%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP318-1 : 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 : n004.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 10:13:37 AM UTC 2026
% Result : Unsatisfiable 3.32s 1.32s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 54
% Syntax : Number of formulae : 378 ( 22 unt; 24 def)
% Number of atoms : 1312 ( 414 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1826 ( 892 ~; 910 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 82 !; 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,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f44,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c11 = inverse(sk_c1)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f64,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f84,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f90]) ).
fof(f104,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c12 = inverse(sk_c2)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c12 = inverse(sk_c2)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f106]) ).
fof(f108,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
fof(f109,plain,
( sk_c12 = inverse(sk_c2)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f108]) ).
fof(f110,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
fof(f111,plain,
( sk_c12 = inverse(sk_c2)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f110]) ).
fof(f124,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| multiply(X0,sk_c11) != sk_c12
| inverse(X0) != sk_c11
| multiply(sk_c12,X1) != sk_c11
| multiply(X2,sk_c12) != X1
| inverse(X2) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| inverse(X3) != sk_c12
| multiply(X4,sk_c11) != sk_c10
| inverse(X4) != sk_c11
| multiply(X5,X6) != sk_c12
| inverse(X5) != X6
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,X1)
| multiply(X2,sk_c12) != X1
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
inference(reorient_equations,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X0,X8,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
inference(equality_resolution,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X0,X8,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X7) != X8
| inverse(X5) != inverse(X8)
| multiply(X7,inverse(X5)) != X8 ),
inference(equality_resolution,[],[f126]) ).
fof(f128,plain,
! [X2,X3,X0,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X5) != inverse(inverse(X7))
| inverse(X7) != multiply(X7,inverse(X5)) ),
inference(equality_resolution,[],[f127]) ).
fof(f130,definition,
( spl0_1
<=> ! [X5,X7] :
( sk_c12 != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f131,plain,
( ! [X7,X5] :
( sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(X5,inverse(X5)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl0_2
<=> ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f134,plain,
( ! [X4] :
( sk_c11 != inverse(X4)
| sk_c10 != multiply(X4,sk_c11) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,definition,
( spl0_3
<=> ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f137,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,definition,
( spl0_4
<=> ! [X2] :
( sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f140,plain,
( ! [X2] :
( sk_c12 != inverse(X2)
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,definition,
( spl0_5
<=> ! [X0] :
( sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f143,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c12 != multiply(X0,sk_c11) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,definition,
( spl0_6
<=> multiply(sk_c11,sk_c12) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f146,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f147,plain,
( multiply(sk_c11,sk_c12) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f128,f145,f142,f139,f136,f133,f130]) ).
fof(f154,definition,
( spl0_8
<=> sk_c12 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f156,plain,
( sk_c12 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f174,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f176,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f179,definition,
( spl0_13
<=> sk_c12 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f181,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f184,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f186,plain,
( sk_c11 = inverse(sk_c5)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f111,f154,f184]) ).
fof(f189,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c5,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f191,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f109,f154,f189]) ).
fof(f194,definition,
( spl0_16
<=> sk_c12 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f196,plain,
( sk_c12 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f107,f154,f194]) ).
fof(f199,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c4,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f201,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f202,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f105,f154,f199]) ).
fof(f204,definition,
( spl0_18
<=> sk_c3 = multiply(sk_c2,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f206,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f213,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f91,f204,f184]) ).
fof(f214,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f89,f204,f189]) ).
fof(f215,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f87,f204,f194]) ).
fof(f216,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f85,f204,f199]) ).
fof(f218,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c12,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f220,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f227,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f71,f218,f184]) ).
fof(f228,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f69,f218,f189]) ).
fof(f229,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f67,f218,f194]) ).
fof(f230,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f65,f218,f199]) ).
fof(f232,definition,
( spl0_20
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f234,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f241,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f51,f232,f184]) ).
fof(f242,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f49,f232,f189]) ).
fof(f243,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f47,f232,f194]) ).
fof(f244,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f45,f232,f199]) ).
fof(f246,definition,
( spl0_21
<=> sk_c12 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f248,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f255,plain,
( spl0_14
| spl0_21 ),
inference(avatar_split_clause,[],[f31,f246,f184]) ).
fof(f256,plain,
( spl0_15
| spl0_21 ),
inference(avatar_split_clause,[],[f29,f246,f189]) ).
fof(f257,plain,
( spl0_16
| spl0_21 ),
inference(avatar_split_clause,[],[f27,f246,f194]) ).
fof(f258,plain,
( spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f25,f246,f199]) ).
fof(f263,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f145,f174]) ).
fof(f264,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f145,f179]) ).
fof(f265,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f145,f184]) ).
fof(f266,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f145,f189]) ).
fof(f267,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f145,f194]) ).
fof(f268,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f145,f199]) ).
fof(f269,plain,
( identity = multiply(sk_c12,sk_c4)
| ~ spl0_16 ),
inference(superposition,[],[f3,f196]) ).
fof(f270,plain,
( identity = multiply(sk_c11,sk_c5)
| ~ spl0_14 ),
inference(superposition,[],[f3,f186]) ).
fof(f276,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f282,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f276,f1]) ).
fof(f285,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c4,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f269]) ).
fof(f286,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c4,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f285,f1]) ).
fof(f299,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f286,f201]) ).
fof(f346,plain,
( sk_c5 = multiply(inverse(sk_c11),identity)
| ~ spl0_14 ),
inference(superposition,[],[f282,f270]) ).
fof(f350,plain,
( sk_c11 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f282,f299]) ).
fof(f354,plain,
( sk_c11 = multiply(inverse(sk_c5),sk_c10)
| ~ spl0_15 ),
inference(superposition,[],[f282,f191]) ).
fof(f356,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c12)
| ~ spl0_13 ),
inference(superposition,[],[f282,f181]) ).
fof(f373,plain,
( sk_c9 = multiply(sk_c9,sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f356,f176]) ).
fof(f375,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f354,f186]) ).
fof(f379,plain,
( identity = sk_c11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f350,f3]) ).
fof(f394,plain,
( sk_c12 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f282,f373]) ).
fof(f396,plain,
( identity = sk_c12
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f394,f3]) ).
fof(f399,plain,
( sk_c11 = sk_c12
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f396,f379]) ).
fof(f404,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f282,f375]) ).
fof(f406,plain,
( identity = sk_c10
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f404,f3]) ).
fof(f409,plain,
( sk_c11 = sk_c10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f406,f379]) ).
fof(f412,plain,
( sk_c5 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f346,f379]) ).
fof(f413,plain,
( identity = sk_c5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f412,f3]) ).
fof(f414,plain,
( sk_c11 = sk_c5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f413,f379]) ).
fof(f425,plain,
( sk_c10 = multiply(sk_c5,sk_c12)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f191,f399]) ).
fof(f437,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f425,f414]) ).
fof(f442,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f437,f147]) ).
fof(f443,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f448,plain,
( sk_c11 = multiply(sk_c11,sk_c12)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f146,f409]) ).
fof(f486,plain,
( identity = multiply(sk_c12,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f156]) ).
fof(f489,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_20 ),
inference(superposition,[],[f3,f234]) ).
fof(f494,plain,
( sk_c12 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_18 ),
inference(superposition,[],[f282,f206]) ).
fof(f496,plain,
( sk_c12 = multiply(sk_c12,sk_c3)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f494,f156]) ).
fof(f501,plain,
( sk_c3 = multiply(inverse(sk_c12),sk_c11)
| ~ spl0_19 ),
inference(superposition,[],[f282,f220]) ).
fof(f504,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c12)
| ~ spl0_21 ),
inference(superposition,[],[f282,f248]) ).
fof(f506,plain,
( sk_c11 = multiply(sk_c11,sk_c12)
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f504,f234]) ).
fof(f509,plain,
( sk_c12 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f282,f448]) ).
fof(f511,plain,
( identity = sk_c12
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f509,f3]) ).
fof(f516,plain,
( sk_c11 = sk_c12
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f511,f379]) ).
fof(f521,plain,
( identity != sk_c11
| sk_c12 != inverse(inverse(sk_c12))
| ~ spl0_3 ),
inference(superposition,[],[f137,f3]) ).
fof(f523,plain,
( sk_c11 != sk_c11
| sk_c12 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f137,f201]) ).
fof(f526,plain,
( sk_c12 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f523]) ).
fof(f534,definition,
( spl0_25
<=> sk_c11 = sk_c12 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f535,plain,
( sk_c11 = sk_c12
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f538,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f526,f196]) ).
fof(f539,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f550,plain,
( spl0_25
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f516,f199,f194,f189,f184,f145,f534]) ).
fof(f554,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c12,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f146]) ).
fof(f556,plain,
( sk_c11 != sk_c12
| sk_c12 != multiply(sk_c4,sk_c11)
| ~ spl0_5
| ~ spl0_16 ),
inference(superposition,[],[f143,f196]) ).
fof(f559,plain,
( sk_c11 != sk_c11
| sk_c12 != multiply(sk_c1,sk_c11)
| ~ spl0_5
| ~ spl0_20 ),
inference(superposition,[],[f143,f234]) ).
fof(f561,plain,
( sk_c12 != multiply(sk_c1,sk_c11)
| ~ spl0_5
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f559]) ).
fof(f567,plain,
( $false
| ~ spl0_5
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f561,f248]) ).
fof(f568,plain,
( ~ spl0_5
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f591,plain,
( sk_c12 != sk_c12
| sk_c11 != multiply(sk_c12,multiply(sk_c4,sk_c12))
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[],[f140,f196]) ).
fof(f595,plain,
( sk_c12 != sk_c12
| sk_c11 != multiply(sk_c12,multiply(sk_c2,sk_c12))
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f140,f156]) ).
fof(f596,plain,
( sk_c11 != multiply(sk_c12,multiply(sk_c2,sk_c12))
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f595]) ).
fof(f597,plain,
( sk_c11 != multiply(sk_c12,multiply(sk_c4,sk_c12))
| ~ spl0_4
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f591]) ).
fof(f598,plain,
( sk_c11 != multiply(sk_c12,sk_c3)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f596,f206]) ).
fof(f610,plain,
( sk_c11 != sk_c12
| ~ spl0_4
| ~ spl0_16 ),
inference(forward_demodulation,[],[f597,f286]) ).
fof(f620,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f598,f220]) ).
fof(f621,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f623,plain,
( ~ spl0_25
| ~ spl0_4
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f610,f194,f139,f534]) ).
fof(f633,plain,
( sk_c11 != sk_c12
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_2
| ~ spl0_16 ),
inference(superposition,[],[f134,f196]) ).
fof(f636,plain,
( sk_c11 != sk_c11
| sk_c10 != multiply(sk_c1,sk_c11)
| ~ spl0_2
| ~ spl0_20 ),
inference(superposition,[],[f134,f234]) ).
fof(f638,plain,
( sk_c10 != multiply(sk_c1,sk_c11)
| ~ spl0_2
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f636]) ).
fof(f644,plain,
( sk_c12 != sk_c10
| ~ spl0_2
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f638,f248]) ).
fof(f652,definition,
( spl0_36
<=> sk_c10 = multiply(sk_c4,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f653,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f654,plain,
( sk_c10 != multiply(sk_c4,sk_c11)
| spl0_36 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f655,plain,
( ~ spl0_36
| ~ spl0_25
| ~ spl0_2
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f633,f194,f133,f534,f652]) ).
fof(f663,definition,
( spl0_38
<=> sk_c12 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f668,plain,
( ~ spl0_38
| ~ spl0_2
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f644,f246,f232,f133,f663]) ).
fof(f745,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(superposition,[],[f299,f535]) ).
fof(f757,plain,
( sk_c10 != multiply(sk_c4,sk_c12)
| ~ spl0_25
| spl0_36 ),
inference(forward_demodulation,[],[f654,f535]) ).
fof(f758,plain,
( sk_c11 != sk_c10
| ~ spl0_17
| ~ spl0_25
| spl0_36 ),
inference(forward_demodulation,[],[f757,f201]) ).
fof(f770,plain,
( sk_c3 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f501,f535]) ).
fof(f775,plain,
( identity = sk_c3
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f770,f3]) ).
fof(f800,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f506,f535]) ).
fof(f885,plain,
( ! [X7,X5] :
( sk_c12 != multiply(inverse(X5),sk_c12)
| sk_c12 != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f131,f535]) ).
fof(f887,plain,
( sk_c12 != sk_c10
| ~ spl0_17
| ~ spl0_25
| spl0_36 ),
inference(forward_demodulation,[],[f758,f535]) ).
fof(f888,plain,
( ~ spl0_38
| ~ spl0_17
| ~ spl0_25
| spl0_36 ),
inference(avatar_split_clause,[],[f887,f652,f534,f199,f663]) ).
fof(f889,plain,
( sk_c10 = multiply(sk_c4,sk_c12)
| ~ spl0_25
| ~ spl0_36 ),
inference(forward_demodulation,[],[f653,f535]) ).
fof(f1003,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f489,f535]) ).
fof(f1022,plain,
( sk_c3 = multiply(sk_c12,sk_c2)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f486,f775]) ).
fof(f1023,plain,
( sk_c3 = multiply(sk_c12,sk_c1)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1003,f775]) ).
fof(f1024,plain,
( multiply(sk_c11,sk_c3) = multiply(sk_c10,sk_c2)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(superposition,[],[f554,f1022]) ).
fof(f1027,plain,
( sk_c2 = multiply(inverse(sk_c12),sk_c3)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(superposition,[],[f282,f1022]) ).
fof(f1030,plain,
( multiply(sk_c12,sk_c3) = multiply(sk_c10,sk_c2)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1024,f535]) ).
fof(f1032,plain,
( sk_c11 = multiply(sk_c10,sk_c2)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1030,f220]) ).
fof(f1033,plain,
( sk_c12 = multiply(sk_c10,sk_c2)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1032,f535]) ).
fof(f1037,plain,
( sk_c1 = multiply(inverse(sk_c12),sk_c3)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_25 ),
inference(superposition,[],[f282,f1023]) ).
fof(f1056,plain,
( sk_c11 = sk_c12
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f220,f496]) ).
fof(f1072,plain,
( multiply(sk_c11,sk_c12) = multiply(sk_c10,sk_c12)
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f554,f800]) ).
fof(f1075,plain,
( sk_c12 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f282,f800]) ).
fof(f1077,plain,
( identity = sk_c12
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1075,f3]) ).
fof(f1080,plain,
( sk_c10 = multiply(sk_c10,sk_c12)
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1072,f146]) ).
fof(f1085,plain,
( sk_c12 = sk_c3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f1077,f775]) ).
fof(f1122,plain,
( sk_c2 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1027,f1085]) ).
fof(f1123,plain,
( identity = sk_c2
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1122,f3]) ).
fof(f1124,plain,
( sk_c3 = sk_c2
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1123,f775]) ).
fof(f1125,plain,
( sk_c12 = sk_c2
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1124,f1085]) ).
fof(f1126,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f156,f1125]) ).
fof(f1130,plain,
( sk_c12 = multiply(sk_c10,sk_c12)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f1033,f1125]) ).
fof(f1135,plain,
( sk_c1 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1037,f1085]) ).
fof(f1136,plain,
( identity = sk_c1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1135,f3]) ).
fof(f1137,plain,
( sk_c12 = sk_c1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1136,f1077]) ).
fof(f1177,plain,
( sk_c12 = sk_c10
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f1080,f1130]) ).
fof(f1191,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1056,f218,f204,f154,f534]) ).
fof(f1202,definition,
( spl0_49
<=> identity = sk_c12 ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f1203,plain,
( identity = sk_c12
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1212,plain,
( spl0_38
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1177,f534,f246,f232,f218,f154,f145,f663]) ).
fof(f1213,plain,
( spl0_49
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1077,f534,f246,f232,f1202]) ).
fof(f1215,plain,
( sk_c11 = sk_c10
| ~ spl0_17
| ~ spl0_25
| ~ spl0_36 ),
inference(forward_demodulation,[],[f889,f201]) ).
fof(f1218,definition,
( spl0_51
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f1219,plain,
( ! [X0] :
( sk_c12 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c12) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f1221,definition,
( spl0_52
<=> sk_c12 = multiply(sk_c12,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1222,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1221]) ).
fof(f1233,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c11)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c2,sk_c12) )
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f131,f156]) ).
fof(f1234,plain,
( ! [X0] :
( identity != sk_c12
| inverse(X0) != multiply(X0,inverse(sk_c11))
| inverse(inverse(X0)) != inverse(sk_c11)
| sk_c12 != multiply(sk_c11,inverse(sk_c11)) )
| ~ spl0_1 ),
inference(superposition,[],[f131,f3]) ).
fof(f1291,plain,
( sk_c11 = multiply(sk_c4,sk_c11)
| ~ spl0_17
| ~ spl0_25
| ~ spl0_36 ),
inference(forward_demodulation,[],[f653,f1215]) ).
fof(f1306,plain,
( sk_c10 = multiply(sk_c12,sk_c12)
| ~ spl0_6
| ~ spl0_25 ),
inference(superposition,[],[f146,f535]) ).
fof(f1309,plain,
( sk_c12 = multiply(sk_c1,sk_c12)
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f248,f535]) ).
fof(f1316,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1309,f1137]) ).
fof(f1318,plain,
( sk_c12 = sk_c10
| ~ spl0_6
| ~ spl0_25
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1306,f1222]) ).
fof(f1322,plain,
( spl0_38
| ~ spl0_6
| ~ spl0_25
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f1318,f1221,f534,f145,f663]) ).
fof(f1329,plain,
( sk_c12 = multiply(sk_c4,sk_c12)
| ~ spl0_17
| ~ spl0_25
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1291,f535]) ).
fof(f1349,plain,
( sk_c12 != inverse(sk_c12)
| sk_c12 != multiply(sk_c12,sk_c12)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_51 ),
inference(superposition,[],[f1219,f1126]) ).
fof(f1356,plain,
( sk_c12 != multiply(sk_c12,sk_c12)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[],[f1349,f1126]) ).
fof(f1370,plain,
( identity != sk_c12
| sk_c12 != inverse(inverse(sk_c12))
| ~ spl0_3
| ~ spl0_25 ),
inference(forward_demodulation,[],[f521,f535]) ).
fof(f1374,plain,
( sk_c12 != inverse(inverse(sk_c12))
| ~ spl0_3
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1370,f1203]) ).
fof(f1380,plain,
( sk_c12 != inverse(sk_c12)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1374,f1126]) ).
fof(f1383,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1380,f1126]) ).
fof(f1384,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1383]) ).
fof(f1404,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c12)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c2,sk_c12) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1233,f535]) ).
fof(f1405,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,inverse(sk_c11))
| inverse(inverse(X0)) != inverse(sk_c11)
| sk_c12 != multiply(sk_c11,inverse(sk_c11)) )
| ~ spl0_1
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1234,f1203]) ).
fof(f1429,plain,
( sk_c12 = inverse(sk_c5)
| ~ spl0_14
| ~ spl0_25 ),
inference(forward_demodulation,[],[f186,f535]) ).
fof(f1437,plain,
( sk_c12 = sk_c5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f414,f535]) ).
fof(f1458,plain,
( spl0_52
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f745,f534,f199,f194,f1221]) ).
fof(f1476,plain,
( ~ spl0_52
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f1356,f1218,f534,f246,f232,f218,f154,f1221]) ).
fof(f1478,plain,
( spl0_52
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1316,f534,f246,f232,f218,f1221]) ).
fof(f1495,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c12)
| sk_c12 != multiply(sk_c12,sk_c12)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1404,f1125]) ).
fof(f1496,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c12)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(duplicate_literal_removal,[],[f1495]) ).
fof(f1497,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,inverse(sk_c12))
| inverse(inverse(X0)) != inverse(sk_c11)
| sk_c12 != multiply(sk_c11,inverse(sk_c11)) )
| ~ spl0_1
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1405,f535]) ).
fof(f1552,plain,
( spl0_51
| ~ spl0_52
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1496,f534,f246,f232,f218,f154,f130,f1221,f1218]) ).
fof(f1553,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c12)
| inverse(inverse(X0)) != inverse(sk_c11)
| sk_c12 != multiply(sk_c11,inverse(sk_c11)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1497,f1126]) ).
fof(f1587,plain,
( ! [X0] :
( inverse(inverse(X0)) != inverse(sk_c12)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != multiply(sk_c11,inverse(sk_c11)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1553,f535]) ).
fof(f1600,plain,
( ! [X0] :
( sk_c12 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != multiply(sk_c11,inverse(sk_c11)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1587,f1126]) ).
fof(f1604,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,inverse(sk_c12))
| sk_c12 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c12) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1600,f535]) ).
fof(f1605,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c12)
| sk_c12 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c12) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1604,f1126]) ).
fof(f1606,plain,
( spl0_51
| ~ spl0_52
| ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1605,f1202,f534,f246,f232,f218,f154,f130,f1221,f1218]) ).
fof(f1625,definition,
( spl0_58
<=> sk_c12 = inverse(sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f1626,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f1681,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1429,f1437]) ).
fof(f1682,plain,
( spl0_58
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1681,f534,f199,f194,f184,f1625]) ).
fof(f1700,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c12)
| sk_c12 != multiply(sk_c12,sk_c12)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_25
| ~ spl0_58 ),
inference(superposition,[],[f885,f1626]) ).
fof(f1707,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c12)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_25
| ~ spl0_58 ),
inference(duplicate_literal_removal,[],[f1700]) ).
fof(f1713,plain,
( spl0_51
| ~ spl0_52
| ~ spl0_1
| ~ spl0_25
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1707,f1625,f534,f130,f1221,f1218]) ).
fof(f1814,plain,
( sk_c12 != inverse(sk_c12)
| sk_c12 != multiply(sk_c12,sk_c12)
| ~ spl0_51
| ~ spl0_58 ),
inference(superposition,[],[f1219,f1626]) ).
fof(f1823,plain,
( sk_c12 != multiply(sk_c12,sk_c12)
| ~ spl0_51
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[],[f1814,f1626]) ).
fof(f1828,plain,
( $false
| ~ spl0_51
| ~ spl0_52
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[],[f1823,f1222]) ).
fof(f1829,plain,
( ~ spl0_51
| ~ spl0_52
| ~ spl0_58 ),
inference(avatar_contradiction_clause,[],[f1828]) ).
fof(f1845,plain,
( sk_c12 != multiply(sk_c4,sk_c11)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f556,f535]) ).
fof(f1872,plain,
( sk_c12 != multiply(sk_c4,sk_c12)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1845,f535]) ).
fof(f1885,plain,
( $false
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1872,f1329]) ).
fof(f1886,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1885]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f148]) ).
cnf(s8,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f187]) ).
cnf(s9,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f192]) ).
cnf(s10,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f197]) ).
cnf(s11,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f202]) ).
cnf(s18,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s19,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s20,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s21,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f216]) ).
cnf(s28,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f227]) ).
cnf(s29,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f228]) ).
cnf(s30,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s31,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s38,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f241]) ).
cnf(s39,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f242]) ).
cnf(s40,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s41,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f244]) ).
cnf(s48,plain,
( spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f255]) ).
cnf(s49,plain,
( spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f256]) ).
cnf(s50,plain,
( spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s51,plain,
( spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f258]) ).
cnf(s56,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f263]) ).
cnf(s57,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f264]) ).
cnf(s58,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f265]) ).
cnf(s59,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f266]) ).
cnf(s60,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f267]) ).
cnf(s61,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f268]) ).
cnf(s62,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f443]) ).
cnf(s68,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f539]) ).
cnf(s72,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_25 ),
inference(sat_conversion,[],[f550]) ).
cnf(s74,plain,
( ~ spl0_5
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f568]) ).
cnf(s80,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f621]) ).
cnf(s82,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_25 ),
inference(sat_conversion,[],[f623]) ).
cnf(s85,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_25
| ~ spl0_36 ),
inference(sat_conversion,[],[f655]) ).
cnf(s88,plain,
( ~ spl0_2
| ~ spl0_20
| ~ spl0_21
| ~ spl0_38 ),
inference(sat_conversion,[],[f668]) ).
cnf(s98,plain,
( ~ spl0_17
| ~ spl0_25
| spl0_36
| ~ spl0_38 ),
inference(sat_conversion,[],[f888]) ).
cnf(s119,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_25 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s124,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| spl0_38 ),
inference(sat_conversion,[],[f1212]) ).
cnf(s125,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| spl0_49 ),
inference(sat_conversion,[],[f1213]) ).
cnf(s146,plain,
( ~ spl0_6
| ~ spl0_25
| spl0_38
| ~ spl0_52 ),
inference(sat_conversion,[],[f1322]) ).
cnf(s158,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49 ),
inference(sat_conversion,[],[f1384]) ).
cnf(s176,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| spl0_52 ),
inference(sat_conversion,[],[f1458]) ).
cnf(s184,plain,
( ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_51
| ~ spl0_52 ),
inference(sat_conversion,[],[f1476]) ).
cnf(s185,plain,
( ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| spl0_52 ),
inference(sat_conversion,[],[f1478]) ).
cnf(s204,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| spl0_51
| ~ spl0_52 ),
inference(sat_conversion,[],[f1552]) ).
cnf(s244,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_25
| ~ spl0_49
| spl0_51
| ~ spl0_52 ),
inference(sat_conversion,[],[f1606]) ).
cnf(s266,plain,
( ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| spl0_58 ),
inference(sat_conversion,[],[f1682]) ).
cnf(s271,plain,
( ~ spl0_1
| ~ spl0_25
| spl0_51
| ~ spl0_52
| ~ spl0_58 ),
inference(sat_conversion,[],[f1713]) ).
cnf(s290,plain,
( ~ spl0_51
| ~ spl0_52
| ~ spl0_58 ),
inference(sat_conversion,[],[f1829]) ).
cnf(s305,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| ~ spl0_36 ),
inference(sat_conversion,[],[f1886]) ).
cnf(s308,plain,
spl0_6,
inference(rat,[],[s62,s56,s57,s58,s59,s60,s61]) ).
cnf(s310,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_52
| ~ spl0_5 ),
inference(rat,[],[s305,s98,s146,s72,s308]) ).
cnf(s311,plain,
( spl0_17
| ~ spl0_5 ),
inference(rat,[],[s74,s41,s51]) ).
cnf(s312,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s74,s40,s50]) ).
cnf(s313,plain,
( spl0_15
| ~ spl0_5 ),
inference(rat,[],[s74,s39,s49]) ).
cnf(s314,plain,
( spl0_14
| ~ spl0_5 ),
inference(rat,[],[s74,s38,s48]) ).
cnf(s315,plain,
( ~ spl0_14
| ~ spl0_5
| ~ spl0_17
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s176,s72,s310,s308]) ).
cnf(s316,plain,
~ spl0_5,
inference(rat,[],[s315,s314,s313,s312,s311]) ).
cnf(s317,plain,
( spl0_25
| ~ spl0_16
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s119,s11,s21,s31,s72,s308]) ).
cnf(s318,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s317,s82]) ).
cnf(s319,plain,
( spl0_16
| ~ spl0_4 ),
inference(rat,[],[s80,s10,s20,s30]) ).
cnf(s320,plain,
( spl0_15
| ~ spl0_4 ),
inference(rat,[],[s80,s9,s19,s29]) ).
cnf(s321,plain,
( ~ spl0_15
| ~ spl0_4
| ~ spl0_16 ),
inference(rat,[],[s80,s8,s18,s28,s318]) ).
cnf(s322,plain,
~ spl0_4,
inference(rat,[],[s321,s320,s319]) ).
cnf(s323,plain,
( ~ spl0_25
| ~ spl0_19
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21
| ~ spl0_8 ),
inference(rat,[],[s125,s158]) ).
cnf(s325,plain,
( spl0_16
| ~ spl0_3 ),
inference(rat,[],[s119,s323,s10,s20,s30,s40,s50]) ).
cnf(s326,plain,
( ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s119,s323,s11,s21,s31,s41,s51,s68]) ).
cnf(s327,plain,
~ spl0_3,
inference(rat,[],[s326,s325]) ).
cnf(s328,plain,
( ~ spl0_17
| spl0_36
| ~ spl0_25
| ~ spl0_16 ),
inference(rat,[],[s146,s176,s98,s308]) ).
cnf(s329,plain,
( ~ spl0_25
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s11,s124,s88,s31,s41,s51,s328,s85,s308]) ).
cnf(s330,plain,
( spl0_15
| spl0_25 ),
inference(rat,[],[s119,s9,s19,s29]) ).
cnf(s331,plain,
( ~ spl0_15
| spl0_25
| ~ spl0_16 ),
inference(rat,[],[s119,s8,s18,s28,s317]) ).
cnf(s332,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s331,s330,s329]) ).
cnf(s333,plain,
~ spl0_2,
inference(rat,[],[s124,s119,s88,s10,s20,s30,s40,s50,s332,s308]) ).
cnf(s334,plain,
spl0_1,
inference(rat,[],[s1,s308,s316,s322,s327,s333]) ).
cnf(s335,plain,
( ~ spl0_17
| ~ spl0_14
| ~ spl0_25
| ~ spl0_16 ),
inference(rat,[],[s271,s290,s176,s266,s334]) ).
cnf(s336,plain,
( ~ spl0_49
| ~ spl0_52
| ~ spl0_20
| ~ spl0_21
| ~ spl0_8
| ~ spl0_19
| ~ spl0_25 ),
inference(rat,[],[s184,s244,s334]) ).
cnf(s337,plain,
( spl0_17
| ~ spl0_25 ),
inference(rat,[],[s336,s185,s125,s11,s31,s41,s51]) ).
cnf(s338,plain,
( ~ spl0_52
| ~ spl0_25
| ~ spl0_20
| ~ spl0_21
| ~ spl0_8
| ~ spl0_19 ),
inference(rat,[],[s204,s184,s334]) ).
cnf(s339,plain,
( ~ spl0_17
| ~ spl0_25
| ~ spl0_16 ),
inference(rat,[],[s338,s8,s28,s38,s48,s176,s335]) ).
cnf(s340,plain,
( ~ spl0_25
| ~ spl0_16 ),
inference(rat,[],[s339,s337]) ).
cnf(s341,plain,
~ spl0_16,
inference(rat,[],[s331,s330,s340]) ).
cnf(s342,plain,
spl0_21,
inference(rat,[],[s50,s341]) ).
cnf(s343,plain,
spl0_20,
inference(rat,[],[s40,s341]) ).
cnf(s344,plain,
spl0_19,
inference(rat,[],[s30,s341]) ).
cnf(s345,plain,
spl0_18,
inference(rat,[],[s20,s341]) ).
cnf(s346,plain,
spl0_8,
inference(rat,[],[s10,s341]) ).
cnf(s347,plain,
spl0_25,
inference(rat,[],[s119,s344,s346,s345]) ).
cnf(s350,plain,
~ spl0_52,
inference(rat,[],[s338,s344,s346,s342,s343,s347]) ).
cnf(s352,plain,
$false,
inference(rat,[],[s185,s344,s343,s342,s347,s350]) ).
fof(f1891,plain,
$false,
inference(avatar_sat_refutation,[],[s352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:49:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.32/1.32 % (3258483)Input is clausal, will run a generic CNF schedule.
% 3.32/1.32 % (3258492)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=765615882:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.32/1.32 % (3258492)Instruction limit reached!
% 3.32/1.32 % (3258492)------------------------------
% 3.32/1.32 % (3258492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.32 % (3258492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.32 % (3258492)CaDiCaL version: 2.1.3
% 3.32/1.32 % (3258492)Termination reason: Instruction limit
% 3.32/1.32 % (3258492)Termination phase: Saturation
% 3.32/1.32 % (3258492)Time elapsed: 0.036 s
% 3.32/1.32 % (3258492)Peak memory usage: 89 MB
% 3.32/1.32 % (3258492)Instructions burned: 117 (million)
% 3.32/1.32 % (3258491)lrs+10_1_sil=8000:sp=occurrence:random_seed=3208115016:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.32/1.32 % (3258494)dis-21_1_sil=8000:lcm=predicate:random_seed=2935485281: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)
% 3.32/1.32 % (3258490)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1126895729:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.32/1.32 % (3258488)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=2934988333:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.32/1.32 % (3258489)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=198209307:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.32/1.32 % (3258493)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1296431571:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.32/1.32 % (3258494)Refutation not found, incomplete strategy
% 3.32/1.32 % (3258494)------------------------------
% 3.32/1.32 % (3258494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.32 % (3258494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.32 % (3258494)CaDiCaL version: 2.1.3
% 3.32/1.32 % (3258494)Termination reason: Refutation not found, incomplete strategy
% 3.32/1.32 % (3258494)Time elapsed: 0.002 s
% 3.32/1.32 % (3258494)Peak memory usage: 88 MB
% 3.32/1.32 % (3258494)Instructions burned: 3 (million)
% 3.32/1.32 % (3258491)Refutation not found, incomplete strategy
% 3.32/1.32 % (3258491)------------------------------
% 3.32/1.32 % (3258491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.32 % (3258491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.32 % (3258491)CaDiCaL version: 2.1.3
% 3.32/1.32 % (3258491)Termination reason: Refutation not found, incomplete strategy
% 3.32/1.32 % (3258491)Time elapsed: 0.004 s
% 3.32/1.32 % (3258491)Peak memory usage: 88 MB
% 3.32/1.32 % (3258491)Instructions burned: 6 (million)
% 3.32/1.32 % (3258493)First to succeed.
% 3.32/1.32 % (3258493)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3258483"
% 3.32/1.32 % (3258496)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=365609960:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.32/1.32 % (3258496)Refutation not found, incomplete strategy
% 3.32/1.32 % (3258496)------------------------------
% 3.32/1.32 % (3258496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.32 % (3258496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.32 % (3258496)CaDiCaL version: 2.1.3
% 3.32/1.32 % (3258496)Termination reason: Refutation not found, incomplete strategy
% 3.32/1.32 % (3258496)Time elapsed: 0.002 s
% 3.32/1.32 % (3258496)Peak memory usage: 88 MB
% 3.32/1.32 % (3258496)Instructions burned: 6 (million)
% 3.32/1.32 % (3258491)------------------------------
% 3.32/1.32 % (3258491)------------------------------
% 3.32/1.32 % (3258494)------------------------------
% 3.32/1.32 % (3258494)------------------------------
% 3.32/1.32 % (3258496)------------------------------
% 3.32/1.32 % (3258496)------------------------------
% 3.32/1.32 % (3258493)Refutation found. Thanks to Tanya!
% 3.32/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.32/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.54 % (3258493)------------------------------
% 3.95/1.54 % (3258493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.54 % (3258493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.54 % (3258493)CaDiCaL version: 2.1.3
% 3.95/1.54 % (3258493)Termination reason: Refutation
% 3.95/1.54 % (3258493)Time elapsed: 0.038 s
% 3.95/1.54 % (3258493)Peak memory usage: 90 MB
% 3.95/1.54 % (3258493)Instructions burned: 61 (million)
% 3.95/1.54 % (3258493)------------------------------
% 3.95/1.54 % (3258493)------------------------------
% 3.95/1.54 % (3258483)Success in time 0.467 s
% 3.95/1.54 % Vampire exiting
%------------------------------------------------------------------------------