%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP281-1 : 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 : n003.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 10:13:31 AM UTC 2026
% Result : Unsatisfiable 2.76s 1.30s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 48
% Syntax : Number of formulae : 294 ( 18 unt; 16 def)
% Number of atoms : 891 ( 280 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1125 ( 528 ~; 581 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,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_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,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_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c7,sk_c8) = 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_c7,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c7,sk_c8) = 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_c7,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| 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_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c7,sk_c8)
| 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_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c8,sk_c7) != 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_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ 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_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = inverse(sk_c5)
| ~ 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 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ 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_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c4)
| ~ 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_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c8 = 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_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ 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_c7,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f111]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f76]) ).
fof(f161,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f155]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f106]) ).
fof(f164,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f161,f1]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f168,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f156]) ).
fof(f169,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f168,f1]) ).
fof(f174,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f164,f92]) ).
fof(f177,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f162,f76]) ).
fof(f201,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f165,f156]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f165,f106]) ).
fof(f217,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f208,f111]) ).
fof(f218,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f160,f217]) ).
fof(f221,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f218,f174]) ).
fof(f228,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f165,f221]) ).
fof(f230,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f228,f3]) ).
fof(f236,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f201,f230]) ).
fof(f238,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f236,f3]) ).
fof(f239,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f238,f230]) ).
fof(f244,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f156,f239]) ).
fof(f247,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f244,f217]) ).
fof(f248,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f247,f230]) ).
fof(f251,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f87,f248]) ).
fof(f265,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f251,f217]) ).
fof(f269,plain,
( sk_c8 != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f265,f248]) ).
fof(f271,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f177,f239]) ).
fof(f272,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f271,f217]) ).
fof(f273,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f272,f248]) ).
fof(f286,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f165,f273]) ).
fof(f288,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f286,f3]) ).
fof(f290,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f288,f230]) ).
fof(f305,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f269,f290]) ).
fof(f306,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f307,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c8,multiply(X2,sk_c8)) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f80,f248]) ).
fof(f318,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f307,f111]) ).
fof(f319,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f318]) ).
fof(f320,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f319,f169]) ).
fof(f321,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f335,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f165,f117]) ).
fof(f337,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f335,f96]) ).
fof(f342,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f165,f144]) ).
fof(f344,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f342,f135]) ).
fof(f345,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f80,f111]) ).
fof(f348,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f80,f96]) ).
fof(f349,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f348]) ).
fof(f351,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_4
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f345]) ).
fof(f352,plain,
( sk_c7 != multiply(sk_c8,sk_c3)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f349,f117]) ).
fof(f359,definition,
( spl0_17
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f360,plain,
( sk_c8 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f363,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f351,f169]) ).
fof(f364,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f352,f126]) ).
fof(f365,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f367,plain,
( ~ spl0_17
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f363,f109,f79,f359]) ).
fof(f375,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f73,f135]) ).
fof(f378,plain,
( sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f375]) ).
fof(f410,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f126,f337]) ).
fof(f420,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f410,f124,f115,f94,f359]) ).
fof(f422,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f86,f360]) ).
fof(f432,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f378,f360]) ).
fof(f433,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f432,f144]) ).
fof(f436,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f433,f360]) ).
fof(f437,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f438,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f70,f360]) ).
fof(f439,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f438,f360]) ).
fof(f445,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f439,f101]) ).
fof(f453,plain,
( sk_c8 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f445,f360]) ).
fof(f454,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f453,f92]) ).
fof(f455,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f454,f360]) ).
fof(f456,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f457,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c8) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f83,f360]) ).
fof(f468,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f457,f111]) ).
fof(f470,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f457,f135]) ).
fof(f473,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f470]) ).
fof(f474,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f468]) ).
fof(f476,plain,
( sk_c8 != sk_c7
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f473,f144]) ).
fof(f478,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f476,f360]) ).
fof(f479,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f481,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f77,f360]) ).
fof(f484,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f422,f481]) ).
fof(f485,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f495,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f76,f360]) ).
fof(f503,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f439,f135]) ).
fof(f506,plain,
( sk_c8 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f503]) ).
fof(f512,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f344,f360]) ).
fof(f517,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f512,f495]) ).
fof(f624,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f506,f517]) ).
fof(f638,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f624,f144]) ).
fof(f653,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f638,f360]) ).
fof(f654,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f653]) ).
fof(f661,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_demodulation,[],[f73,f360]) ).
fof(f673,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f106,f360]) ).
fof(f710,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f661,f111]) ).
fof(f712,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f710]) ).
fof(f714,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f712,f673]) ).
fof(f715,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f714]) ).
fof(f722,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f474,f673]) ).
fof(f723,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f722]) ).
fof(f728,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f248,f109,f104,f99,f90,f75,f359]) ).
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,[],[f306]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f321]) ).
cnf(s36,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f365]) ).
cnf(s37,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f367]) ).
cnf(s41,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f420]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f437]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(sat_conversion,[],[f456]) ).
cnf(s45,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f479]) ).
cnf(s46,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(sat_conversion,[],[f485]) ).
cnf(s58,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f654]) ).
cnf(s60,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f715]) ).
cnf(s63,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f723]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f728]) ).
cnf(s68,plain,
spl0_3,
inference(rat,[],[s41,s46,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,[],[s66,s63,s68]) ).
cnf(s71,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s41,s45,s10,s15,s20,s25]) ).
cnf(s72,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s41,s45,s9,s14,s19,s24]) ).
cnf(s73,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s41,s8,s13,s63,s70,s72,s71]) ).
cnf(s74,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s70,s3,s4,s5,s73]) ).
cnf(s75,plain,
~ spl0_5,
inference(rat,[],[s41,s45,s2,s7,s12,s17,s22,s74]) ).
cnf(s76,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s36,s5,s10,s15]) ).
cnf(s77,plain,
( spl0_10
| spl0_17 ),
inference(rat,[],[s41,s4,s9,s14]) ).
cnf(s78,plain,
( spl0_9
| spl0_17 ),
inference(rat,[],[s41,s3,s8,s13]) ).
cnf(s79,plain,
( ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s41,s2,s7,s12,s33,s78,s77,s37,s68]) ).
cnf(s80,plain,
~ spl0_4,
inference(rat,[],[s79,s76]) ).
cnf(s82,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s41,s43,s5,s10,s15,s20,s25]) ).
cnf(s83,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s43,s77,s19,s24]) ).
cnf(s84,plain,
( spl0_17
| ~ spl0_11
| ~ spl0_10
| ~ spl0_9 ),
inference(rat,[],[s41,s2,s7,s12,s66,s68]) ).
cnf(s85,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s84,s78,s60]) ).
cnf(s86,plain,
~ spl0_2,
inference(rat,[],[s85,s83,s82]) ).
cnf(s87,plain,
spl0_1,
inference(rat,[],[s1,s69,s75,s68,s80,s86]) ).
cnf(s88,plain,
( ~ spl0_17
| ~ spl0_9 ),
inference(rat,[],[s58,s17,s22,s44,s87,s68]) ).
cnf(s89,plain,
( spl0_11
| spl0_17 ),
inference(rat,[],[s41,s5,s10,s15]) ).
cnf(s90,plain,
~ spl0_9,
inference(rat,[],[s84,s77,s89,s88]) ).
cnf(s91,plain,
spl0_15,
inference(rat,[],[s23,s90]) ).
cnf(s92,plain,
spl0_14,
inference(rat,[],[s18,s90]) ).
cnf(s96,plain,
spl0_17,
inference(rat,[],[s78,s90]) ).
cnf(s97,plain,
$false,
inference(rat,[],[s58,s87,s68,s96,s91,s92]) ).
fof(f731,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP281-1 : 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 : n003.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
% 0.11/0.38 % DateTime : Sun Sep 27 09:45:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.76/1.30 % (258674)Input is clausal, will run a generic CNF schedule.
% 2.76/1.30 % (258685)dis-21_1_sil=8000:lcm=predicate:random_seed=1742131904: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)
% 2.76/1.30 % (258685)Refutation not found, incomplete strategy
% 2.76/1.30 % (258685)------------------------------
% 2.76/1.30 % (258685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.30 % (258685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.30 % (258685)CaDiCaL version: 2.1.3
% 2.76/1.30 % (258685)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.30 % (258685)Time elapsed: 0.001 s
% 2.76/1.30 % (258685)Peak memory usage: 88 MB
% 2.76/1.30 % (258685)Instructions burned: 2 (million)
% 2.76/1.30 % (258682)lrs+10_1_sil=8000:sp=occurrence:random_seed=1324242899:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.76/1.30 % (258679)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=4268166496:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.76/1.30 % (258683)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=999263467:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.76/1.30 % (258681)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3087183472:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.76/1.30 % (258680)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1497769872:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.76/1.30 % (258684)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=441533311:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.76/1.30 % (258682)Refutation not found, incomplete strategy
% 2.76/1.30 % (258682)------------------------------
% 2.76/1.30 % (258682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.30 % (258682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.30 % (258682)CaDiCaL version: 2.1.3
% 2.76/1.30 % (258682)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.30 % (258682)Time elapsed: 0.003 s
% 2.76/1.30 % (258682)Peak memory usage: 88 MB
% 2.76/1.30 % (258682)Instructions burned: 3 (million)
% 2.76/1.30 % (258684)First to succeed.
% 2.76/1.30 % (258684)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-258674"
% 2.76/1.30 % (258683)Instruction limit reached!
% 2.76/1.30 % (258683)------------------------------
% 2.76/1.30 % (258683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.30 % (258683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.30 % (258683)CaDiCaL version: 2.1.3
% 2.76/1.30 % (258683)Termination reason: Instruction limit
% 2.76/1.30 % (258683)Termination phase: Saturation
% 2.76/1.30 % (258683)Time elapsed: 0.068 s
% 2.76/1.30 % (258683)Peak memory usage: 89 MB
% 2.76/1.30 % (258683)Instructions burned: 115 (million)
% 2.76/1.30 % (258685)------------------------------
% 2.76/1.30 % (258685)------------------------------
% 2.76/1.30 % (258694)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3451375639: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)
% 2.76/1.30 % (258693)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=874161538:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.76/1.30 % (258694)Refutation not found, incomplete strategy
% 2.76/1.30 % (258694)------------------------------
% 2.76/1.30 % (258694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.30 % (258694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.30 % (258694)CaDiCaL version: 2.1.3
% 2.76/1.30 % (258694)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.30 % (258694)Time elapsed: 0.002 s
% 2.76/1.30 % (258694)Peak memory usage: 88 MB
% 2.76/1.30 % (258694)Instructions burned: 3 (million)
% 2.76/1.30 % (258693)Refutation not found, incomplete strategy
% 2.76/1.30 % (258693)------------------------------
% 2.76/1.30 % (258693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.30 % (258693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.30 % (258693)CaDiCaL version: 2.1.3
% 2.76/1.30 % (258693)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.30 % (258693)Time elapsed: 0.003 s
% 2.76/1.30 % (258693)Peak memory usage: 88 MB
% 2.76/1.30 % (258693)Instructions burned: 3 (million)
% 2.76/1.30 % (258682)------------------------------
% 2.76/1.30 % (258682)------------------------------
% 2.76/1.30 % (258684)Refutation found. Thanks to Tanya!
% 2.76/1.30 % SZS status Unsatisfiable for theBenchmark
% 2.76/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.40 % (258684)------------------------------
% 2.76/1.40 % (258684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.40 % (258684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.40 % (258684)CaDiCaL version: 2.1.3
% 3.76/1.40 % (258684)Termination reason: Refutation
% 3.76/1.40 % (258684)Time elapsed: 0.018 s
% 3.76/1.40 % (258684)Peak memory usage: 89 MB
% 3.76/1.40 % (258684)Instructions burned: 26 (million)
% 3.76/1.40 % (258684)------------------------------
% 3.76/1.40 % (258684)------------------------------
% 3.76/1.40 % (258674)Success in time 0.45 s
% 3.76/1.40 % Vampire exiting
%------------------------------------------------------------------------------