%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP323-1 : 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 : n012.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 10:13:38 AM UTC 2026
% Result : Unsatisfiable 0.44s 0.83s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 50
% Syntax : Number of formulae : 286 ( 25 unt; 18 def)
% Number of atoms : 788 ( 263 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 925 ( 423 ~; 484 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 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
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f75,f72,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f94,f90]) ).
fof(f99,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f94,f99]) ).
fof(f104,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f94,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f113,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f75]) ).
fof(f115,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f115,f90]) ).
fof(f119,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f115,f99]) ).
fof(f120,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f115,f104]) ).
fof(f121,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f115,f109]) ).
fof(f122,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f115,f75]) ).
fof(f124,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f124,f90]) ).
fof(f128,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f124,f99]) ).
fof(f129,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f124,f104]) ).
fof(f130,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f124,f109]) ).
fof(f131,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f124,f75]) ).
fof(f133,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f133,f90]) ).
fof(f137,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f133,f99]) ).
fof(f138,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f133,f104]) ).
fof(f139,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f133,f109]) ).
fof(f142,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f142,f90]) ).
fof(f146,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f142,f99]) ).
fof(f147,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f142,f104]) ).
fof(f148,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f142,f109]) ).
fof(f150,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f90]) ).
fof(f151,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f85,f99]) ).
fof(f152,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f104]) ).
fof(f153,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f109]) ).
fof(f154,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f75]) ).
fof(f155,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f161,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f155]) ).
fof(f164,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f161,f1]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f173,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f164,f101]) ).
fof(f205,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f165,f3]) ).
fof(f206,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f165,f165]) ).
fof(f210,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f165,f76]) ).
fof(f211,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f165,f173]) ).
fof(f214,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f165,f111]) ).
fof(f223,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f214,f106]) ).
fof(f224,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f211,f3]) ).
fof(f227,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f223,f76]) ).
fof(f238,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f210,f227]) ).
fof(f239,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f238,f3]) ).
fof(f241,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f224,f239]) ).
fof(f243,plain,
( sk_c7 = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f241,f227]) ).
fof(f416,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c6) = X0
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f205,f224]) ).
fof(f417,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c8) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f416,f227]) ).
fof(f433,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f417]) ).
fof(f465,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f87,f433]) ).
fof(f479,plain,
( sk_c7 != sk_c8
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f465,f227]) ).
fof(f486,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f479,f243]) ).
fof(f487,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f511,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f165,f117]) ).
fof(f513,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f511,f96]) ).
fof(f521,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f80,f92]) ).
fof(f522,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f80,f96]) ).
fof(f524,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f522]) ).
fof(f525,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f521]) ).
fof(f531,definition,
( spl0_17
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f532,plain,
( sk_c7 = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f535,plain,
( sk_c7 != multiply(sk_c8,sk_c3)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f524,f117]) ).
fof(f536,plain,
( sk_c7 != sk_c8
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f525,f164]) ).
fof(f537,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f535,f126]) ).
fof(f538,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f539,plain,
( ~ spl0_17
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f536,f90,f79,f531]) ).
fof(f544,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f73,f92]) ).
fof(f546,plain,
( sk_c7 != sk_c8
| sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f73,f135]) ).
fof(f548,plain,
( sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f544]) ).
fof(f550,definition,
( spl0_18
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f551,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f552,plain,
( sk_c7 != multiply(sk_c1,sk_c8)
| spl0_18 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f553,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f546,f133,f72,f531,f550]) ).
fof(f555,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f548,f101]) ).
fof(f610,definition,
( spl0_20
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f661,plain,
( sk_c7 = sk_c8
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f126,f513]) ).
fof(f678,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f661,f124,f115,f94,f531]) ).
fof(f679,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f76,f532]) ).
fof(f680,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f86,f532]) ).
fof(f681,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f144,f532]) ).
fof(f693,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_17
| spl0_18 ),
inference(forward_demodulation,[],[f552,f532]) ).
fof(f723,plain,
( $false
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f681,f693]) ).
fof(f724,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f723]) ).
fof(f725,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f551,f532]) ).
fof(f733,plain,
( sk_c8 != sk_c8
| sk_c6 != multiply(sk_c5,sk_c8)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f70,f92]) ).
fof(f734,plain,
( sk_c7 != sk_c8
| sk_c6 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f70,f135]) ).
fof(f737,plain,
( sk_c6 != multiply(sk_c5,sk_c8)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f733]) ).
fof(f739,plain,
( sk_c6 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f734,f532]) ).
fof(f740,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f737,f101]) ).
fof(f741,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f747,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c8)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f83,f532]) ).
fof(f748,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c8) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f747,f532]) ).
fof(f750,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f748,f92]) ).
fof(f751,plain,
( sk_c7 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f748,f135]) ).
fof(f754,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f750]) ).
fof(f756,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f751,f532]) ).
fof(f757,plain,
( sk_c8 != sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f754,f101]) ).
fof(f766,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f165,f725]) ).
fof(f768,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f766,f135]) ).
fof(f769,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f768,f532]) ).
fof(f770,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f756,f725]) ).
fof(f771,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f770]) ).
fof(f776,plain,
( sk_c8 != sk_c6
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f739,f725]) ).
fof(f832,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f679,f769]) ).
fof(f850,plain,
( ~ spl0_20
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f776,f550,f531,f133,f69,f610]) ).
fof(f851,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f832,f550,f531,f133,f75,f610]) ).
fof(f852,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f243,f109,f104,f99,f90,f75,f531]) ).
fof(f853,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f227,f109,f104,f75,f610]) ).
fof(f871,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f555,f532]) ).
fof(f872,plain,
( ~ spl0_20
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f871,f531,f99,f90,f72,f610]) ).
fof(f884,plain,
( ~ spl0_20
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f757,f531,f99,f90,f82,f610]) ).
fof(f886,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f77,f532]) ).
fof(f932,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f680,f886]) ).
fof(f933,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f932]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s22,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f487]) ).
cnf(s35,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f538]) ).
cnf(s36,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(sat_conversion,[],[f539]) ).
cnf(s37,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f553]) ).
cnf(s41,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f678]) ).
cnf(s44,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f724]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f741]) ).
cnf(s48,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f771]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f850]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f851]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f852]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f853]) ).
cnf(s59,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f872]) ).
cnf(s62,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f884]) ).
cnf(s67,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(sat_conversion,[],[f933]) ).
cnf(s68,plain,
spl0_3,
inference(rat,[],[s41,s67,s6,s11,s16,s31]) ).
cnf(s69,plain,
spl0_6,
inference(rat,[],[s32,s27,s28,s29,s30,s68]) ).
cnf(s70,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s62,s56,s57,s68]) ).
cnf(s71,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s48,s44,s41,s10,s15,s20,s25]) ).
cnf(s72,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s48,s44,s41,s9,s14,s19,s24]) ).
cnf(s73,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s48,s44,s41,s8,s13,s18,s23,s70,s72,s71]) ).
cnf(s74,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s70,s3,s4,s5,s73]) ).
cnf(s75,plain,
~ spl0_5,
inference(rat,[],[s48,s44,s41,s2,s7,s12,s17,s22,s74]) ).
cnf(s76,plain,
( spl0_11
| spl0_17 ),
inference(rat,[],[s41,s5,s10,s15]) ).
cnf(s77,plain,
( spl0_10
| spl0_17 ),
inference(rat,[],[s41,s4,s9,s14]) ).
cnf(s78,plain,
( ~ spl0_10
| ~ spl0_7
| spl0_17
| ~ spl0_11 ),
inference(rat,[],[s41,s3,s8,s13,s56,s68]) ).
cnf(s79,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s78,s77,s76,s36]) ).
cnf(s80,plain,
~ spl0_4,
inference(rat,[],[s35,s2,s7,s12,s79]) ).
cnf(s81,plain,
( ~ spl0_17
| ~ spl0_20
| ~ spl0_2
| ~ spl0_7 ),
inference(rat,[],[s37,s44,s18,s23,s59]) ).
cnf(s82,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s81,s78,s57,s68]) ).
cnf(s83,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s37,s44,s76,s20,s25]) ).
cnf(s84,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s37,s44,s77,s19,s24]) ).
cnf(s85,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(rat,[],[s37,s44,s41,s2,s7,s12,s17,s22,s82]) ).
cnf(s86,plain,
~ spl0_2,
inference(rat,[],[s85,s84,s83]) ).
cnf(s87,plain,
spl0_1,
inference(rat,[],[s1,s68,s69,s75,s80,s86]) ).
cnf(s88,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_14 ),
inference(rat,[],[s54,s51,s87,s68]) ).
cnf(s89,plain,
spl0_9,
inference(rat,[],[s88,s44,s41,s3,s8,s13,s18,s23]) ).
cnf(s90,plain,
~ spl0_7,
inference(rat,[],[s45,s87,s89]) ).
cnf(s91,plain,
spl0_15,
inference(rat,[],[s22,s90]) ).
cnf(s92,plain,
spl0_14,
inference(rat,[],[s17,s90]) ).
cnf(s93,plain,
spl0_13,
inference(rat,[],[s12,s90]) ).
cnf(s94,plain,
spl0_12,
inference(rat,[],[s7,s90]) ).
cnf(s95,plain,
spl0_8,
inference(rat,[],[s2,s90]) ).
cnf(s96,plain,
spl0_17,
inference(rat,[],[s41,s94,s93,s95]) ).
cnf(s97,plain,
spl0_18,
inference(rat,[],[s44,s91,s96]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s88,s92,s96,s97]) ).
fof(f934,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP323-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 09:49:50 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.44/0.83 % (2127404)Input is clausal, will run a generic CNF schedule.
% 0.44/0.83 % (2127413)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4120100969:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.44/0.83 % (2127414)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3321529544:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.44/0.83 % (2127415)dis-21_1_sil=8000:lcm=predicate:random_seed=3395048952: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)
% 0.44/0.83 % (2127409)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=2418831652:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.44/0.83 % (2127412)lrs+10_1_sil=8000:sp=occurrence:random_seed=1051815118:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.44/0.83 % (2127410)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3570268373:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.44/0.83 % (2127411)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3472529542:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.44/0.83 % (2127415)Refutation not found, incomplete strategy
% 0.44/0.83 % (2127415)------------------------------
% 0.44/0.83 % (2127415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/0.83 % (2127415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.83 % (2127415)CaDiCaL version: 2.1.3
% 0.44/0.83 % (2127415)Termination reason: Refutation not found, incomplete strategy
% 0.44/0.83 % (2127415)Time elapsed: 0.001 s
% 0.44/0.83 % (2127415)Peak memory usage: 88 MB
% 0.44/0.83 % (2127415)Instructions burned: 2 (million)
% 0.44/0.83 % (2127412)Refutation not found, incomplete strategy
% 0.44/0.83 % (2127412)------------------------------
% 0.44/0.83 % (2127412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/0.83 % (2127412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.83 % (2127412)CaDiCaL version: 2.1.3
% 0.44/0.83 % (2127412)Termination reason: Refutation not found, incomplete strategy
% 0.44/0.83 % (2127412)Time elapsed: 0.002 s
% 0.44/0.83 % (2127412)Peak memory usage: 88 MB
% 0.44/0.83 % (2127412)Instructions burned: 3 (million)
% 0.44/0.83 % (2127414)First to succeed.
% 0.44/0.83 % (2127414)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2127404"
% 0.44/0.83 % (2127413)Instruction limit reached!
% 0.44/0.83 % (2127413)------------------------------
% 0.44/0.83 % (2127413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/0.83 % (2127413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.83 % (2127413)CaDiCaL version: 2.1.3
% 0.44/0.83 % (2127413)Termination reason: Instruction limit
% 0.44/0.83 % (2127413)Termination phase: Saturation
% 0.44/0.83 % (2127413)Time elapsed: 0.037 s
% 0.44/0.83 % (2127413)Peak memory usage: 89 MB
% 0.44/0.83 % (2127413)Instructions burned: 115 (million)
% 0.44/0.83 % (2127412)------------------------------
% 0.44/0.83 % (2127412)------------------------------
% 0.44/0.83 % (2127415)------------------------------
% 0.44/0.83 % (2127415)------------------------------
% 0.44/0.83 % (2127414)Refutation found. Thanks to Tanya!
% 0.44/0.83 % SZS status Unsatisfiable for theBenchmark
% 0.44/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.38/0.93 % (2127414)------------------------------
% 2.38/0.93 % (2127414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/0.93 % (2127414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.93 % (2127414)CaDiCaL version: 2.1.3
% 2.38/0.93 % (2127414)Termination reason: Refutation
% 2.38/0.93 % (2127414)Time elapsed: 0.011 s
% 2.38/0.93 % (2127414)Peak memory usage: 90 MB
% 2.38/0.93 % (2127414)Instructions burned: 32 (million)
% 2.38/0.93 % (2127414)------------------------------
% 2.38/0.93 % (2127414)------------------------------
% 2.38/0.93 % (2127404)Success in time 0.304 s
% 2.38/0.93 % Vampire exiting
%------------------------------------------------------------------------------