%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP386-1 : 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 : n014.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 10:17:40 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 56
% Syntax : Number of formulae : 385 ( 24 unt; 22 def)
% Number of atoms : 1427 ( 446 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2039 ( 997 ~;1020 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 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,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c10) = sk_c9
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f71,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c7,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c1)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f79]) ).
fof(f83,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f85]) ).
fof(f91,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c7,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f96,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f98,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f100,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f99]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(X3,X4) != sk_c10
| inverse(X3) != X4
| multiply(X4,sk_c9) != sk_c10
| inverse(X5) != X6
| inverse(X6) != X4
| multiply(X5,X4) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c10 != multiply(X4,sk_c9)
| inverse(X5) != X6
| inverse(X6) != X4
| multiply(X5,X4) != X6 ),
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X5] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,inverse(X3))
| sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X5) != X6
| inverse(X3) != inverse(X6)
| multiply(X5,inverse(X3)) != X6 ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X5] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,inverse(X3))
| sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X3) != inverse(inverse(X5))
| inverse(X5) != multiply(X5,inverse(X3)) ),
inference(equality_resolution,[],[f105]) ).
fof(f108,definition,
( spl0_1
<=> ! [X5,X3] :
( sk_c10 != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f109,plain,
( ! [X3,X5] :
( inverse(X5) != multiply(X5,inverse(X3))
| sk_c10 != multiply(X3,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X1] :
( sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> ! [X0] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X0] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_5
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f121,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl0_6
<=> sk_c10 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f125,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f126,plain,
( sk_c10 != multiply(sk_c9,sk_c8)
| spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f128,definition,
( spl0_7
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f129,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f130,plain,
( inverse(sk_c10) != sk_c9
| spl0_7 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f106,f128,f124,f120,f117,f114,f111,f108]) ).
fof(f137,definition,
( spl0_9
<=> sk_c10 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f139,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f142,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f100,f137,f142]) ).
fof(f147,definition,
( spl0_11
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f149,plain,
( inverse(sk_c6) = sk_c5
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f98,f137,f147]) ).
fof(f152,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c7,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f154,plain,
( sk_c10 = multiply(sk_c7,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f96,f137,f152]) ).
fof(f157,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f159,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f94,f137,f157]) ).
fof(f162,definition,
( spl0_14
<=> sk_c10 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f164,plain,
( sk_c10 = multiply(sk_c4,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f92,f137,f162]) ).
fof(f167,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f169,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f172,definition,
( spl0_16
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f174,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f177,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f179,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
( spl0_17
| spl0_9 ),
inference(avatar_split_clause,[],[f86,f137,f177]) ).
fof(f182,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f184,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f185,plain,
( spl0_18
| spl0_9 ),
inference(avatar_split_clause,[],[f84,f137,f182]) ).
fof(f187,definition,
( spl0_19
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f189,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,plain,
( spl0_10
| spl0_19 ),
inference(avatar_split_clause,[],[f80,f187,f142]) ).
fof(f192,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f78,f187,f147]) ).
fof(f193,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f76,f187,f152]) ).
fof(f194,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f74,f187,f157]) ).
fof(f195,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f72,f187,f162]) ).
fof(f198,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f66,f187,f177]) ).
fof(f199,plain,
( spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f64,f187,f182]) ).
fof(f204,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f120,f157]) ).
fof(f205,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f120,f162]) ).
fof(f206,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f120,f167]) ).
fof(f207,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f120,f172]) ).
fof(f208,plain,
( spl0_17
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f120,f177]) ).
fof(f209,plain,
( spl0_18
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f120,f182]) ).
fof(f214,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f34,f124,f157]) ).
fof(f215,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f32,f124,f162]) ).
fof(f216,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f30,f124,f167]) ).
fof(f217,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f124,f172]) ).
fof(f218,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f124,f177]) ).
fof(f219,plain,
( spl0_18
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f124,f182]) ).
fof(f224,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f15,f128,f157]) ).
fof(f225,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f13,f128,f162]) ).
fof(f228,plain,
( spl0_17
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f128,f177]) ).
fof(f229,plain,
( spl0_18
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f128,f182]) ).
fof(f230,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_17 ),
inference(superposition,[],[f3,f179]) ).
fof(f232,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f159]) ).
fof(f233,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f3,f149]) ).
fof(f237,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f243,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f237,f1]) ).
fof(f246,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c2,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f230]) ).
fof(f247,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c2,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f246,f1]) ).
fof(f260,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f247,f184]) ).
fof(f307,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl0_17 ),
inference(superposition,[],[f243,f230]) ).
fof(f309,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f243,f260]) ).
fof(f314,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f243,f174]) ).
fof(f317,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_14 ),
inference(superposition,[],[f243,f164]) ).
fof(f321,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_12 ),
inference(superposition,[],[f243,f154]) ).
fof(f322,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_13 ),
inference(superposition,[],[f243,f232]) ).
fof(f326,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl0_11 ),
inference(superposition,[],[f243,f233]) ).
fof(f329,plain,
( sk_c6 = multiply(sk_c7,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f326,f144]) ).
fof(f334,plain,
( sk_c7 = multiply(sk_c7,sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f317,f159]) ).
fof(f337,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f314,f169]) ).
fof(f341,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f309,f3]) ).
fof(f374,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f243,f334]) ).
fof(f376,plain,
( identity = sk_c10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f374,f3]) ).
fof(f379,plain,
( sk_c9 != inverse(identity)
| spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f130,f376]) ).
fof(f392,plain,
( identity != inverse(identity)
| spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f379,f341]) ).
fof(f395,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f337,f341]) ).
fof(f396,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f395,f1]) ).
fof(f399,plain,
( sk_c2 = multiply(inverse(identity),identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f307,f376]) ).
fof(f400,plain,
( identity = sk_c2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f399,f3]) ).
fof(f405,plain,
( sk_c10 = inverse(identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f179,f400]) ).
fof(f406,plain,
( identity = inverse(identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f405,f376]) ).
fof(f416,plain,
( sk_c9 = multiply(inverse(sk_c7),identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f321,f376]) ).
fof(f417,plain,
( identity = multiply(inverse(sk_c7),identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f416,f341]) ).
fof(f426,plain,
( identity = sk_c4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f417,f322]) ).
fof(f434,plain,
( sk_c10 = multiply(identity,sk_c7)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f164,f426]) ).
fof(f436,plain,
( sk_c10 = sk_c7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f434,f1]) ).
fof(f438,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f436,f376]) ).
fof(f455,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f329,f438]) ).
fof(f459,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f455,f1]) ).
fof(f504,plain,
( $false
| spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f392,f406]) ).
fof(f505,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f506,plain,
( sk_c9 != multiply(sk_c10,identity)
| spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f122,f396]) ).
fof(f508,plain,
( sk_c9 != multiply(identity,identity)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f506,f376]) ).
fof(f510,plain,
( identity != sk_c9
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f508,f1]) ).
fof(f511,plain,
( $false
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f510,f341]) ).
fof(f512,plain,
( spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f514,plain,
( sk_c10 != multiply(sk_c9,identity)
| spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f126,f396]) ).
fof(f516,plain,
( sk_c10 != multiply(identity,identity)
| spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f514,f341]) ).
fof(f518,plain,
( identity != sk_c10
| spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f516,f1]) ).
fof(f519,plain,
( $false
| spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f518,f376]) ).
fof(f520,plain,
( spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f521,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c10 != multiply(X0,sk_c9) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f118,f376]) ).
fof(f523,plain,
( ! [X0] :
( sk_c10 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f521,f341]) ).
fof(f525,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f523,f376]) ).
fof(f529,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f525,f3]) ).
fof(f534,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f529]) ).
fof(f539,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f534,f406]) ).
fof(f545,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f539,f406]) ).
fof(f546,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f554,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f112,f341]) ).
fof(f585,plain,
( ! [X1] :
( sk_c9 != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f115,f376]) ).
fof(f586,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f585,f341]) ).
fof(f587,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f586,f376]) ).
fof(f590,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f587,f3]) ).
fof(f595,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f590]) ).
fof(f600,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f595,f406]) ).
fof(f606,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f600,f406]) ).
fof(f607,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f606]) ).
fof(f615,plain,
( ! [X3,X5] :
( identity != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f109,f376]) ).
fof(f616,plain,
( ! [X3,X5] :
( sk_c10 != multiply(inverse(X3),identity)
| identity != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f615,f341]) ).
fof(f617,plain,
( ! [X3,X5] :
( inverse(X5) != multiply(X5,inverse(X3))
| identity != multiply(X3,inverse(X3))
| identity != multiply(inverse(X3),identity)
| inverse(X3) != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f616,f376]) ).
fof(f621,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c7)
| identity != multiply(sk_c4,sk_c7)
| identity != multiply(sk_c7,identity)
| sk_c7 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f617,f159]) ).
fof(f631,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c4,sk_c7)
| identity != multiply(sk_c7,identity)
| sk_c7 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f621,f438]) ).
fof(f638,plain,
( ! [X0] :
( identity != sk_c10
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c7,identity)
| sk_c7 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f631,f164]) ).
fof(f645,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c7,identity)
| sk_c7 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f638,f376]) ).
fof(f650,plain,
( ! [X0] :
( identity != sk_c6
| inverse(X0) != multiply(X0,identity)
| sk_c7 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f645,f329]) ).
fof(f655,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c7 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f650,f459]) ).
fof(f660,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f655,f438]) ).
fof(f676,plain,
( sk_c4 != inverse(inverse(sk_c7))
| identity != inverse(inverse(inverse(sk_c7)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f660,f322]) ).
fof(f679,plain,
( sk_c4 != inverse(inverse(identity))
| identity != inverse(inverse(inverse(sk_c7)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f676,f438]) ).
fof(f684,plain,
( sk_c4 != inverse(identity)
| identity != inverse(inverse(inverse(sk_c7)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f679,f406]) ).
fof(f689,plain,
( identity != sk_c4
| identity != inverse(inverse(inverse(sk_c7)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f684,f406]) ).
fof(f695,plain,
( identity != inverse(inverse(inverse(sk_c7)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f689,f426]) ).
fof(f699,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f695,f438]) ).
fof(f705,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f699,f406]) ).
fof(f707,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f705,f406]) ).
fof(f710,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f707,f406]) ).
fof(f711,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f806,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c8 != multiply(X2,identity) )
| ~ spl0_2
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f554,f341]) ).
fof(f808,plain,
( sk_c9 = multiply(identity,sk_c8)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f121,f376]) ).
fof(f812,plain,
( sk_c9 = sk_c8
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f808,f1]) ).
fof(f815,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f812,f341]) ).
fof(f821,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f806,f815]) ).
fof(f828,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f821,f3]) ).
fof(f831,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f828]) ).
fof(f838,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f831,f406]) ).
fof(f841,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f838,f406]) ).
fof(f842,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f841]) ).
fof(f998,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_7 ),
inference(superposition,[],[f3,f129]) ).
fof(f1000,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f189]) ).
fof(f1002,plain,
( sk_c8 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_5 ),
inference(superposition,[],[f243,f121]) ).
fof(f1004,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1002,f129]) ).
fof(f1007,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_9 ),
inference(superposition,[],[f243,f139]) ).
fof(f1009,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1007,f189]) ).
fof(f1017,plain,
( ! [X0] :
( identity != inverse(inverse(inverse(X0)))
| sk_c10 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(inverse(inverse(X0))))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_1 ),
inference(superposition,[],[f109,f3]) ).
fof(f1019,definition,
( spl0_33
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f1020,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1021,plain,
( sk_c10 != multiply(sk_c10,sk_c9)
| spl0_33 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1032,definition,
( spl0_36
<=> sk_c10 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f1033,plain,
( sk_c10 = multiply(sk_c9,sk_c9)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1032]) ).
fof(f1044,definition,
( spl0_38
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f1045,plain,
( identity = sk_c10
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f1077,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_9
| ~ spl0_19 ),
inference(superposition,[],[f243,f1009]) ).
fof(f1079,plain,
( sk_c10 = multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1077,f129]) ).
fof(f1081,plain,
( spl0_36
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1079,f187,f137,f128,f1032]) ).
fof(f1082,plain,
( sk_c10 = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_36 ),
inference(superposition,[],[f1033,f1004]) ).
fof(f1088,plain,
( sk_c10 = multiply(sk_c9,sk_c10)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_36 ),
inference(superposition,[],[f125,f1082]) ).
fof(f1090,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1088,f998]) ).
fof(f1091,plain,
( spl0_38
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1090,f1032,f128,f124,f120,f1044]) ).
fof(f1093,plain,
( sk_c9 = inverse(identity)
| ~ spl0_7
| ~ spl0_38 ),
inference(superposition,[],[f129,f1045]) ).
fof(f1097,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_19
| ~ spl0_38 ),
inference(superposition,[],[f1000,f1045]) ).
fof(f1100,plain,
( identity != multiply(identity,sk_c9)
| spl0_33
| ~ spl0_38 ),
inference(superposition,[],[f1021,f1045]) ).
fof(f1101,plain,
( identity != sk_c9
| spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1100,f1]) ).
fof(f1104,plain,
( identity = sk_c1
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1097,f1]) ).
fof(f1116,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_9
| ~ spl0_19
| ~ spl0_38 ),
inference(superposition,[],[f139,f1104]) ).
fof(f1119,plain,
( sk_c10 = sk_c9
| ~ spl0_9
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1116,f1]) ).
fof(f1121,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1119,f1045]) ).
fof(f1122,plain,
( $false
| ~ spl0_9
| ~ spl0_19
| spl0_33
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f1121,f1101]) ).
fof(f1123,plain,
( ~ spl0_9
| ~ spl0_19
| spl0_33
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1122]) ).
fof(f1124,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1020,f1045]) ).
fof(f1126,plain,
( identity = sk_c9
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1124,f1]) ).
fof(f1151,definition,
( spl0_41
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f1152,plain,
( identity = inverse(identity)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f1232,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| identity != inverse(inverse(inverse(X0)))
| inverse(X0) != inverse(inverse(inverse(inverse(X0))))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_1
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1017,f1045]) ).
fof(f1233,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0))
| identity != inverse(inverse(inverse(X0)))
| inverse(X0) != inverse(inverse(inverse(inverse(X0)))) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1232,f1126]) ).
fof(f1234,plain,
( ! [X0] :
( inverse(X0) != inverse(inverse(inverse(inverse(X0))))
| identity != multiply(X0,inverse(X0))
| identity != inverse(inverse(inverse(X0)))
| identity != multiply(inverse(X0),identity) )
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1233,f1045]) ).
fof(f1235,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1093,f1126]) ).
fof(f1236,plain,
( spl0_41
| ~ spl0_7
| ~ spl0_33
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1235,f1044,f1019,f128,f1151]) ).
fof(f1271,plain,
( identity != inverse(inverse(inverse(identity)))
| identity != multiply(identity,identity)
| identity != inverse(inverse(identity))
| identity != multiply(identity,identity)
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(superposition,[],[f1234,f1152]) ).
fof(f1278,plain,
( identity != inverse(inverse(inverse(identity)))
| identity != multiply(identity,identity)
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(duplicate_literal_removal,[],[f1271]) ).
fof(f1281,plain,
( identity != inverse(inverse(inverse(identity)))
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1278,f1]) ).
fof(f1286,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1281,f1152]) ).
fof(f1287,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(duplicate_literal_removal,[],[f1286]) ).
fof(f1288,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1287,f1152]) ).
fof(f1289,plain,
( $false
| ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1288,f1152]) ).
fof(f1290,plain,
( ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1289]) ).
fof(f1291,plain,
( ! [X1] :
( sk_c9 != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_38 ),
inference(forward_demodulation,[],[f115,f1045]) ).
fof(f1292,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1291,f1126]) ).
fof(f1293,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1292,f1045]) ).
fof(f1296,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_33
| ~ spl0_38 ),
inference(superposition,[],[f1293,f3]) ).
fof(f1300,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_33
| ~ spl0_38 ),
inference(trivial_inequality_removal,[],[f1296]) ).
fof(f1302,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1300,f1152]) ).
fof(f1305,plain,
( $false
| ~ spl0_3
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1302,f1152]) ).
fof(f1306,plain,
( ~ spl0_3
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1305]) ).
fof(f1307,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f112,f1126]) ).
fof(f1308,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1307,f1082]) ).
fof(f1309,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1308,f1045]) ).
fof(f1310,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1309,f1126]) ).
fof(f1313,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38 ),
inference(superposition,[],[f1310,f3]) ).
fof(f1317,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38 ),
inference(trivial_inequality_removal,[],[f1313]) ).
fof(f1319,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1317,f1152]) ).
fof(f1322,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1319,f1152]) ).
fof(f1323,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1322]) ).
fof(f1324,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c10 != multiply(X0,sk_c9) )
| ~ spl0_4
| ~ spl0_38 ),
inference(forward_demodulation,[],[f118,f1045]) ).
fof(f1325,plain,
( ! [X0] :
( sk_c10 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_4
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1324,f1126]) ).
fof(f1326,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_4
| ~ spl0_33
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1325,f1045]) ).
fof(f1331,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_33
| ~ spl0_38 ),
inference(superposition,[],[f1326,f3]) ).
fof(f1335,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_33
| ~ spl0_38 ),
inference(trivial_inequality_removal,[],[f1331]) ).
fof(f1337,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1335,f1152]) ).
fof(f1340,plain,
( $false
| ~ spl0_4
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1337,f1152]) ).
fof(f1341,plain,
( ~ spl0_4
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1340]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f145]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f150]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f155]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s10,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s11,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f185]) ).
cnf(s13,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f191]) ).
cnf(s14,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f192]) ).
cnf(s15,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f193]) ).
cnf(s16,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f194]) ).
cnf(s17,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f195]) ).
cnf(s20,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f198]) ).
cnf(s21,plain,
( spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f199]) ).
cnf(s26,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f204]) ).
cnf(s27,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f205]) ).
cnf(s28,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f206]) ).
cnf(s29,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f207]) ).
cnf(s30,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s31,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s36,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f214]) ).
cnf(s37,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f215]) ).
cnf(s38,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f216]) ).
cnf(s39,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f217]) ).
cnf(s40,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f218]) ).
cnf(s41,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f219]) ).
cnf(s46,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f224]) ).
cnf(s47,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f225]) ).
cnf(s50,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f228]) ).
cnf(s51,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f229]) ).
cnf(s52,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f505]) ).
cnf(s53,plain,
( spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f512]) ).
cnf(s54,plain,
( spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f520]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f546]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f607]) ).
cnf(s74,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f711]) ).
cnf(s90,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f842]) ).
cnf(s112,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| spl0_36 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s113,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_36
| spl0_38 ),
inference(sat_conversion,[],[f1091]) ).
cnf(s114,plain,
( ~ spl0_9
| ~ spl0_19
| spl0_33
| ~ spl0_38 ),
inference(sat_conversion,[],[f1123]) ).
cnf(s132,plain,
( ~ spl0_7
| ~ spl0_33
| ~ spl0_38
| spl0_41 ),
inference(sat_conversion,[],[f1236]) ).
cnf(s136,plain,
( ~ spl0_1
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(sat_conversion,[],[f1290]) ).
cnf(s138,plain,
( ~ spl0_3
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s140,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33
| ~ spl0_36
| ~ spl0_38
| ~ spl0_41 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s142,plain,
( ~ spl0_4
| ~ spl0_33
| ~ spl0_38
| ~ spl0_41 ),
inference(sat_conversion,[],[f1341]) ).
cnf(s143,plain,
spl0_5,
inference(rat,[],[s53,s26,s27,s28,s29,s30,s31]) ).
cnf(s144,plain,
spl0_6,
inference(rat,[],[s54,s36,s37,s38,s39,s40,s41]) ).
cnf(s145,plain,
spl0_7,
inference(rat,[],[s52,s46,s47,s50,s51]) ).
cnf(s146,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s56,s6,s7,s10,s11]) ).
cnf(s148,plain,
( ~ spl0_33
| ~ spl0_38
| ~ spl0_4 ),
inference(rat,[],[s132,s142,s145]) ).
cnf(s149,plain,
( ~ spl0_19
| ~ spl0_4 ),
inference(rat,[],[s148,s114,s113,s112,s146,s143,s144,s145]) ).
cnf(s150,plain,
~ spl0_4,
inference(rat,[],[s56,s16,s17,s20,s21,s149]) ).
cnf(s152,plain,
( ~ spl0_33
| ~ spl0_38
| ~ spl0_3 ),
inference(rat,[],[s132,s138,s145]) ).
cnf(s153,plain,
( ~ spl0_19
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s152,s114,s113,s112,s143,s144,s145]) ).
cnf(s154,plain,
( spl0_19
| ~ spl0_3 ),
inference(rat,[],[s66,s16,s17,s20,s21]) ).
cnf(s155,plain,
( ~ spl0_19
| ~ spl0_3 ),
inference(rat,[],[s66,s6,s7,s10,s11,s153]) ).
cnf(s156,plain,
~ spl0_3,
inference(rat,[],[s155,s154]) ).
cnf(s158,plain,
( ~ spl0_19
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s140,s132,s114,s113,s112,s145,s143,s144]) ).
cnf(s159,plain,
( spl0_19
| ~ spl0_2 ),
inference(rat,[],[s90,s16,s17,s20,s21,s143]) ).
cnf(s160,plain,
( ~ spl0_19
| ~ spl0_2 ),
inference(rat,[],[s90,s6,s7,s10,s11,s158,s143]) ).
cnf(s161,plain,
~ spl0_2,
inference(rat,[],[s160,s159]) ).
cnf(s162,plain,
spl0_1,
inference(rat,[],[s1,s144,s143,s150,s145,s156,s161]) ).
cnf(s163,plain,
( spl0_19
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s74,s13,s14,s15,s20,s21,s162]) ).
cnf(s166,plain,
( ~ spl0_33
| ~ spl0_38 ),
inference(rat,[],[s132,s136,s162,s145]) ).
cnf(s167,plain,
( ~ spl0_38
| ~ spl0_19
| ~ spl0_9 ),
inference(rat,[],[s166,s114]) ).
cnf(s168,plain,
( ~ spl0_19
| ~ spl0_9 ),
inference(rat,[],[s167,s113,s112,s145,s144,s143]) ).
cnf(s169,plain,
spl0_19,
inference(rat,[],[s163,s16,s17]) ).
cnf(s170,plain,
~ spl0_9,
inference(rat,[],[s168,s169]) ).
cnf(s171,plain,
spl0_18,
inference(rat,[],[s11,s170]) ).
cnf(s172,plain,
spl0_17,
inference(rat,[],[s10,s170]) ).
cnf(s175,plain,
spl0_14,
inference(rat,[],[s7,s170]) ).
cnf(s176,plain,
spl0_13,
inference(rat,[],[s6,s170]) ).
cnf(s177,plain,
spl0_12,
inference(rat,[],[s5,s170]) ).
cnf(s178,plain,
spl0_11,
inference(rat,[],[s4,s170]) ).
cnf(s179,plain,
spl0_10,
inference(rat,[],[s3,s170]) ).
cnf(s181,plain,
$false,
inference(rat,[],[s74,s175,s176,s177,s178,s179,s162,s171,s172]) ).
fof(f1342,plain,
$false,
inference(avatar_sat_refutation,[],[s181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP386-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:00:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.17/0.46 % (558660)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (558668)dis+10_1_sil=32000:sp=arity:random_seed=2608706652:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (558666)% WARNING: option uhcvi not known.
% 0.17/0.46 % (558667)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3750441081:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (558665)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2155667941_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (558666)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=738914621:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (558669)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1825269864:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (558671)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1138917457:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (558670)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1219004584:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % (558668) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-558660-558668"...
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % (558668)...printing done.
% 0.17/0.46 % (558668)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (558668)------------------------------
% 0.17/0.47 % (558668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (558668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (558668)CaDiCaL version: 2.1.3
% 0.17/0.47 % (558668)Termination reason: Refutation
% 0.17/0.47 % (558668)Time elapsed: 0.015 s
% 0.17/0.47 % (558668)Peak memory usage: 13 MB
% 0.17/0.47 % (558668)Instructions burned: 44 (million)
% 0.17/0.47 % (558660)Success in time 0.042 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------