%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 10:13:48 AM UTC 2026
% Result : Unsatisfiable 0.59s 0.91s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 60
% Syntax : Number of formulae : 361 ( 24 unt; 22 def)
% Number of atoms : 1200 ( 405 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1596 ( 757 ~; 817 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f56,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f58,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f60,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f62,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c2 = inverse(sk_c1)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c2 = inverse(sk_c1)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f82,plain,
( sk_c2 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| multiply(X1,sk_c9) != sk_c10
| 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/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| sk_c10 != multiply(X1,sk_c9)
| 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(sk_c10,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| 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(sk_c10,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| 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(sk_c10,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| 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_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10) )
| ~ 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
<=> ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f119,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_5
<=> sk_c11 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f122,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( sk_c11 != multiply(sk_c10,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
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,f121,f118,f115,f112,f109]) ).
fof(f130,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f132,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f136,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f139,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f141,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f144,definition,
( spl0_10
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f146,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f149,definition,
( spl0_11
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f151,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f154,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f159,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f161,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f164,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f166,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f90,f134,f164]) ).
fof(f169,definition,
( spl0_15
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f171,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f88,f134,f169]) ).
fof(f174,definition,
( spl0_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f176,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f86,f134,f174]) ).
fof(f179,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f84,f134,f179]) ).
fof(f184,definition,
( spl0_18
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f186,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_7
| spl0_18 ),
inference(avatar_split_clause,[],[f82,f184,f130]) ).
fof(f188,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f80,f184,f139]) ).
fof(f189,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f78,f184,f144]) ).
fof(f190,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f76,f184,f149]) ).
fof(f191,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f74,f184,f154]) ).
fof(f192,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f72,f184,f159]) ).
fof(f193,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f70,f184,f164]) ).
fof(f194,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f68,f184,f169]) ).
fof(f195,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f66,f184,f174]) ).
fof(f196,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f64,f184,f179]) ).
fof(f198,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f200,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( spl0_7
| spl0_19 ),
inference(avatar_split_clause,[],[f62,f198,f130]) ).
fof(f202,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f60,f198,f139]) ).
fof(f203,plain,
( spl0_10
| spl0_19 ),
inference(avatar_split_clause,[],[f58,f198,f144]) ).
fof(f204,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f56,f198,f149]) ).
fof(f205,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f54,f198,f154]) ).
fof(f206,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f52,f198,f159]) ).
fof(f207,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f50,f198,f164]) ).
fof(f208,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f48,f198,f169]) ).
fof(f209,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f46,f198,f174]) ).
fof(f210,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f44,f198,f179]) ).
fof(f215,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f34,f121,f154]) ).
fof(f216,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f32,f121,f159]) ).
fof(f217,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f30,f121,f164]) ).
fof(f218,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f121,f169]) ).
fof(f219,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f121,f174]) ).
fof(f220,plain,
( spl0_17
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f121,f179]) ).
fof(f225,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f125,f154]) ).
fof(f226,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f125,f159]) ).
fof(f229,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f125,f174]) ).
fof(f230,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f125,f179]) ).
fof(f231,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_16 ),
inference(superposition,[],[f3,f176]) ).
fof(f234,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f3,f146]) ).
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_17 ),
inference(superposition,[],[f4,f181]) ).
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_16 ),
inference(superposition,[],[f4,f231]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f247,f1]) ).
fof(f261,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f248,f181]) ).
fof(f270,plain,
( multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f239,f261]) ).
fof(f272,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f270,f181]) ).
fof(f308,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_16 ),
inference(superposition,[],[f244,f231]) ).
fof(f310,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f244,f261]) ).
fof(f315,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f244,f171]) ).
fof(f318,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_13 ),
inference(superposition,[],[f244,f161]) ).
fof(f327,plain,
( sk_c7 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f244,f234]) ).
fof(f330,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f327,f141]) ).
fof(f335,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f318,f156]) ).
fof(f338,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f315,f166]) ).
fof(f342,plain,
( identity = sk_c10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f310,f3]) ).
fof(f344,plain,
( multiply(sk_c8,sk_c10) = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f330,f342]) ).
fof(f345,plain,
( sk_c11 = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f344,f151]) ).
fof(f356,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f244,f335]) ).
fof(f358,plain,
( identity = sk_c11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f356,f3]) ).
fof(f361,plain,
( sk_c11 = sk_c10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f358,f342]) ).
fof(f368,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f335,f361]) ).
fof(f369,plain,
( sk_c11 = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f368,f151]) ).
fof(f371,plain,
( sk_c10 = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f369,f361]) ).
fof(f372,plain,
( sk_c11 != sk_c10
| spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f123,f338]) ).
fof(f375,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f244,f338]) ).
fof(f377,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f375,f3]) ).
fof(f380,plain,
( $false
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f372,f361]) ).
fof(f381,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f382,plain,
( sk_c10 = sk_c9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f377,f342]) ).
fof(f385,plain,
( sk_c10 != inverse(sk_c10)
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f127,f361]) ).
fof(f388,plain,
( sk_c6 = multiply(sk_c7,sk_c10)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f132,f371]) ).
fof(f405,plain,
( sk_c6 = multiply(sk_c11,sk_c10)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f388,f345]) ).
fof(f407,plain,
( sk_c11 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f405,f261]) ).
fof(f408,plain,
( sk_c10 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f407,f361]) ).
fof(f409,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f308,f342]) ).
fof(f410,plain,
( sk_c3 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f409,f361]) ).
fof(f411,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f410,f3]) ).
fof(f412,plain,
( sk_c10 = sk_c3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f411,f342]) ).
fof(f417,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f176,f412]) ).
fof(f418,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f417,f361]) ).
fof(f423,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f418,f385]) ).
fof(f424,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f426,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c10)
| sk_c10 != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f119,f382]) ).
fof(f427,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f126,f361]) ).
fof(f444,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f426,f166]) ).
fof(f454,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f444,f272]) ).
fof(f462,plain,
( sk_c10 != sk_c9
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f454,f171]) ).
fof(f469,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f462,f382]) ).
fof(f470,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f482,plain,
( ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f110,f361]) ).
fof(f483,plain,
( ! [X6,X4] :
( sk_c10 != multiply(inverse(X4),sk_c10)
| sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f482,f361]) ).
fof(f484,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f483,f427]) ).
fof(f491,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f484]) ).
fof(f498,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f491,f272]) ).
fof(f533,plain,
( sk_c10 != inverse(sk_c6)
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f498,f146]) ).
fof(f536,plain,
( sk_c10 != sk_c8
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f533,f141]) ).
fof(f542,plain,
( sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f536,f371]) ).
fof(f549,plain,
( sk_c6 != multiply(sk_c11,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f542,f345]) ).
fof(f555,plain,
( sk_c11 != sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f549,f261]) ).
fof(f559,plain,
( sk_c11 != sk_c10
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f555,f408]) ).
fof(f562,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f559,f361]) ).
fof(f563,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f562]) ).
fof(f564,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c10) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f113,f382]) ).
fof(f567,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f564,f166]) ).
fof(f571,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f567]) ).
fof(f576,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f571,f171]) ).
fof(f582,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f576,f382]) ).
fof(f583,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f592,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f116,f361]) ).
fof(f593,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f592,f361]) ).
fof(f597,plain,
( sk_c11 != sk_c10
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f593,f176]) ).
fof(f608,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f597,f361]) ).
fof(f615,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f608,f412]) ).
fof(f619,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f615,f272]) ).
fof(f620,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f661,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_19 ),
inference(superposition,[],[f244,f200]) ).
fof(f662,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c2,X0))
| ~ spl0_19 ),
inference(superposition,[],[f4,f200]) ).
fof(f663,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f661,f186]) ).
fof(f697,definition,
( spl0_23
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f698,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f700,definition,
( spl0_24
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f701,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f766,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6 ),
inference(superposition,[],[f3,f126]) ).
fof(f823,definition,
( spl0_36
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f824,plain,
( sk_c11 = sk_c10
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f891,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f244,f663]) ).
fof(f893,plain,
( identity = sk_c10
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f891,f3]) ).
fof(f903,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_36 ),
inference(superposition,[],[f126,f824]) ).
fof(f962,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c10,X0))
| ~ spl0_24 ),
inference(superposition,[],[f4,f701]) ).
fof(f989,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c10,sk_c10) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_36 ),
inference(superposition,[],[f110,f903]) ).
fof(f992,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_36 ),
inference(duplicate_literal_removal,[],[f989]) ).
fof(f994,plain,
( ! [X0] :
( sk_c11 != sk_c10
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_demodulation,[],[f992,f701]) ).
fof(f998,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f994,f824]) ).
fof(f1001,plain,
( spl0_23
| ~ spl0_1
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f998,f823,f700,f125,f109,f697]) ).
fof(f1017,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f698,f701]) ).
fof(f1030,plain,
( sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_6
| ~ spl0_23
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1017,f903]) ).
fof(f1033,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_6
| ~ spl0_23
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1030,f903]) ).
fof(f1036,plain,
( $false
| ~ spl0_6
| ~ spl0_23
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1033,f903]) ).
fof(f1037,plain,
( ~ spl0_6
| ~ spl0_23
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1036]) ).
fof(f1047,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_36 ),
inference(forward_demodulation,[],[f116,f824]) ).
fof(f1048,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1047,f824]) ).
fof(f1049,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c11,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_36 ),
inference(superposition,[],[f1048,f126]) ).
fof(f1055,plain,
( sk_c10 != multiply(sk_c11,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_36 ),
inference(trivial_inequality_removal,[],[f1049]) ).
fof(f1058,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1055,f824]) ).
fof(f1059,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1058,f701]) ).
fof(f1060,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1059]) ).
fof(f1061,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c11,sk_c10)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f113,f126]) ).
fof(f1067,plain,
( sk_c9 != multiply(sk_c11,sk_c10)
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f1061]) ).
fof(f1070,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1067,f824]) ).
fof(f1071,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1070,f701]) ).
fof(f1122,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c10,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f662,f663]) ).
fof(f1167,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c10),multiply(sk_c10,X0))
| ~ spl0_24 ),
inference(superposition,[],[f244,f962]) ).
fof(f1170,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1167,f244]) ).
fof(f1174,plain,
( sk_c11 = sk_c9
| ~ spl0_5
| ~ spl0_24 ),
inference(superposition,[],[f1170,f122]) ).
fof(f1184,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1174,f824]) ).
fof(f1187,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1184,f1071]) ).
fof(f1188,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1187]) ).
fof(f1193,plain,
( sk_c10 != multiply(sk_c2,sk_c9)
| sk_c10 != multiply(sk_c1,sk_c2)
| ~ spl0_4
| ~ spl0_18 ),
inference(superposition,[],[f119,f186]) ).
fof(f1196,plain,
( sk_c10 != multiply(sk_c1,sk_c2)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1193,f136]) ).
fof(f1201,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1196,f200]) ).
fof(f1202,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1201]) ).
fof(f1223,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_24 ),
inference(forward_demodulation,[],[f766,f1170]) ).
fof(f1227,plain,
( sk_c11 = sk_c10
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1223,f893]) ).
fof(f1229,plain,
( spl0_36
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1227,f700,f198,f184,f125,f823]) ).
fof(f1234,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1122,f200]) ).
fof(f1236,plain,
( spl0_24
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1234,f198,f184,f700]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f128]) ).
cnf(s8,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s9,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s11,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f182]) ).
cnf(s12,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f187]) ).
cnf(s13,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f188]) ).
cnf(s14,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f189]) ).
cnf(s15,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f190]) ).
cnf(s16,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f191]) ).
cnf(s17,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f192]) ).
cnf(s18,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f193]) ).
cnf(s19,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s20,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s21,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s22,plain,
( spl0_7
| spl0_19 ),
inference(sat_conversion,[],[f201]) ).
cnf(s23,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f202]) ).
cnf(s24,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f203]) ).
cnf(s25,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f204]) ).
cnf(s26,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f205]) ).
cnf(s27,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f206]) ).
cnf(s28,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f207]) ).
cnf(s29,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f208]) ).
cnf(s30,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f209]) ).
cnf(s31,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f210]) ).
cnf(s36,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f215]) ).
cnf(s37,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f216]) ).
cnf(s38,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f217]) ).
cnf(s39,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f218]) ).
cnf(s40,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f219]) ).
cnf(s41,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f220]) ).
cnf(s46,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f225]) ).
cnf(s47,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f226]) ).
cnf(s50,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f229]) ).
cnf(s51,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f230]) ).
cnf(s52,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f381]) ).
cnf(s53,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f424]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f470]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f563]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f583]) ).
cnf(s74,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f620]) ).
cnf(s116,plain,
( ~ spl0_1
| ~ spl0_6
| spl0_23
| ~ spl0_24
| ~ spl0_36 ),
inference(sat_conversion,[],[f1001]) ).
cnf(s122,plain,
( ~ spl0_6
| ~ spl0_23
| ~ spl0_24
| ~ spl0_36 ),
inference(sat_conversion,[],[f1037]) ).
cnf(s126,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(sat_conversion,[],[f1060]) ).
cnf(s136,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_24
| ~ spl0_36 ),
inference(sat_conversion,[],[f1188]) ).
cnf(s137,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1202]) ).
cnf(s144,plain,
( ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_24
| spl0_36 ),
inference(sat_conversion,[],[f1229]) ).
cnf(s146,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_24 ),
inference(sat_conversion,[],[f1236]) ).
cnf(s147,plain,
spl0_5,
inference(rat,[],[s52,s36,s37,s38,s39,s40,s41]) ).
cnf(s148,plain,
spl0_6,
inference(rat,[],[s53,s46,s47,s50,s51]) ).
cnf(s149,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s56,s8,s9,s10,s11]) ).
cnf(s150,plain,
( spl0_17
| ~ spl0_4 ),
inference(rat,[],[s137,s21,s31,s149]) ).
cnf(s151,plain,
( spl0_16
| ~ spl0_4 ),
inference(rat,[],[s137,s20,s30,s149]) ).
cnf(s152,plain,
( spl0_15
| ~ spl0_4 ),
inference(rat,[],[s137,s19,s29,s149]) ).
cnf(s153,plain,
~ spl0_4,
inference(rat,[],[s137,s18,s28,s56,s152,s151,s150,s149]) ).
cnf(s155,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s144,s126,s146,s148]) ).
cnf(s156,plain,
( spl0_19
| ~ spl0_3 ),
inference(rat,[],[s74,s26,s27,s30,s31]) ).
cnf(s157,plain,
( ~ spl0_19
| ~ spl0_3 ),
inference(rat,[],[s74,s16,s17,s20,s21,s155]) ).
cnf(s158,plain,
~ spl0_3,
inference(rat,[],[s157,s156]) ).
cnf(s159,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s136,s144,s146,s148,s147]) ).
cnf(s160,plain,
( spl0_19
| ~ spl0_2 ),
inference(rat,[],[s67,s28,s29,s30,s31]) ).
cnf(s161,plain,
( ~ spl0_19
| ~ spl0_2 ),
inference(rat,[],[s67,s18,s19,s20,s21,s159]) ).
cnf(s162,plain,
~ spl0_2,
inference(rat,[],[s161,s160]) ).
cnf(s163,plain,
spl0_1,
inference(rat,[],[s1,s147,s153,s148,s158,s162]) ).
cnf(s164,plain,
( ~ spl0_36
| ~ spl0_24 ),
inference(rat,[],[s116,s122,s148,s163]) ).
cnf(s165,plain,
( ~ spl0_24
| ~ spl0_19
| ~ spl0_18 ),
inference(rat,[],[s164,s144,s148]) ).
cnf(s166,plain,
( ~ spl0_19
| ~ spl0_18 ),
inference(rat,[],[s165,s146]) ).
cnf(s167,plain,
spl0_19,
inference(rat,[],[s65,s22,s23,s24,s25,s26,s27,s30,s31,s163,s148]) ).
cnf(s168,plain,
~ spl0_18,
inference(rat,[],[s166,s167]) ).
cnf(s169,plain,
spl0_17,
inference(rat,[],[s21,s168]) ).
cnf(s170,plain,
spl0_16,
inference(rat,[],[s20,s168]) ).
cnf(s173,plain,
spl0_13,
inference(rat,[],[s17,s168]) ).
cnf(s174,plain,
spl0_12,
inference(rat,[],[s16,s168]) ).
cnf(s175,plain,
spl0_11,
inference(rat,[],[s15,s168]) ).
cnf(s176,plain,
spl0_10,
inference(rat,[],[s14,s168]) ).
cnf(s177,plain,
spl0_9,
inference(rat,[],[s13,s168]) ).
cnf(s178,plain,
spl0_7,
inference(rat,[],[s12,s168]) ).
cnf(s182,plain,
$false,
inference(rat,[],[s65,s169,s170,s175,s176,s177,s178,s148,s163,s173,s174]) ).
fof(f1237,plain,
$false,
inference(avatar_sat_refutation,[],[s182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 10:00:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.91 % (994619)Input is clausal, will run a generic CNF schedule.
% 0.59/0.91 % (994629)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1253959106:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.59/0.91 % (994629)First to succeed.
% 0.59/0.91 % (994629)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-994619"
% 0.59/0.91 % (994628)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2921606018:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.59/0.91 % (994625)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1633886421:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.59/0.91 % (994626)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1251304409:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.59/0.91 % (994627)lrs+10_1_sil=8000:sp=occurrence:random_seed=1855672952:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.59/0.91 % (994630)dis-21_1_sil=8000:lcm=predicate:random_seed=991886409: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)
% 0.59/0.91 % (994624)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=645193584:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.59/0.91 % (994630)Refutation not found, incomplete strategy
% 0.59/0.91 % (994630)------------------------------
% 0.59/0.91 % (994630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.91 % (994630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.91 % (994630)CaDiCaL version: 2.1.3
% 0.59/0.91 % (994630)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.91 % (994630)Time elapsed: 0.002 s
% 0.59/0.91 % (994630)Peak memory usage: 88 MB
% 0.59/0.91 % (994630)Instructions burned: 2 (million)
% 0.59/0.91 % (994627)Refutation not found, incomplete strategy
% 0.59/0.91 % (994627)------------------------------
% 0.59/0.91 % (994627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.91 % (994627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.91 % (994627)CaDiCaL version: 2.1.3
% 0.59/0.91 % (994627)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.91 % (994627)Time elapsed: 0.004 s
% 0.59/0.91 % (994627)Peak memory usage: 88 MB
% 0.59/0.91 % (994627)Instructions burned: 5 (million)
% 0.59/0.91 % (994628)Instruction limit reached!
% 0.59/0.91 % (994628)------------------------------
% 0.59/0.91 % (994628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.91 % (994628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.91 % (994628)CaDiCaL version: 2.1.3
% 0.59/0.91 % (994628)Termination reason: Instruction limit
% 0.59/0.91 % (994628)Termination phase: Saturation
% 0.59/0.91 % (994628)Time elapsed: 0.065 s
% 0.59/0.91 % (994628)Peak memory usage: 89 MB
% 0.59/0.91 % (994628)Instructions burned: 115 (million)
% 0.59/0.91 % (994629)Refutation found. Thanks to Tanya!
% 0.59/0.91 % SZS status Unsatisfiable for theBenchmark
% 0.59/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.11 % (994629)------------------------------
% 2.48/1.11 % (994629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.11 % (994629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.11 % (994629)CaDiCaL version: 2.1.3
% 2.48/1.11 % (994629)Termination reason: Refutation
% 2.48/1.11 % (994629)Time elapsed: 0.014 s
% 2.48/1.11 % (994629)Peak memory usage: 90 MB
% 2.48/1.11 % (994629)Instructions burned: 39 (million)
% 2.48/1.11 % (994629)------------------------------
% 2.48/1.11 % (994629)------------------------------
% 2.48/1.11 % (994619)Success in time 0.303 s
% 2.48/1.11 % Vampire exiting
%------------------------------------------------------------------------------