%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP365-1 : 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 : n019.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 10:13:45 AM UTC 2026
% Result : Unsatisfiable 2.17s 1.19s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 52
% Syntax : Number of formulae : 332 ( 24 unt; 18 def)
% Number of atoms : 1061 ( 306 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1371 ( 642 ~; 711 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 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 : 45 ( 0 sgn 45 !; 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_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| multiply(X2,sk_c6) != sk_c8
| inverse(X2) != sk_c6
| 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_c6,sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c6)
| sk_c6 != 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,X1,X4] :
( multiply(sk_c6,sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c6)
| sk_c6 != 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_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c8 != multiply(X2,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c6,sk_c8) != sk_c7
| 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_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c6 = inverse(sk_c3)
| ~ 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_c8 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| ~ 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_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( sk_c8 = inverse(sk_c1)
| ~ 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_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ 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(f140,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f133,f75]) ).
fof(f142,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ 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(f149,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f142,f75]) ).
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(f156,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f106]) ).
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(f163,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f101]) ).
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(f209,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f165,f173]) ).
fof(f210,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f165,f76]) ).
fof(f211,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f165,f156]) ).
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(f225,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f209,f3]) ).
fof(f227,plain,
( sk_c6 = sk_c8
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f223,f76]) ).
fof(f231,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f165,f223]) ).
fof(f233,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f231,f3]) ).
fof(f236,plain,
( sk_c6 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f233,f225]) ).
fof(f240,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f210,f227]) ).
fof(f241,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f240,f3]) ).
fof(f242,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f241,f225]) ).
fof(f243,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f227]) ).
fof(f250,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f211,f225]) ).
fof(f251,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f250,f227]) ).
fof(f252,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f251,f3]) ).
fof(f253,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f252,f225]) ).
fof(f254,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f253,f227]) ).
fof(f258,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f106,f254]) ).
fof(f403,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c6) = X0
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f205,f225]) ).
fof(f404,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c8) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f403,f227]) ).
fof(f420,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f404]) ).
fof(f450,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f87,f420]) ).
fof(f464,plain,
( sk_c6 != sk_c8
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f450,f243]) ).
fof(f471,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f464,f227]) ).
fof(f472,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f473,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c8)
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f80,f227]) ).
fof(f475,plain,
( ! [X2] :
( sk_c8 != X2
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f473,f420]) ).
fof(f477,plain,
( ! [X2] :
( sk_c8 != X2
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f475,f227]) ).
fof(f478,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(equality_resolution,[],[f477]) ).
fof(f479,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f478,f258]) ).
fof(f480,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f493,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f86]) ).
fof(f494,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_12 ),
inference(superposition,[],[f165,f117]) ).
fof(f496,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f494,f96]) ).
fof(f497,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f165,f135]) ).
fof(f499,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f497,f126]) ).
fof(f505,plain,
( sk_c6 != sk_c6
| sk_c8 != multiply(sk_c3,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f80,f96]) ).
fof(f507,plain,
( sk_c8 != multiply(sk_c3,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f505]) ).
fof(f513,definition,
( spl0_17
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f514,plain,
( sk_c6 = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f515,plain,
( sk_c6 != sk_c8
| spl0_17 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f517,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f507,f117]) ).
fof(f518,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f528,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f83,f92]) ).
fof(f530,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f83,f126]) ).
fof(f531,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f530]) ).
fof(f532,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f528]) ).
fof(f533,plain,
( sk_c7 != multiply(sk_c8,sk_c2)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f531,f135]) ).
fof(f539,plain,
( sk_c8 != sk_c7
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f532,f164]) ).
fof(f540,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f533,f144]) ).
fof(f541,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f545,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f73,f92]) ).
fof(f549,plain,
( sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f545]) ).
fof(f552,plain,
( sk_c6 != sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f549,f101]) ).
fof(f615,plain,
( sk_c8 != sk_c8
| sk_c6 != multiply(sk_c5,sk_c8)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f70,f92]) ).
fof(f616,plain,
( sk_c8 != sk_c8
| sk_c6 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f70,f126]) ).
fof(f617,plain,
( sk_c6 != sk_c8
| sk_c6 != multiply(sk_c3,sk_c8)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f70,f96]) ).
fof(f618,plain,
( sk_c6 != multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f616]) ).
fof(f619,plain,
( sk_c6 != multiply(sk_c5,sk_c8)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f615]) ).
fof(f622,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f619,f101]) ).
fof(f623,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f622]) ).
fof(f627,definition,
( spl0_20
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f634,definition,
( spl0_21
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f635,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f636,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| spl0_21 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f642,plain,
( sk_c8 = multiply(sk_c3,sk_c8)
| ~ spl0_12
| ~ spl0_17 ),
inference(superposition,[],[f117,f514]) ).
fof(f645,plain,
( sk_c6 != sk_c8
| sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f73,f96]) ).
fof(f647,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f645,f514]) ).
fof(f649,plain,
( ~ spl0_21
| ~ spl0_2
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f647,f513,f94,f72,f634]) ).
fof(f669,plain,
( sk_c8 != sk_c7
| ~ spl0_12
| ~ spl0_17
| spl0_21 ),
inference(superposition,[],[f636,f642]) ).
fof(f700,plain,
( sk_c8 = sk_c7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f499,f144]) ).
fof(f704,plain,
( multiply(sk_c5,sk_c8) = multiply(sk_c6,sk_c2)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f163,f499]) ).
fof(f706,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f165,f499]) ).
fof(f708,plain,
( identity = sk_c2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f706,f3]) ).
fof(f710,plain,
( multiply(sk_c5,sk_c8) = multiply(sk_c8,sk_c2)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f704,f514]) ).
fof(f715,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f700,f669]) ).
fof(f716,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f715]) ).
fof(f717,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f710,f144]) ).
fof(f718,plain,
( sk_c6 = sk_c7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f717,f101]) ).
fof(f719,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f718,f514]) ).
fof(f720,plain,
( $false
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f719,f669]) ).
fof(f721,plain,
( ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f720]) ).
fof(f740,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f496,f86]) ).
fof(f748,plain,
( sk_c6 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f740,f700]) ).
fof(f751,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f748,f515]) ).
fof(f752,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f751]) ).
fof(f756,plain,
( spl0_20
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f236,f109,f104,f99,f90,f627]) ).
fof(f758,plain,
( ~ spl0_20
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f552,f99,f90,f72,f627]) ).
fof(f770,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f227,f109,f104,f75,f513]) ).
fof(f779,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f780,plain,
( sk_c2 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f779,f708]) ).
fof(f812,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f243,f539]) ).
fof(f813,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f812]) ).
fof(f814,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f77,f514]) ).
fof(f815,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f96,f514]) ).
fof(f877,plain,
( multiply(sk_c7,sk_c5) = multiply(sk_c6,sk_c2)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f493,f780]) ).
fof(f884,plain,
( multiply(sk_c8,sk_c2) = multiply(sk_c7,sk_c5)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f877,f514]) ).
fof(f887,plain,
( multiply(sk_c8,sk_c2) = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f884,f700]) ).
fof(f888,plain,
( sk_c2 = multiply(sk_c8,sk_c2)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f887,f780]) ).
fof(f889,plain,
( sk_c7 = sk_c2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f888,f144]) ).
fof(f890,plain,
( sk_c8 = sk_c2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f889,f700]) ).
fof(f1016,plain,
( sk_c6 != sk_c2
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f618,f135]) ).
fof(f1020,plain,
( sk_c8 = multiply(sk_c3,sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f635,f700]) ).
fof(f1027,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1016,f890]) ).
fof(f1033,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1027,f514]) ).
fof(f1034,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1033]) ).
fof(f1036,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f814,f700]) ).
fof(f1041,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f165,f1020]) ).
fof(f1043,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1041,f815]) ).
fof(f1044,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1043,f1036]) ).
fof(f1045,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1044]) ).
fof(f1049,plain,
( sk_c6 != multiply(sk_c3,sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f617,f514]) ).
fof(f1063,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1049,f1020]) ).
fof(f1067,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1063,f514]) ).
fof(f1068,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1067]) ).
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(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
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(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
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,[],[f472]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f480]) ).
cnf(s35,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f518]) ).
cnf(s38,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f541]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f623]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f649]) ).
cnf(s50,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f716]) ).
cnf(s51,plain,
( ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f721]) ).
cnf(s53,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f752]) ).
cnf(s54,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f756]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20 ),
inference(sat_conversion,[],[f758]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f770]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f813]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s66,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f1045]) ).
cnf(s68,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f1068]) ).
cnf(s69,plain,
spl0_3,
inference(rat,[],[s50,s66,s53,s6,s11,s16,s21,s26,s31]) ).
cnf(s70,plain,
spl0_6,
inference(rat,[],[s32,s27,s28,s29,s30,s69]) ).
cnf(s71,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s38,s15,s20,s25]) ).
cnf(s72,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s38,s14,s19,s24]) ).
cnf(s73,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s38,s13,s18,s23]) ).
cnf(s74,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_5
| ~ spl0_10 ),
inference(rat,[],[s38,s12,s17,s22,s61,s69]) ).
cnf(s75,plain,
~ spl0_5,
inference(rat,[],[s74,s73,s72,s71]) ).
cnf(s76,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s35,s5,s10]) ).
cnf(s77,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s35,s4,s9]) ).
cnf(s78,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s35,s3,s8]) ).
cnf(s79,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s35,s2,s7,s33,s69]) ).
cnf(s80,plain,
~ spl0_4,
inference(rat,[],[s79,s78,s77,s76]) ).
cnf(s81,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s53,s5,s10,s15,s20,s25,s70]) ).
cnf(s82,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s53,s4,s9,s14,s19,s24,s70]) ).
cnf(s83,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s54,s55,s81,s82]) ).
cnf(s84,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s3,s8,s13,s18,s23,s59,s82,s81,s69]) ).
cnf(s85,plain,
~ spl0_2,
inference(rat,[],[s48,s51,s2,s7,s12,s17,s22,s83,s84,s59,s82,s81,s69]) ).
cnf(s86,plain,
spl0_1,
inference(rat,[],[s1,s69,s70,s75,s80,s85]) ).
cnf(s87,plain,
~ spl0_7,
inference(rat,[],[s53,s65,s3,s8,s13,s18,s23,s44,s70,s86]) ).
cnf(s88,plain,
spl0_15,
inference(rat,[],[s22,s87]) ).
cnf(s89,plain,
spl0_14,
inference(rat,[],[s17,s87]) ).
cnf(s90,plain,
spl0_13,
inference(rat,[],[s12,s87]) ).
cnf(s91,plain,
spl0_12,
inference(rat,[],[s7,s87]) ).
cnf(s92,plain,
spl0_8,
inference(rat,[],[s2,s87]) ).
cnf(s93,plain,
spl0_17,
inference(rat,[],[s53,s92,s88,s89,s90,s70,s91]) ).
cnf(s94,plain,
spl0_21,
inference(rat,[],[s50,s93,s90,s88,s89,s91]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s68,s94,s90,s88,s89,s86,s93,s92]) ).
fof(f1069,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP365-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:56:19 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.17/1.19 % (2847905)Input is clausal, will run a generic CNF schedule.
% 2.17/1.19 % (2847915)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1730945171:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.17/1.19 % (2847915)First to succeed.
% 2.17/1.19 % (2847915)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2847905"
% 2.17/1.19 % (2847912)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2784452270:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.17/1.19 % (2847910)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=3145239350:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.17/1.19 % (2847913)lrs+10_1_sil=8000:sp=occurrence:random_seed=3076215154:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.17/1.19 % (2847911)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2585245686:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.17/1.19 % (2847914)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2287814159:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.17/1.19 % (2847913)Refutation not found, incomplete strategy
% 2.17/1.19 % (2847913)------------------------------
% 2.17/1.19 % (2847913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.19 % (2847913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.19 % (2847913)CaDiCaL version: 2.1.3
% 2.17/1.19 % (2847913)Termination reason: Refutation not found, incomplete strategy
% 2.17/1.19 % (2847913)Time elapsed: 0.003 s
% 2.17/1.19 % (2847913)Peak memory usage: 88 MB
% 2.17/1.19 % (2847913)Instructions burned: 3 (million)
% 2.17/1.19 % (2847916)dis-21_1_sil=8000:lcm=predicate:random_seed=1445761266: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)
% 2.17/1.19 % (2847916)Refutation not found, incomplete strategy
% 2.17/1.19 % (2847916)------------------------------
% 2.17/1.19 % (2847916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.19 % (2847916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.19 % (2847916)CaDiCaL version: 2.1.3
% 2.17/1.19 % (2847916)Termination reason: Refutation not found, incomplete strategy
% 2.17/1.19 % (2847916)Time elapsed: 0.002 s
% 2.17/1.19 % (2847916)Peak memory usage: 88 MB
% 2.17/1.19 % (2847916)Instructions burned: 2 (million)
% 2.17/1.19 % (2847914)Instruction limit reached!
% 2.17/1.19 % (2847914)------------------------------
% 2.17/1.19 % (2847914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.19 % (2847914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.19 % (2847914)CaDiCaL version: 2.1.3
% 2.17/1.19 % (2847914)Termination reason: Instruction limit
% 2.17/1.19 % (2847914)Termination phase: Saturation
% 2.17/1.19 % (2847914)Time elapsed: 0.066 s
% 2.17/1.19 % (2847914)Peak memory usage: 89 MB
% 2.17/1.19 % (2847914)Instructions burned: 114 (million)
% 2.17/1.19 % (2847915)Refutation found. Thanks to Tanya!
% 2.17/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.17/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.38 % (2847915)------------------------------
% 2.73/1.38 % (2847915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.38 % (2847915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.38 % (2847915)CaDiCaL version: 2.1.3
% 2.73/1.38 % (2847915)Termination reason: Refutation
% 2.73/1.38 % (2847915)Time elapsed: 0.013 s
% 2.73/1.38 % (2847915)Peak memory usage: 90 MB
% 2.73/1.38 % (2847915)Instructions burned: 36 (million)
% 2.73/1.38 % (2847915)------------------------------
% 2.73/1.38 % (2847915)------------------------------
% 2.73/1.38 % (2847905)Success in time 0.305 s
% 2.73/1.38 % Vampire exiting
%------------------------------------------------------------------------------