_c7) != sk_c9
| inverse(X2) != sk_c7
| inverse(sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(X5,sk_c9) != sk_c7
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != multiply(sk_c9,X0)
| multiply(X1,sk_c9) != X0
| sk_c9 != inverse(X1)
| sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X1,X4,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != multiply(sk_c9,multiply(X1,sk_c9))
| sk_c9 != inverse(X1)
| sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ 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_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( sk_c7 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,definition,
( spl0_5
<=> ! [X2] :
( sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f107,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,definition,
( spl0_6
<=> ! [X1] :
( sk_c8 != multiply(sk_c9,multiply(X1,sk_c9))
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f110,plain,
( ! [X1] :
( sk_c8 != multiply(sk_c9,multiply(X1,sk_c9))
| sk_c9 != inverse(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_7
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f113,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( multiply(sk_c7,sk_c9) != sk_c8
| spl0_7 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f91,f112,f109,f106,f102,f99,f96,f93]) ).
fof(f117,definition,
( spl0_8
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f119,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f121,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f123,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f88,f121,f117]) ).
fof(f126,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f127,plain,
( sk_c7 != multiply(sk_c6,sk_c9)
| spl0_10 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f86,f121,f126]) ).
fof(f131,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f133,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f84,f121,f131]) ).
fof(f136,definition,
( spl0_12
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f138,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f82,f121,f136]) ).
fof(f141,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f80,f121,f141]) ).
fof(f146,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f148,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f78,f121,f146]) ).
fof(f150,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f121,f102]) ).
fof(f152,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f154,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f74,f152,f117]) ).
fof(f156,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f72,f152,f126]) ).
fof(f157,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f70,f152,f131]) ).
fof(f158,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f68,f152,f136]) ).
fof(f159,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f66,f152,f141]) ).
fof(f160,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f64,f152,f146]) ).
fof(f161,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f62,f152,f102]) ).
fof(f163,definition,
( spl0_16
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f165,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f60,f163,f117]) ).
fof(f167,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f58,f163,f126]) ).
fof(f170,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f163,f141]) ).
fof(f172,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f48,f163,f102]) ).
fof(f174,definition,
( spl0_17
<=> sk_c2 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f176,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f46,f174,f117]) ).
fof(f178,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f44,f174,f126]) ).
fof(f183,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f174,f102]) ).
fof(f185,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c9,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f187,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f185,f117]) ).
fof(f189,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f185,f126]) ).
fof(f194,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f185,f102]) ).
fof(f195,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f18,f112,f117]) ).
fof(f196,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f112,f126]) ).
fof(f197,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f112,f131]) ).
fof(f198,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f112,f136]) ).
fof(f199,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f112,f141]) ).
fof(f200,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f112,f146]) ).
fof(f201,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f112,f102]) ).
fof(f202,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f103]) ).
fof(f203,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f143]) ).
fof(f204,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_11 ),
inference(superposition,[],[f3,f133]) ).
fof(f205,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f119]) ).
fof(f208,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f209,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f202]) ).
fof(f213,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f209,f1]) ).
fof(f214,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f208,f1]) ).
fof(f217,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f203]) ).
fof(f218,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f217,f1]) ).
fof(f228,plain,
( sk_c4 = multiply(sk_c7,identity)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f213,f203]) ).
fof(f252,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_4 ),
inference(superposition,[],[f214,f202]) ).
fof(f257,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f214,f204]) ).
fof(f258,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f214,f148]) ).
fof(f262,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f214,f128]) ).
fof(f267,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f262,f119]) ).
fof(f271,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f258,f143]) ).
fof(f272,plain,
( sk_c5 = multiply(sk_c7,identity)
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f257,f103]) ).
fof(f274,plain,
( sk_c4 = sk_c5
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f272,f228]) ).
fof(f277,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f138,f274]) ).
fof(f279,plain,
( sk_c7 = sk_c9
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f277,f148]) ).
fof(f282,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f214,f267]) ).
fof(f284,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f282,f3]) ).
fof(f304,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f214,f271]) ).
fof(f306,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f304,f3]) ).
fof(f310,plain,
( sk_c8 != multiply(identity,sk_c9)
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f114,f284]) ).
fof(f320,plain,
( sk_c9 != sk_c8
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f310,f1]) ).
fof(f322,plain,
( sk_c7 != sk_c8
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f320,f279]) ).
fof(f323,plain,
( identity != sk_c8
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f322,f284]) ).
fof(f324,plain,
( sk_c8 = multiply(inverse(identity),identity)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f252,f284]) ).
fof(f325,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f324,f3]) ).
fof(f372,plain,
( ! [X0] : multiply(identity,multiply(sk_c4,X0)) = X0
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f218,f325]) ).
fof(f373,plain,
( ! [X0] : multiply(sk_c4,X0) = X0
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f372,f1]) ).
fof(f442,plain,
( $false
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f323,f325]) ).
fof(f443,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f444,plain,
( ! [X3] :
( sk_c7 != multiply(X3,identity)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f100,f325]) ).
fof(f445,plain,
( identity = multiply(sk_c7,sk_c9)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f113,f325]) ).
fof(f446,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f444,f284]) ).
fof(f448,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f446,f325]) ).
fof(f454,plain,
( identity != identity
| identity != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f448,f373]) ).
fof(f455,plain,
( identity != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f454]) ).
fof(f458,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f455,f143]) ).
fof(f460,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f458,f325]) ).
fof(f461,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f472,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f113,f279]) ).
fof(f496,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f472,f306]) ).
fof(f497,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f496,f1]) ).
fof(f498,plain,
( sk_c7 = inverse(identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f103,f497]) ).
fof(f519,plain,
( identity = inverse(identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f498,f306]) ).
fof(f579,plain,
( sk_c8 = multiply(identity,sk_c9)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f113,f306]) ).
fof(f582,plain,
( sk_c9 = sk_c8
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f579,f1]) ).
fof(f664,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f165]) ).
fof(f667,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f214,f154]) ).
fof(f669,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f667,f123]) ).
fof(f678,plain,
( sk_c7 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_3 ),
inference(superposition,[],[f100,f1]) ).
fof(f688,definition,
( spl0_20
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f689,plain,
( identity = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f690,plain,
( identity != sk_c7
| spl0_20 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f698,definition,
( spl0_22
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f699,plain,
( sk_c7 = sk_c8
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f717,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f113,f669]) ).
fof(f718,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f214,f669]) ).
fof(f720,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f718,f3]) ).
fof(f725,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f717,f152,f121,f112,f698]) ).
fof(f737,plain,
( sk_c8 = multiply(identity,sk_c2)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f187,f720]) ).
fof(f738,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f205,f720]) ).
fof(f739,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f664,f720]) ).
fof(f743,plain,
( identity = sk_c1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f739,f1]) ).
fof(f744,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f738,f1]) ).
fof(f745,plain,
( sk_c8 = sk_c2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f737,f1]) ).
fof(f747,plain,
( sk_c7 = sk_c2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f745,f699]) ).
fof(f750,plain,
( sk_c2 = multiply(identity,sk_c9)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f176,f743]) ).
fof(f753,plain,
( sk_c9 = sk_c2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f750,f1]) ).
fof(f755,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f753,f720]) ).
fof(f756,plain,
( sk_c7 != multiply(identity,sk_c9)
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f127,f744]) ).
fof(f761,plain,
( sk_c7 != sk_c9
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f756,f1]) ).
fof(f762,plain,
( identity != sk_c7
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f761,f720]) ).
fof(f763,plain,
( ~ spl0_20
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f762,f152,f126,f121,f117,f688]) ).
fof(f790,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(superposition,[],[f755,f747]) ).
fof(f796,plain,
( $false
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f790,f690]) ).
fof(f797,plain,
( ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f796]) ).
fof(f804,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f284,f126,f117,f688]) ).
fof(f816,plain,
( identity = sk_c9
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f582,f497]) ).
fof(f932,plain,
( ! [X1] :
( sk_c8 != multiply(identity,multiply(X1,identity))
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f110,f816]) ).
fof(f933,plain,
( ! [X1] :
( sk_c8 != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f932,f1]) ).
fof(f934,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f933,f497]) ).
fof(f935,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f934,f816]) ).
fof(f938,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f935,f3]) ).
fof(f942,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f938]) ).
fof(f954,plain,
( ! [X4] :
( sk_c9 != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f97,f497]) ).
fof(f955,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f954,f816]) ).
fof(f956,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f955,f497]) ).
fof(f967,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f956,f3]) ).
fof(f971,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f967]) ).
fof(f983,plain,
( ! [X2] :
( sk_c9 != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_5
| ~ spl0_20 ),
inference(forward_demodulation,[],[f107,f689]) ).
fof(f1037,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f942,f519]) ).
fof(f1045,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1037,f519]) ).
fof(f1046,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1045]) ).
fof(f1063,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f971,f519]) ).
fof(f1071,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1063,f519]) ).
fof(f1072,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1071]) ).
fof(f1104,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f669,f689]) ).
fof(f1114,plain,
( identity = sk_c8
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f699,f689]) ).
fof(f1117,plain,
( identity = multiply(sk_c6,sk_c9)
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f128,f689]) ).
fof(f1118,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f445,f689]) ).
fof(f1120,plain,
( ! [X5] :
( identity != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f94,f689]) ).
fof(f1121,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1104,f1]) ).
fof(f1124,plain,
( identity = sk_c9
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1118,f1]) ).
fof(f1172,plain,
( identity = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1117,f1124]) ).
fof(f1182,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1120,f1124]) ).
fof(f1183,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1182,f1124]) ).
fof(f1193,plain,
( identity != identity
| identity != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f1183,f1172]) ).
fof(f1194,plain,
( identity != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1193]) ).
fof(f1197,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1194,f119]) ).
fof(f1199,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1197,f1124]) ).
fof(f1200,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f1199]) ).
fof(f1206,definition,
( spl0_24
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f1210,plain,
( ! [X1] :
( sk_c8 != multiply(identity,multiply(X1,identity))
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f110,f1124]) ).
fof(f1211,plain,
( ! [X1] :
( sk_c8 != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1210,f1]) ).
fof(f1212,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1211,f1114]) ).
fof(f1213,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1212,f1124]) ).
fof(f1219,plain,
( identity != identity
| identity != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f1213,f1172]) ).
fof(f1220,plain,
( identity != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1219]) ).
fof(f1223,plain,
( identity != sk_c9
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1220,f119]) ).
fof(f1226,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1223,f1124]) ).
fof(f1227,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1226]) ).
fof(f1229,plain,
( ! [X4] :
( sk_c9 != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f97,f1114]) ).
fof(f1230,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1229,f1124]) ).
fof(f1231,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1230,f1114]) ).
fof(f1236,plain,
( identity != identity
| identity != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f1231,f1172]) ).
fof(f1237,plain,
( identity != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1236]) ).
fof(f1240,plain,
( identity != sk_c9
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1237,f119]) ).
fof(f1243,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1240,f1124]) ).
fof(f1244,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1243]) ).
fof(f1247,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f983,f1124]) ).
fof(f1249,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1247,f689]) ).
fof(f1255,plain,
( identity != identity
| identity != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f1249,f1172]) ).
fof(f1256,plain,
( identity != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1255]) ).
fof(f1259,plain,
( identity != sk_c9
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1256,f119]) ).
fof(f1262,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1259,f1124]) ).
fof(f1263,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f1262]) ).
fof(f1265,plain,
( ! [X1] :
( identity != multiply(sk_c9,multiply(X1,sk_c9))
| sk_c9 != inverse(X1) )
| ~ spl0_6
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f110,f1114]) ).
fof(f1280,plain,
( identity = inverse(sk_c1)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f165,f1121]) ).
fof(f1282,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(superposition,[],[f3,f1280]) ).
fof(f1283,plain,
( identity = sk_c1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1282,f1]) ).
fof(f1285,plain,
( identity = inverse(identity)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(superposition,[],[f1280,f1283]) ).
fof(f1288,plain,
( spl0_24
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1285,f688,f163,f152,f121,f1206]) ).
fof(f1299,plain,
( ! [X1] :
( identity != multiply(identity,multiply(X1,identity))
| sk_c9 != inverse(X1) )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1265,f1121]) ).
fof(f1300,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1299,f1]) ).
fof(f1301,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1300,f1121]) ).
fof(f1302,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f1301,f1]) ).
fof(f1309,plain,
( identity != inverse(identity)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1302]) ).
fof(f1311,plain,
( ~ spl0_24
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1309,f698,f688,f152,f121,f109,f1206]) ).
fof(f1314,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1229,f1121]) ).
fof(f1316,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1314,f1114]) ).
fof(f1318,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f1316,f1]) ).
fof(f1325,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1318]) ).
fof(f1327,plain,
( ~ spl0_24
| ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1325,f698,f688,f152,f121,f96,f1206]) ).
fof(f1330,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f983,f1121]) ).
fof(f1333,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1330,f689]) ).
fof(f1337,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f1333,f1]) ).
fof(f1344,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1337]) ).
fof(f1346,plain,
( ~ spl0_24
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1344,f688,f152,f121,f106,f1206]) ).
fof(f1349,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1120,f1121]) ).
fof(f1351,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1349,f1121]) ).
fof(f1354,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f1351,f1]) ).
fof(f1361,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1354]) ).
fof(f1363,plain,
( ~ spl0_24
| ~ spl0_1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1361,f688,f152,f121,f93,f1206]) ).
fof(f1366,plain,
( identity != sk_c7
| sk_c8 != inverse(identity)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f678,f1114]) ).
fof(f1378,plain,
( sk_c8 != inverse(identity)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1366,f689]) ).
fof(f1387,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1378,f1114]) ).
fof(f1391,plain,
( ~ spl0_24
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1387,f698,f688,f99,f1206]) ).
fof(f1394,plain,
( sk_c7 != inverse(identity)
| spl0_4
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f104,f1114]) ).
fof(f1399,plain,
( identity != inverse(identity)
| spl0_4
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1394,f689]) ).
fof(f1404,plain,
( ~ spl0_24
| spl0_4
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1399,f698,f688,f102,f1206]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f115]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f124]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f129]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f134]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f139]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s8,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f150]) ).
cnf(s9,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s10,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s11,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s12,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s13,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s14,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s15,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s16,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s17,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s20,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f170]) ).
cnf(s22,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f172]) ).
cnf(s23,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f177]) ).
cnf(s24,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f178]) ).
cnf(s29,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f183]) ).
cnf(s30,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f188]) ).
cnf(s31,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f189]) ).
cnf(s36,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s37,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f195]) ).
cnf(s38,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f196]) ).
cnf(s39,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f197]) ).
cnf(s40,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f198]) ).
cnf(s41,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f199]) ).
cnf(s42,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f200]) ).
cnf(s43,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f201]) ).
cnf(s44,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f443]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(sat_conversion,[],[f461]) ).
cnf(s53,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f725]) ).
cnf(s55,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f763]) ).
cnf(s57,plain,
( ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f797]) ).
cnf(s61,plain,
( ~ spl0_8
| ~ spl0_10
| spl0_20 ),
inference(sat_conversion,[],[f804]) ).
cnf(s85,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1046]) ).
cnf(s92,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1072]) ).
cnf(s102,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(sat_conversion,[],[f1200]) ).
cnf(s106,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f1227]) ).
cnf(s109,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f1244]) ).
cnf(s112,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20 ),
inference(sat_conversion,[],[f1263]) ).
cnf(s114,plain,
( ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f1288]) ).
cnf(s115,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f1311]) ).
cnf(s117,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f1327]) ).
cnf(s119,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f1346]) ).
cnf(s122,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_15
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f1363]) ).
cnf(s128,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f1391]) ).
cnf(s134,plain,
( spl0_4
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f1404]) ).
cnf(s136,plain,
spl0_4,
inference(rat,[],[s114,s134,s57,s53,s8,s15,s22,s29,s36,s43]) ).
cnf(s137,plain,
spl0_7,
inference(rat,[],[s44,s37,s38,s39,s40,s41,s42,s136]) ).
cnf(s138,plain,
( spl0_15
| ~ spl0_6 ),
inference(rat,[],[s85,s11,s12,s13,s14,s136,s137]) ).
cnf(s139,plain,
( ~ spl0_10
| ~ spl0_22
| ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s106,s61,s136,s137]) ).
cnf(s140,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s57,s55,s17,s24,s31,s139,s53,s138,s137]) ).
cnf(s141,plain,
( spl0_9
| ~ spl0_6 ),
inference(rat,[],[s85,s4,s5,s6,s7,s136,s137]) ).
cnf(s142,plain,
~ spl0_6,
inference(rat,[],[s114,s115,s57,s16,s23,s30,s140,s53,s141,s138,s137]) ).
cnf(s143,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s112,s61,s136,s137]) ).
cnf(s144,plain,
( ~ spl0_9
| spl0_10
| ~ spl0_8 ),
inference(rat,[],[s57,s53,s55,s31,s24,s17,s10,s137]) ).
cnf(s145,plain,
( spl0_10
| ~ spl0_8 ),
inference(rat,[],[s3,s144]) ).
cnf(s146,plain,
( ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s145,s143]) ).
cnf(s147,plain,
~ spl0_5,
inference(rat,[],[s119,s114,s57,s53,s2,s9,s16,s23,s30,s146,s137]) ).
cnf(s148,plain,
( ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s128,s114,s53,s6,s13,s20,s45,s61,s145,s137,s136]) ).
cnf(s149,plain,
~ spl0_3,
inference(rat,[],[s114,s128,s57,s53,s2,s9,s16,s23,s30,s148,s137]) ).
cnf(s150,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s92,s11,s12,s13,s14,s137,s136]) ).
cnf(s151,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s92,s4,s5,s6,s7,s137,s136]) ).
cnf(s152,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s109,s61,s145,s53,s151,s150,s136,s137]) ).
cnf(s153,plain,
~ spl0_2,
inference(rat,[],[s117,s114,s57,s16,s23,s30,s152,s53,s151,s150,s137]) ).
cnf(s154,plain,
spl0_1,
inference(rat,[],[s1,s137,s136,s147,s142,s149,s153]) ).
cnf(s155,plain,
( ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s102,s61,s137,s136,s154]) ).
cnf(s156,plain,
~ spl0_8,
inference(rat,[],[s155,s145]) ).
cnf(s157,plain,
spl0_18,
inference(rat,[],[s30,s156]) ).
cnf(s158,plain,
spl0_17,
inference(rat,[],[s23,s156]) ).
cnf(s159,plain,
spl0_16,
inference(rat,[],[s16,s156]) ).
cnf(s160,plain,
spl0_15,
inference(rat,[],[s9,s156]) ).
cnf(s161,plain,
spl0_9,
inference(rat,[],[s2,s156]) ).
cnf(s162,plain,
spl0_22,
inference(rat,[],[s53,s160,s137,s161]) ).
cnf(s163,plain,
spl0_20,
inference(rat,[],[s57,s160,s159,s157,s158,s161,s162]) ).
cnf(s164,plain,
spl0_24,
inference(rat,[],[s114,s159,s160,s161,s163]) ).
cnf(s165,plain,
$false,
inference(rat,[],[s122,s160,s154,s161,s163,s164]) ).
fof(f1407,plain,
$false,
inference(avatar_sat_refutation,[],[s165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP369-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n018.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 09:59:09 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 % (2092130)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2092138)dis+10_1_sil=32000:sp=arity:random_seed=791007905:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2092136)% WARNING: option uhcvi not known.
% 0.16/0.48 % (2092135)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1951192651_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (2092139)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=119520021:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2092136)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1257441715:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2092137)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1361868694:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2092141)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=535830678:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (2092140)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4166566541:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % (2092138) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2092130-2092138"...
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (2092138)...printing done.
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (2092138)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (2092138)------------------------------
% 0.16/0.49 % (2092138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (2092138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (2092138)CaDiCaL version: 2.1.3
% 0.16/0.49 % (2092138)Termination reason: Refutation
% 0.16/0.49 % (2092138)Time elapsed: 0.015 s
% 0.16/0.49 % (2092138)Peak memory usage: 12 MB
% 0.16/0.49 % (2092138)Instructions burned: 45 (million)
% 0.16/0.49 % (2092130)Success in time 0.045 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------