%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP314-1 : 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 : n001.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 0.73s 0.99s
% Output : Refutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 42
% Syntax : Number of formulae : 286 ( 23 unt; 21 def)
% Number of atoms : 910 ( 245 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1212 ( 588 ~; 603 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 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_c7,sk_c8) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f16]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f30,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f67,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,definition,
( spl0_5
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f70,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f73,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f55,f72,f69,f66,f63,f60,f57]) ).
fof(f77,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f83,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f53,f81,f77]) ).
fof(f86,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f88,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f51,f81,f86]) ).
fof(f91,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f93,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f49,f81,f91]) ).
fof(f96,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f98,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f47,f81,f96]) ).
fof(f101,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f103,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f45,f101,f77]) ).
fof(f105,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f43,f101,f86]) ).
fof(f106,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f41,f101,f91]) ).
fof(f107,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f39,f101,f96]) ).
fof(f109,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f115,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f31,f109,f96]) ).
fof(f117,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f119,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f123,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f23,f117,f96]) ).
fof(f125,definition,
( spl0_15
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f127,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f125,f77]) ).
fof(f130,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f17,f125,f91]) ).
fof(f131,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f15,f125,f96]) ).
fof(f133,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f135,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f13,f133,f77]) ).
fof(f138,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f9,f133,f91]) ).
fof(f139,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f7,f133,f96]) ).
fof(f140,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f72]) ).
fof(f148,plain,
( sk_c8 != sk_c6
| sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f61,f119]) ).
fof(f149,plain,
( sk_c7 != sk_c8
| sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f148,f111]) ).
fof(f151,definition,
( spl0_17
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f152,plain,
( sk_c8 = sk_c6
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( sk_c8 != sk_c6
| spl0_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl0_18
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f156,plain,
( sk_c7 = sk_c8
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( sk_c7 != sk_c8
| spl0_18 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f149,f117,f109,f60,f155,f151]) ).
fof(f161,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f127]) ).
fof(f162,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f98]) ).
fof(f166,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f61,f3]) ).
fof(f168,definition,
( spl0_19
<=> sk_c8 = inverse(inverse(sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f170,plain,
( sk_c8 != inverse(inverse(sk_c7))
| spl0_19 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f172,definition,
( spl0_20
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f173,plain,
( identity = sk_c8
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f174,plain,
( identity != sk_c8
| spl0_20 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( ~ spl0_19
| ~ spl0_20
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f166,f60,f172,f168]) ).
fof(f178,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f179,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_6 ),
inference(superposition,[],[f4,f73]) ).
fof(f180,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f161]) ).
fof(f184,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f103]) ).
fof(f186,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c1,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f180,f1]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f178,f1]) ).
fof(f203,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f186,f135]) ).
fof(f295,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f187,f203]) ).
fof(f301,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f187,f79]) ).
fof(f305,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_12 ),
inference(superposition,[],[f187,f103]) ).
fof(f311,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f83]) ).
fof(f315,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f301,f88]) ).
fof(f319,plain,
( identity = sk_c7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f295,f3]) ).
fof(f326,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f311,f73]) ).
fof(f330,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f187,f311]) ).
fof(f332,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f330,f3]) ).
fof(f338,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f332,f101,f81,f172]) ).
fof(f339,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_20 ),
inference(superposition,[],[f1,f173]) ).
fof(f341,plain,
( sk_c7 = sk_c8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_20 ),
inference(superposition,[],[f319,f173]) ).
fof(f346,plain,
( $false
| ~ spl0_15
| ~ spl0_16
| spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f341,f157]) ).
fof(f347,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f350,plain,
( sk_c7 != sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_17 ),
inference(superposition,[],[f153,f326]) ).
fof(f352,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f187,f93]) ).
fof(f354,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f352,f98]) ).
fof(f355,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c4,sk_c8)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f70,f98]) ).
fof(f358,plain,
( sk_c7 != sk_c8
| sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f70,f83]) ).
fof(f359,plain,
( sk_c7 != multiply(sk_c4,sk_c8)
| ~ spl0_5
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f355]) ).
fof(f384,plain,
( identity = sk_c4
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f162,f339]) ).
fof(f387,plain,
( sk_c8 = sk_c4
| ~ spl0_11
| ~ spl0_20 ),
inference(forward_demodulation,[],[f384,f173]) ).
fof(f389,plain,
( sk_c7 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(forward_demodulation,[],[f354,f339]) ).
fof(f392,plain,
( ~ spl0_18
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f350,f151,f101,f81,f72,f155]) ).
fof(f394,definition,
( spl0_22
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f396,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| spl0_22 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f397,plain,
( ~ spl0_22
| ~ spl0_18
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f358,f81,f69,f155,f394]) ).
fof(f408,plain,
( spl0_18
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f389,f172,f96,f91,f155]) ).
fof(f411,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f73,f156]) ).
fof(f418,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f359,f156]) ).
fof(f419,plain,
( sk_c7 != sk_c8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f418,f93]) ).
fof(f423,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f419,f156]) ).
fof(f424,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f426,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c7) )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f64,f156]) ).
fof(f427,plain,
( sk_c7 != sk_c8
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f426,f98]) ).
fof(f430,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f426,f83]) ).
fof(f431,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f430]) ).
fof(f434,plain,
( sk_c7 != sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_demodulation,[],[f431,f103]) ).
fof(f436,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f427,f156]) ).
fof(f437,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f434,f156]) ).
fof(f438,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f437]) ).
fof(f441,plain,
( sk_c7 != sk_c8
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f436,f93]) ).
fof(f442,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f441,f156]) ).
fof(f443,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f444,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f58,f326]) ).
fof(f445,plain,
( sk_c7 = sk_c4
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f387,f156]) ).
fof(f449,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f444,f83]) ).
fof(f450,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f449]) ).
fof(f453,plain,
( sk_c7 != sk_c8
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f450,f103]) ).
fof(f456,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f453,f156]) ).
fof(f457,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f463,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f67,f326]) ).
fof(f468,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f463,f83]) ).
fof(f469,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f468]) ).
fof(f472,plain,
( sk_c7 != sk_c8
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f469,f103]) ).
fof(f475,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f472,f156]) ).
fof(f476,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f486,plain,
( sk_c7 = sk_c6
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f152,f156]) ).
fof(f494,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f98,f445]) ).
fof(f495,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f494,f156]) ).
fof(f499,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f58,f486]) ).
fof(f500,plain,
( sk_c7 != sk_c8
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f499,f98]) ).
fof(f506,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f500,f156]) ).
fof(f509,plain,
( sk_c7 != sk_c8
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f506,f93]) ).
fof(f510,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f509,f156]) ).
fof(f511,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f512,plain,
( sk_c7 != sk_c6
| spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f153,f156]) ).
fof(f525,plain,
( sk_c7 != sk_c8
| sk_c6 != multiply(sk_c4,sk_c7)
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f67,f98]) ).
fof(f535,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_18
| spl0_22 ),
inference(forward_demodulation,[],[f396,f156]) ).
fof(f536,plain,
( sk_c7 != sk_c8
| ~ spl0_12
| ~ spl0_18
| spl0_22 ),
inference(forward_demodulation,[],[f535,f103]) ).
fof(f537,plain,
( $false
| ~ spl0_12
| ~ spl0_18
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f536,f156]) ).
fof(f538,plain,
( ~ spl0_12
| ~ spl0_18
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f540,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_11
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f170,f495]) ).
fof(f546,plain,
( sk_c7 != sk_c8
| ~ spl0_11
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f540,f495]) ).
fof(f548,plain,
( $false
| ~ spl0_11
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f546,f156]) ).
fof(f549,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f562,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f187,f411]) ).
fof(f564,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f562,f495]) ).
fof(f587,plain,
( multiply(sk_c3,sk_c7) = multiply(sk_c8,sk_c6)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f184,f564]) ).
fof(f589,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f187,f564]) ).
fof(f591,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f589,f3]) ).
fof(f593,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f587,f339]) ).
fof(f595,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f591,f173]) ).
fof(f596,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f593,f103]) ).
fof(f598,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f595,f156]) ).
fof(f599,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f596,f156]) ).
fof(f601,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f598,f512]) ).
fof(f602,plain,
( ~ spl0_6
| ~ spl0_11
| spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f603,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f599,f512]) ).
fof(f604,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f617,plain,
( identity != sk_c7
| ~ spl0_18
| spl0_20 ),
inference(forward_demodulation,[],[f174,f156]) ).
fof(f619,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f354,f156]) ).
fof(f675,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f187,f619]) ).
fof(f677,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f675,f3]) ).
fof(f685,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f677,f617]) ).
fof(f686,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f685]) ).
fof(f697,plain,
( sk_c8 != sk_c6
| sk_c7 != sk_c8
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f525,f93]) ).
fof(f698,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f697,f96,f91,f66,f151,f155]) ).
fof(f714,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c8)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f179,f354]) ).
fof(f717,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f714,f315]) ).
fof(f731,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f187,f717]) ).
fof(f733,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f731,f3]) ).
fof(f735,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f733,f174]) ).
fof(f736,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f735]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f75]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f94]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s6,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s7,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s8,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s9,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s13,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f123]) ).
cnf(s18,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f128]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f130]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f131]) ).
cnf(s22,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f136]) ).
cnf(s24,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f138]) ).
cnf(s25,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f139]) ).
cnf(s26,plain,
spl0_6,
inference(sat_conversion,[],[f140]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f158]) ).
cnf(s30,plain,
( ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f175]) ).
cnf(s33,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f338]) ).
cnf(s35,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f347]) ).
cnf(s37,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f392]) ).
cnf(s38,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f397]) ).
cnf(s41,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f408]) ).
cnf(s43,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(sat_conversion,[],[f424]) ).
cnf(s44,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f438]) ).
cnf(s46,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(sat_conversion,[],[f443]) ).
cnf(s47,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f457]) ).
cnf(s50,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f476]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f511]) ).
cnf(s57,plain,
( ~ spl0_12
| ~ spl0_18
| spl0_22 ),
inference(sat_conversion,[],[f538]) ).
cnf(s58,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f549]) ).
cnf(s59,plain,
( ~ spl0_6
| ~ spl0_11
| spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f602]) ).
cnf(s60,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f604]) ).
cnf(s68,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f686]) ).
cnf(s71,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f698]) ).
cnf(s73,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f736]) ).
cnf(s74,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1,s26]) ).
cnf(s75,plain,
( spl0_7
| ~ spl0_5 ),
inference(rat,[],[s38,s57,s35,s33,s2,s6,s18,s22]) ).
cnf(s76,plain,
( ~ spl0_18
| ~ spl0_12
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s38,s57]) ).
cnf(s77,plain,
( spl0_16
| spl0_18
| ~ spl0_20 ),
inference(rat,[],[s41,s24,s25]) ).
cnf(s78,plain,
( ~ spl0_16
| ~ spl0_20
| spl0_18 ),
inference(rat,[],[s41,s20,s21,s35]) ).
cnf(s79,plain,
( spl0_18
| ~ spl0_20 ),
inference(rat,[],[s78,s77]) ).
cnf(s80,plain,
( ~ spl0_12
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s79,s76,s33]) ).
cnf(s81,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s79,s73,s43,s7,s8,s9,s75,s26]) ).
cnf(s82,plain,
~ spl0_5,
inference(rat,[],[s79,s73,s43,s3,s4,s5,s80,s81,s75,s26]) ).
cnf(s83,plain,
( spl0_12
| ~ spl0_20
| ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s71,s59,s8,s9,s26]) ).
cnf(s84,plain,
( ~ spl0_20
| ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s71,s60,s4,s5,s50,s83,s26]) ).
cnf(s85,plain,
( spl0_12
| spl0_20
| ~ spl0_18 ),
inference(rat,[],[s68,s8,s9]) ).
cnf(s86,plain,
( ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s68,s4,s5,s50,s85,s84,s26]) ).
cnf(s87,plain,
( spl0_12
| spl0_20 ),
inference(rat,[],[s73,s6,s7,s8,s9,s26]) ).
cnf(s88,plain,
( ~ spl0_12
| spl0_20 ),
inference(rat,[],[s73,s2,s3,s4,s5,s33,s26]) ).
cnf(s89,plain,
spl0_20,
inference(rat,[],[s88,s87]) ).
cnf(s90,plain,
spl0_18,
inference(rat,[],[s79,s89]) ).
cnf(s91,plain,
~ spl0_4,
inference(rat,[],[s86,s90]) ).
cnf(s92,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s46,s8,s9,s90]) ).
cnf(s93,plain,
( ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s46,s4,s5,s44,s90]) ).
cnf(s94,plain,
~ spl0_3,
inference(rat,[],[s93,s92]) ).
cnf(s95,plain,
~ spl0_2,
inference(rat,[],[s37,s28,s5,s9,s13,s17,s58,s30,s26,s90,s89]) ).
cnf(s96,plain,
spl0_1,
inference(rat,[],[s74,s82,s91,s94,s95]) ).
cnf(s97,plain,
spl0_12,
inference(rat,[],[s54,s59,s8,s9,s96,s90,s26,s89]) ).
cnf(s99,plain,
~ spl0_8,
inference(rat,[],[s47,s90,s96,s26,s97]) ).
cnf(s100,plain,
spl0_11,
inference(rat,[],[s5,s99]) ).
cnf(s101,plain,
spl0_10,
inference(rat,[],[s4,s99]) ).
cnf(s104,plain,
spl0_17,
inference(rat,[],[s60,s89,s90,s97,s26,s100]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s54,s90,s96,s100,s104,s101]) ).
fof(f737,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP314-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n001.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 09:55:30 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.73/0.99 % (3314408)Input is clausal, will run a generic CNF schedule.
% 0.73/0.99 % (3314418)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=99401941:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.73/0.99 % (3314414)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3126785333:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.73/0.99 % (3314417)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2159912687:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.73/0.99 % (3314416)lrs+10_1_sil=8000:sp=occurrence:random_seed=908955819:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.73/0.99 % (3314413)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=4123673017:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.73/0.99 % (3314415)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1905087016:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.73/0.99 % (3314419)dis-21_1_sil=8000:lcm=predicate:random_seed=2940379259: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)
% 0.73/0.99 % (3314419)Refutation not found, incomplete strategy
% 0.73/0.99 % (3314419)------------------------------
% 0.73/0.99 % (3314419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.99 % (3314419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.99 % (3314419)CaDiCaL version: 2.1.3
% 0.73/0.99 % (3314419)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.99 % (3314419)Time elapsed: 0.002 s
% 0.73/0.99 % (3314419)Peak memory usage: 88 MB
% 0.73/0.99 % (3314419)Instructions burned: 1 (million)
% 0.73/0.99 % (3314418)First to succeed.
% 0.73/0.99 % (3314418)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3314408"
% 0.73/0.99 % (3314416)Instruction limit reached!
% 0.73/0.99 % (3314416)------------------------------
% 0.73/0.99 % (3314416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.99 % (3314416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.99 % (3314416)CaDiCaL version: 2.1.3
% 0.73/0.99 % (3314416)Termination reason: Instruction limit
% 0.73/0.99 % (3314416)Termination phase: Saturation
% 0.73/0.99 % (3314416)Time elapsed: 0.052 s
% 0.73/0.99 % (3314416)Peak memory usage: 89 MB
% 0.73/0.99 % (3314416)Instructions burned: 108 (million)
% 0.73/0.99 % (3314417)Instruction limit reached!
% 0.73/0.99 % (3314417)------------------------------
% 0.73/0.99 % (3314417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.99 % (3314417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.99 % (3314417)CaDiCaL version: 2.1.3
% 0.73/0.99 % (3314417)Termination reason: Instruction limit
% 0.73/0.99 % (3314417)Termination phase: Saturation
% 0.73/0.99 % (3314417)Time elapsed: 0.066 s
% 0.73/0.99 % (3314417)Peak memory usage: 89 MB
% 0.73/0.99 % (3314417)Instructions burned: 114 (million)
% 0.73/0.99 % (3314427)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=2708277438:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.73/0.99 % (3314428)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1602714669:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.73/0.99 % (3314419)------------------------------
% 0.73/0.99 % (3314419)------------------------------
% 0.73/0.99 % (3314427)Instruction limit reached!
% 0.73/0.99 % (3314427)------------------------------
% 0.73/0.99 % (3314427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.99 % (3314427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.99 % (3314427)CaDiCaL version: 2.1.3
% 0.73/0.99 % (3314427)Termination reason: Instruction limit
% 0.73/0.99 % (3314427)Termination phase: Saturation
% 0.73/0.99 % (3314427)Time elapsed: 0.070 s
% 0.73/0.99 % (3314427)Peak memory usage: 90 MB
% 0.73/0.99 % (3314427)Instructions burned: 143 (million)
% 0.73/0.99 % (3314418)Refutation found. Thanks to Tanya!
% 0.73/0.99 % SZS status Unsatisfiable for theBenchmark
% 0.73/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 3.21/1.19 % (3314418)------------------------------
% 3.21/1.19 % (3314418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.19 % (3314418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.19 % (3314418)CaDiCaL version: 2.1.3
% 3.21/1.19 % (3314418)Termination reason: Refutation
% 3.21/1.19 % (3314418)Time elapsed: 0.017 s
% 3.21/1.19 % (3314418)Peak memory usage: 89 MB
% 3.21/1.19 % (3314418)Instructions burned: 26 (million)
% 3.21/1.19 % (3314418)------------------------------
% 3.21/1.19 % (3314418)------------------------------
% 3.21/1.19 % (3314408)Success in time 0.403 s
% 3.21/1.19 % Vampire exiting
%------------------------------------------------------------------------------