%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP371-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:46 AM UTC 2026
% Result : Unsatisfiable 3.00s 1.37s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 58
% Syntax : Number of formulae : 393 ( 23 unt; 23 def)
% Number of atoms : 1424 ( 432 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2003 ( 972 ~;1008 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f20,plain,
( inverse(sk_c11) = sk_c10
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c2 = inverse(sk_c1)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| multiply(X0,X1) != sk_c11
| inverse(X0) != X1
| multiply(X1,sk_c10) != sk_c11
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| multiply(X0,X1) != sk_c11
| inverse(X0) != X1
| sk_c11 != multiply(X1,sk_c10)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(X0,inverse(X0))
| sk_c11 != multiply(inverse(X0),sk_c10)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X6,X7,X4] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(X0,inverse(X0))
| sk_c11 != multiply(inverse(X0),sk_c10)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f105]) ).
fof(f107,plain,
! [X2,X3,X0,X6,X4] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(X0,inverse(X0))
| sk_c11 != multiply(inverse(X0),sk_c10)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f106]) ).
fof(f109,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f110,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f113,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f116,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl0_4
<=> sk_c11 = multiply(sk_c9,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f119,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( sk_c11 != multiply(sk_c9,sk_c10)
| spl0_4 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl0_5
<=> ! [X0] :
( sk_c11 != multiply(X0,inverse(X0))
| sk_c11 != multiply(inverse(X0),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f123,plain,
( ! [X0] :
( sk_c11 != multiply(X0,inverse(X0))
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,definition,
( spl0_6
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f126,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( inverse(sk_c11) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f107,f125,f122,f118,f115,f112,f109]) ).
fof(f135,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f137,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f140,definition,
( spl0_9
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f142,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f145,definition,
( spl0_10
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f147,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f150,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f152,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f94,f118,f150]) ).
fof(f155,definition,
( spl0_12
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f157,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f92,f118,f155]) ).
fof(f160,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f162,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f90,f118,f160]) ).
fof(f165,definition,
( spl0_14
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f167,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f88,f118,f165]) ).
fof(f170,definition,
( spl0_15
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f172,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_15
| spl0_4 ),
inference(avatar_split_clause,[],[f86,f118,f170]) ).
fof(f175,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f176,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| spl0_16 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f177,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl0_16
| spl0_4 ),
inference(avatar_split_clause,[],[f84,f118,f175]) ).
fof(f180,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f182,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f187,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f74,f180,f150]) ).
fof(f188,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f72,f180,f155]) ).
fof(f189,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f70,f180,f160]) ).
fof(f190,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f68,f180,f165]) ).
fof(f191,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f66,f180,f170]) ).
fof(f192,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f180,f175]) ).
fof(f194,definition,
( spl0_18
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f196,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f201,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f54,f194,f150]) ).
fof(f202,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f52,f194,f155]) ).
fof(f203,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f50,f194,f160]) ).
fof(f204,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f48,f194,f165]) ).
fof(f205,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f46,f194,f170]) ).
fof(f206,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f44,f194,f175]) ).
fof(f208,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f210,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f215,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f34,f208,f150]) ).
fof(f216,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f32,f208,f155]) ).
fof(f217,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f30,f208,f160]) ).
fof(f218,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f28,f208,f165]) ).
fof(f219,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f26,f208,f170]) ).
fof(f220,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f24,f208,f175]) ).
fof(f222,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f125,f135]) ).
fof(f223,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f125,f140]) ).
fof(f224,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f17,f125,f145]) ).
fof(f225,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f125,f150]) ).
fof(f226,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f125,f155]) ).
fof(f229,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f125,f170]) ).
fof(f230,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f125,f175]) ).
fof(f231,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_15 ),
inference(superposition,[],[f3,f172]) ).
fof(f232,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f162]) ).
fof(f234,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f3,f142]) ).
fof(f235,plain,
( identity = multiply(sk_c8,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f137]) ).
fof(f238,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f239,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c11,X0)) = multiply(sk_c10,X0)
| ~ spl0_16 ),
inference(superposition,[],[f4,f177]) ).
fof(f244,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f238,f1]) ).
fof(f247,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f231]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f247,f1]) ).
fof(f261,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f248,f177]) ).
fof(f270,plain,
( multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f239,f261]) ).
fof(f272,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f270,f177]) ).
fof(f309,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_15 ),
inference(superposition,[],[f244,f231]) ).
fof(f311,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f244,f261]) ).
fof(f312,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_13 ),
inference(superposition,[],[f244,f232]) ).
fof(f316,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f244,f167]) ).
fof(f319,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_12 ),
inference(superposition,[],[f244,f157]) ).
fof(f323,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c11)
| ~ spl0_10 ),
inference(superposition,[],[f244,f147]) ).
fof(f325,plain,
( sk_c6 = multiply(inverse(sk_c8),identity)
| ~ spl0_8 ),
inference(superposition,[],[f244,f235]) ).
fof(f328,plain,
( sk_c7 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f244,f234]) ).
fof(f331,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f328,f137]) ).
fof(f336,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f319,f152]) ).
fof(f339,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f316,f162]) ).
fof(f343,plain,
( identity = sk_c10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f311,f3]) ).
fof(f345,plain,
( multiply(sk_c8,sk_c10) = sk_c7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f331,f343]) ).
fof(f346,plain,
( sk_c11 = sk_c7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f345,f147]) ).
fof(f350,plain,
( inverse(sk_c11) = sk_c6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f142,f346]) ).
fof(f357,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f244,f336]) ).
fof(f359,plain,
( identity = sk_c11
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f357,f3]) ).
fof(f362,plain,
( sk_c11 = sk_c10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f359,f343]) ).
fof(f367,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f244,f339]) ).
fof(f369,plain,
( identity = sk_c9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f367,f3]) ).
fof(f372,plain,
( sk_c10 = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f369,f343]) ).
fof(f375,plain,
( sk_c11 != multiply(sk_c10,sk_c10)
| spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f120,f372]) ).
fof(f376,plain,
( sk_c11 != sk_c10
| spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f375,f272]) ).
fof(f378,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f312,f343]) ).
fof(f379,plain,
( identity = sk_c4
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f378,f3]) ).
fof(f380,plain,
( sk_c10 = sk_c4
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f379,f343]) ).
fof(f390,plain,
( $false
| spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f362,f376]) ).
fof(f391,plain,
( spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f392,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f119,f372]) ).
fof(f415,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f392,f362]) ).
fof(f436,plain,
( sk_c10 != sk_c6
| spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f127,f350]) ).
fof(f440,plain,
( sk_c11 != sk_c6
| spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f436,f362]) ).
fof(f490,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c10)
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f325,f343]) ).
fof(f491,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c11)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f490,f362]) ).
fof(f492,plain,
( sk_c10 = sk_c6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f491,f323]) ).
fof(f493,plain,
( sk_c11 = sk_c6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f492,f362]) ).
fof(f494,plain,
( $false
| spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f493,f440]) ).
fof(f495,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f494]) ).
fof(f496,plain,
( ! [X0] :
( sk_c11 != multiply(inverse(X0),sk_c11)
| sk_c11 != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f123,f362]) ).
fof(f497,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f126,f362]) ).
fof(f517,plain,
( sk_c11 != multiply(sk_c10,sk_c11)
| sk_c11 != multiply(sk_c4,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f496,f162]) ).
fof(f529,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c4,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f517,f362]) ).
fof(f538,plain,
( sk_c11 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f529,f415]) ).
fof(f547,plain,
( sk_c11 != sk_c9
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f538,f167]) ).
fof(f550,plain,
( sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f547,f372]) ).
fof(f555,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f550,f362]) ).
fof(f556,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f557,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),sk_c11)
| sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f110,f362]) ).
fof(f580,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f557,f497]) ).
fof(f589,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(duplicate_literal_removal,[],[f580]) ).
fof(f598,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f589,f415]) ).
fof(f645,plain,
( sk_c11 != inverse(sk_c10)
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f598,f162]) ).
fof(f652,plain,
( sk_c11 != inverse(sk_c11)
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f645,f362]) ).
fof(f659,plain,
( sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f652,f497]) ).
fof(f668,plain,
( sk_c10 != multiply(sk_c10,sk_c11)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f659,f380]) ).
fof(f674,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f668,f362]) ).
fof(f681,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f674,f415]) ).
fof(f682,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f683,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f113,f362]) ).
fof(f684,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f683,f372]) ).
fof(f685,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f684,f362]) ).
fof(f686,plain,
( ! [X3] :
( sk_c11 != inverse(X3)
| sk_c11 != multiply(X3,sk_c11) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f685,f362]) ).
fof(f690,plain,
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c4,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f686,f162]) ).
fof(f699,plain,
( sk_c11 != multiply(sk_c4,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f690,f362]) ).
fof(f709,plain,
( sk_c11 != multiply(sk_c10,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f699,f380]) ).
fof(f716,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f709,f362]) ).
fof(f717,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f716,f415]) ).
fof(f718,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f719,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c11) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f116,f362]) ).
fof(f722,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f719,f172]) ).
fof(f727,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f722]) ).
fof(f759,plain,
( sk_c11 != sk_c10
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f727,f177]) ).
fof(f768,definition,
( spl0_21
<=> sk_c11 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f769,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f773,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f759,f362]) ).
fof(f774,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f773]) ).
fof(f784,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6 ),
inference(superposition,[],[f3,f126]) ).
fof(f797,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c11)
| ~ spl0_4 ),
inference(superposition,[],[f244,f119]) ).
fof(f818,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c2,multiply(sk_c10,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f182]) ).
fof(f834,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_19 ),
inference(superposition,[],[f244,f210]) ).
fof(f835,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c1,multiply(sk_c2,X0))
| ~ spl0_19 ),
inference(superposition,[],[f4,f210]) ).
fof(f836,plain,
( sk_c2 = multiply(sk_c2,sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f834,f196]) ).
fof(f906,definition,
( spl0_22
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c2)
| sk_c2 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f907,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c2)
| sk_c2 != inverse(inverse(X0)) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f995,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_21 ),
inference(superposition,[],[f244,f769]) ).
fof(f997,plain,
( identity = sk_c11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f995,f3]) ).
fof(f1054,plain,
( sk_c3 = multiply(sk_c10,identity)
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f309,f126]) ).
fof(f1062,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c2,sk_c10)
| inverse(X0) != multiply(X0,sk_c2)
| sk_c2 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c1,sk_c2) )
| ~ spl0_1
| ~ spl0_18 ),
inference(superposition,[],[f110,f196]) ).
fof(f1065,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c2)
| sk_c2 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c1,sk_c2) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1062,f182]) ).
fof(f1096,definition,
( spl0_32
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f1097,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f1109,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c2)
| sk_c2 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1065,f210]) ).
fof(f1118,plain,
( spl0_22
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1109,f208,f194,f180,f109,f906]) ).
fof(f1119,plain,
( sk_c11 = multiply(sk_c10,sk_c11)
| ~ spl0_6
| ~ spl0_21 ),
inference(forward_demodulation,[],[f784,f997]) ).
fof(f1120,plain,
( sk_c2 != inverse(identity)
| sk_c2 != inverse(inverse(identity))
| ~ spl0_22 ),
inference(superposition,[],[f907,f1]) ).
fof(f1126,plain,
( inverse(sk_c11) != sk_c2
| sk_c2 != inverse(inverse(identity))
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1120,f997]) ).
fof(f1137,plain,
( sk_c10 != sk_c2
| sk_c2 != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1126,f126]) ).
fof(f1139,definition,
( spl0_39
<=> sk_c11 = sk_c2 ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f1140,plain,
( sk_c11 = sk_c2
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1147,plain,
( sk_c2 != inverse(inverse(sk_c11))
| sk_c10 != sk_c2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1137,f997]) ).
fof(f1148,plain,
( sk_c2 != inverse(sk_c10)
| sk_c10 != sk_c2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1147,f126]) ).
fof(f1167,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f244,f836]) ).
fof(f1169,plain,
( identity = sk_c11
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1167,f3]) ).
fof(f1171,plain,
( sk_c3 = multiply(sk_c10,sk_c11)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1054,f997]) ).
fof(f1172,plain,
( sk_c11 = sk_c3
| ~ spl0_6
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1171,f1119]) ).
fof(f1188,plain,
( multiply(sk_c11,sk_c11) = multiply(sk_c2,sk_c11)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f818,f1119]) ).
fof(f1192,plain,
( sk_c2 = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1188,f836]) ).
fof(f1195,plain,
( sk_c11 = sk_c2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1192,f769]) ).
fof(f1222,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c11,sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f835,f836]) ).
fof(f1229,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1222,f210]) ).
fof(f1234,plain,
( spl0_39
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1195,f768,f208,f194,f180,f125,f1139]) ).
fof(f1235,plain,
( spl0_21
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1229,f208,f194,f768]) ).
fof(f1238,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_39 ),
inference(superposition,[],[f182,f1140]) ).
fof(f1265,plain,
( spl0_32
| ~ spl0_17
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f1238,f1139,f180,f1096]) ).
fof(f1272,definition,
( spl0_47
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f1273,plain,
( sk_c11 = sk_c10
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1272]) ).
fof(f1288,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c11,multiply(sk_c11,X0))
| ~ spl0_21 ),
inference(superposition,[],[f4,f769]) ).
fof(f1291,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_15
| spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f176,f1172]) ).
fof(f1295,plain,
( sk_c11 != sk_c10
| ~ spl0_6
| ~ spl0_15
| spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1291,f769]) ).
fof(f1296,plain,
( ~ spl0_47
| ~ spl0_6
| ~ spl0_15
| spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1295,f768,f175,f170,f125,f1272]) ).
fof(f1298,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_32 ),
inference(superposition,[],[f244,f1097]) ).
fof(f1300,plain,
( identity = sk_c10
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1298,f3]) ).
fof(f1301,plain,
( sk_c11 = sk_c10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1300,f1169]) ).
fof(f1304,plain,
( spl0_47
| ~ spl0_18
| ~ spl0_19
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1301,f1096,f208,f194,f1272]) ).
fof(f1339,plain,
( inverse(sk_c11) != sk_c2
| sk_c10 != sk_c2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1148,f1273]) ).
fof(f1350,plain,
( sk_c11 != inverse(sk_c11)
| sk_c10 != sk_c2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1339,f1140]) ).
fof(f1357,plain,
( sk_c11 != sk_c10
| sk_c10 != sk_c2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1350,f126]) ).
fof(f1364,plain,
( sk_c10 != sk_c2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1357,f1273]) ).
fof(f1369,plain,
( sk_c11 != sk_c10
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1364,f1140]) ).
fof(f1374,plain,
( $false
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1369,f1273]) ).
fof(f1375,plain,
( ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f1374]) ).
fof(f1390,plain,
( ! [X0] :
( sk_c11 != multiply(inverse(X0),sk_c11)
| sk_c11 != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_47 ),
inference(forward_demodulation,[],[f123,f1273]) ).
fof(f1403,plain,
( sk_c11 != multiply(sk_c2,sk_c11)
| sk_c11 != multiply(sk_c1,sk_c2)
| ~ spl0_5
| ~ spl0_18
| ~ spl0_47 ),
inference(superposition,[],[f1390,f196]) ).
fof(f1408,plain,
( sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_5
| ~ spl0_18
| ~ spl0_19
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1403,f210]) ).
fof(f1422,plain,
( sk_c11 != sk_c2
| ~ spl0_5
| ~ spl0_18
| ~ spl0_19
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1408,f836]) ).
fof(f1428,plain,
( $false
| ~ spl0_5
| ~ spl0_18
| ~ spl0_19
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1422,f1140]) ).
fof(f1429,plain,
( ~ spl0_5
| ~ spl0_18
| ~ spl0_19
| ~ spl0_39
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f1428]) ).
fof(f1430,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_47 ),
inference(forward_demodulation,[],[f113,f1273]) ).
fof(f1431,plain,
( ! [X3] :
( sk_c11 != inverse(X3)
| sk_c9 != multiply(X3,sk_c11) )
| ~ spl0_2
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1430,f1273]) ).
fof(f1435,plain,
( sk_c11 != sk_c10
| sk_c9 != multiply(sk_c11,sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_47 ),
inference(superposition,[],[f1431,f126]) ).
fof(f1462,plain,
( sk_c9 != multiply(sk_c11,sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1435,f1273]) ).
fof(f1463,plain,
( sk_c11 != sk_c9
| ~ spl0_2
| ~ spl0_6
| ~ spl0_21
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1462,f769]) ).
fof(f1482,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c11),multiply(sk_c11,X0))
| ~ spl0_21 ),
inference(superposition,[],[f244,f1288]) ).
fof(f1485,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1482,f244]) ).
fof(f1647,plain,
( sk_c11 = multiply(inverse(sk_c9),sk_c11)
| ~ spl0_4
| ~ spl0_47 ),
inference(forward_demodulation,[],[f797,f1273]) ).
fof(f1664,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c9),multiply(sk_c11,X0))
| ~ spl0_4
| ~ spl0_47 ),
inference(superposition,[],[f4,f1647]) ).
fof(f1665,plain,
( ! [X0] : multiply(inverse(sk_c9),X0) = X0
| ~ spl0_4
| ~ spl0_21
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1664,f1485]) ).
fof(f1708,plain,
( identity = sk_c9
| ~ spl0_4
| ~ spl0_21
| ~ spl0_47 ),
inference(superposition,[],[f1665,f3]) ).
fof(f1715,plain,
( sk_c11 = sk_c9
| ~ spl0_4
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1708,f1169]) ).
fof(f1718,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1715,f1463]) ).
fof(f1719,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f1718]) ).
fof(f1720,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c11) )
| ~ spl0_3
| ~ spl0_47 ),
inference(forward_demodulation,[],[f116,f1273]) ).
fof(f1758,plain,
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_47 ),
inference(superposition,[],[f1720,f126]) ).
fof(f1767,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1758,f1273]) ).
fof(f1773,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_21
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1767,f769]) ).
fof(f1774,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_21
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f1773]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f128]) ).
cnf(s6,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f153]) ).
cnf(s7,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f158]) ).
cnf(s8,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f163]) ).
cnf(s9,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f168]) ).
cnf(s10,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f173]) ).
cnf(s11,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f178]) ).
cnf(s16,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s17,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s18,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s19,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s20,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s21,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f192]) ).
cnf(s26,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s27,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f202]) ).
cnf(s28,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f203]) ).
cnf(s29,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f204]) ).
cnf(s30,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f205]) ).
cnf(s31,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f206]) ).
cnf(s36,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f215]) ).
cnf(s37,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f216]) ).
cnf(s38,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f217]) ).
cnf(s39,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f218]) ).
cnf(s40,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f219]) ).
cnf(s41,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f220]) ).
cnf(s43,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f222]) ).
cnf(s44,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f223]) ).
cnf(s45,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f224]) ).
cnf(s46,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f225]) ).
cnf(s47,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f226]) ).
cnf(s50,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f229]) ).
cnf(s51,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f230]) ).
cnf(s52,plain,
( spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f391]) ).
cnf(s53,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f495]) ).
cnf(s59,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f556]) ).
cnf(s66,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f682]) ).
cnf(s73,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f718]) ).
cnf(s83,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f774]) ).
cnf(s118,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_22 ),
inference(sat_conversion,[],[f1118]) ).
cnf(s126,plain,
( ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| spl0_39 ),
inference(sat_conversion,[],[f1234]) ).
cnf(s127,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f1235]) ).
cnf(s132,plain,
( ~ spl0_17
| spl0_32
| ~ spl0_39 ),
inference(sat_conversion,[],[f1265]) ).
cnf(s136,plain,
( ~ spl0_6
| ~ spl0_15
| spl0_16
| ~ spl0_21
| ~ spl0_47 ),
inference(sat_conversion,[],[f1296]) ).
cnf(s138,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_32
| spl0_47 ),
inference(sat_conversion,[],[f1304]) ).
cnf(s145,plain,
( ~ spl0_6
| ~ spl0_21
| ~ spl0_22
| ~ spl0_39
| ~ spl0_47 ),
inference(sat_conversion,[],[f1375]) ).
cnf(s155,plain,
( ~ spl0_5
| ~ spl0_18
| ~ spl0_19
| ~ spl0_39
| ~ spl0_47 ),
inference(sat_conversion,[],[f1429]) ).
cnf(s174,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_47 ),
inference(sat_conversion,[],[f1719]) ).
cnf(s183,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_21
| ~ spl0_47 ),
inference(sat_conversion,[],[f1774]) ).
cnf(s185,plain,
spl0_4,
inference(rat,[],[s52,s6,s7,s8,s9,s10,s11]) ).
cnf(s186,plain,
spl0_6,
inference(rat,[],[s53,s43,s44,s45,s46,s47,s50,s51]) ).
cnf(s187,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s138,s136,s132,s126,s127,s21,s31,s41,s59,s185,s186]) ).
cnf(s188,plain,
( spl0_15
| ~ spl0_5 ),
inference(rat,[],[s138,s155,s132,s126,s127,s20,s30,s40,s186]) ).
cnf(s189,plain,
( spl0_14
| ~ spl0_5 ),
inference(rat,[],[s138,s155,s132,s126,s127,s19,s29,s39,s186]) ).
cnf(s190,plain,
( spl0_13
| ~ spl0_5 ),
inference(rat,[],[s138,s155,s132,s126,s127,s18,s28,s38,s186]) ).
cnf(s191,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s138,s155,s132,s126,s127,s17,s27,s37,s186]) ).
cnf(s192,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15 ),
inference(rat,[],[s138,s155,s132,s126,s127,s16,s26,s36,s187,s186]) ).
cnf(s193,plain,
~ spl0_5,
inference(rat,[],[s192,s191,s190,s189,s188]) ).
cnf(s194,plain,
( spl0_16
| ~ spl0_3 ),
inference(rat,[],[s138,s183,s132,s126,s127,s21,s31,s41,s186]) ).
cnf(s195,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s138,s183,s132,s126,s127,s20,s30,s40,s186]) ).
cnf(s196,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s138,s183,s132,s126,s127,s17,s27,s37,s186]) ).
cnf(s197,plain,
( ~ spl0_12
| ~ spl0_16
| ~ spl0_3
| ~ spl0_15 ),
inference(rat,[],[s138,s183,s132,s126,s127,s16,s26,s36,s83,s186]) ).
cnf(s198,plain,
~ spl0_3,
inference(rat,[],[s197,s196,s195,s194]) ).
cnf(s199,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s138,s132,s174,s126,s127,s185,s186]) ).
cnf(s200,plain,
( spl0_19
| ~ spl0_15
| ~ spl0_12
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s73,s38,s39,s41,s185]) ).
cnf(s201,plain,
( spl0_18
| ~ spl0_15
| ~ spl0_12
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s73,s28,s29,s31,s185]) ).
cnf(s202,plain,
( ~ spl0_15
| ~ spl0_12
| ~ spl0_2
| ~ spl0_11 ),
inference(rat,[],[s73,s18,s19,s21,s199,s201,s200,s185]) ).
cnf(s203,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s199,s20,s30,s40]) ).
cnf(s204,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s199,s17,s27,s37]) ).
cnf(s205,plain,
( ~ spl0_12
| ~ spl0_15
| ~ spl0_2 ),
inference(rat,[],[s199,s16,s26,s36,s202]) ).
cnf(s206,plain,
~ spl0_2,
inference(rat,[],[s205,s204,s203]) ).
cnf(s207,plain,
spl0_1,
inference(rat,[],[s1,s186,s185,s193,s198,s206]) ).
cnf(s208,plain,
( ~ spl0_19
| ~ spl0_21
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s138,s145,s132,s118,s126,s207,s186]) ).
cnf(s209,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s208,s127]) ).
cnf(s210,plain,
spl0_19,
inference(rat,[],[s66,s36,s37,s38,s39,s40,s41,s207,s185,s186]) ).
cnf(s211,plain,
spl0_18,
inference(rat,[],[s66,s26,s27,s28,s29,s30,s31,s207,s185,s186]) ).
cnf(s212,plain,
~ spl0_17,
inference(rat,[],[s209,s210,s211]) ).
cnf(s214,plain,
spl0_16,
inference(rat,[],[s21,s212]) ).
cnf(s215,plain,
spl0_15,
inference(rat,[],[s20,s212]) ).
cnf(s216,plain,
spl0_14,
inference(rat,[],[s19,s212]) ).
cnf(s217,plain,
spl0_13,
inference(rat,[],[s18,s212]) ).
cnf(s218,plain,
spl0_12,
inference(rat,[],[s17,s212]) ).
cnf(s219,plain,
spl0_11,
inference(rat,[],[s16,s212]) ).
cnf(s224,plain,
$false,
inference(rat,[],[s66,s216,s217,s218,s219,s186,s185,s207,s214,s215]) ).
fof(f1777,plain,
$false,
inference(avatar_sat_refutation,[],[s224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP371-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 % Computer : n016.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Sun Sep 27 10:03:02 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.45 Running first-order theorem proving
% 0.10/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.00/1.37 % (2386249)Input is clausal, will run a generic CNF schedule.
% 3.00/1.37 % (2386257)lrs+10_1_sil=8000:sp=occurrence:random_seed=1412768671:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.00/1.37 % (2386257)Refutation not found, incomplete strategy
% 3.00/1.37 % (2386257)------------------------------
% 3.00/1.37 % (2386257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.37 % (2386257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.37 % (2386257)CaDiCaL version: 2.1.3
% 3.00/1.37 % (2386257)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.37 % (2386257)Time elapsed: 0.002 s
% 3.00/1.37 % (2386257)Peak memory usage: 88 MB
% 3.00/1.37 % (2386257)Instructions burned: 5 (million)
% 3.00/1.37 % (2386256)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3209057295:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.00/1.37 % (2386260)dis-21_1_sil=8000:lcm=predicate:random_seed=2980531018:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.00/1.37 % (2386259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3981427530:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.00/1.37 % (2386255)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1553256775:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.00/1.37 % (2386258)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4276493311:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.00/1.37 % (2386254)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2457495466:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.00/1.37 % (2386260)Refutation not found, incomplete strategy
% 3.00/1.37 % (2386260)------------------------------
% 3.00/1.37 % (2386260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.37 % (2386260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.37 % (2386260)CaDiCaL version: 2.1.3
% 3.00/1.37 % (2386260)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.37 % (2386260)Time elapsed: 0.002 s
% 3.00/1.37 % (2386260)Peak memory usage: 88 MB
% 3.00/1.37 % (2386260)Instructions burned: 2 (million)
% 3.00/1.37 % (2386259)First to succeed.
% 3.00/1.37 % (2386259)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2386249"
% 3.00/1.37 % (2386258)Instruction limit reached!
% 3.00/1.37 % (2386258)------------------------------
% 3.00/1.37 % (2386258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.37 % (2386258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.37 % (2386258)CaDiCaL version: 2.1.3
% 3.00/1.37 % (2386258)Termination reason: Instruction limit
% 3.00/1.37 % (2386258)Termination phase: Saturation
% 3.00/1.37 % (2386258)Time elapsed: 0.066 s
% 3.00/1.37 % (2386258)Peak memory usage: 89 MB
% 3.00/1.37 % (2386258)Instructions burned: 115 (million)
% 3.00/1.37 % (2386257)------------------------------
% 3.00/1.37 % (2386257)------------------------------
% 3.00/1.37 % (2386268)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=4069042080:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.00/1.37 % (2386268)Refutation not found, incomplete strategy
% 3.00/1.37 % (2386268)------------------------------
% 3.00/1.37 % (2386268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.37 % (2386268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.37 % (2386268)CaDiCaL version: 2.1.3
% 3.00/1.37 % (2386268)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.37 % (2386268)Time elapsed: 0.004 s
% 3.00/1.37 % (2386268)Peak memory usage: 88 MB
% 3.00/1.37 % (2386268)Instructions burned: 5 (million)
% 3.00/1.37 % (2386260)------------------------------
% 3.00/1.37 % (2386260)------------------------------
% 3.00/1.37 % (2386269)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1905270690:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 3.00/1.37 % (2386269)Refutation not found, incomplete strategy
% 3.00/1.37 % (2386269)------------------------------
% 3.00/1.37 % (2386269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.37 % (2386269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.37 % (2386269)CaDiCaL version: 2.1.3
% 3.00/1.37 % (2386269)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.37 % (2386269)Time elapsed: 0.003 s
% 3.00/1.37 % (2386269)Peak memory usage: 88 MB
% 3.00/1.37 % (2386269)Instructions burned: 6 (million)
% 3.00/1.37 % (2386259)Refutation found. Thanks to Tanya!
% 3.00/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.00/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.56 % (2386259)------------------------------
% 3.94/1.56 % (2386259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.56 % (2386259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.56 % (2386259)CaDiCaL version: 2.1.3
% 3.94/1.56 % (2386259)Termination reason: Refutation
% 3.94/1.56 % (2386259)Time elapsed: 0.033 s
% 3.94/1.56 % (2386259)Peak memory usage: 90 MB
% 3.94/1.56 % (2386259)Instructions burned: 53 (million)
% 3.94/1.56 % (2386259)------------------------------
% 3.94/1.56 % (2386259)------------------------------
% 3.94/1.56 % (2386249)Success in time 0.476 s
% 3.94/1.56 % Vampire exiting
%------------------------------------------------------------------------------