%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP294-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:34 AM UTC 2026
% Result : Unsatisfiable 0.44s 0.83s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 49
% Syntax : Number of formulae : 306 ( 19 unt; 15 def)
% Number of atoms : 1093 ( 291 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1496 ( 709 ~; 772 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(X1,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,sk_c5)
| sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f82,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( sk_c6 != multiply(sk_c7,sk_c5)
| spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl0_6
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_7
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f89,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( multiply(sk_c7,sk_c6) != sk_c5
| spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f66,f88,f85,f81,f78,f74,f71,f68]) ).
fof(f93,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f64,f97,f93]) ).
fof(f102,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f62,f97,f102]) ).
fof(f107,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f109,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f97,f107]) ).
fof(f112,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f58,f97,f112]) ).
fof(f116,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f97,f74]) ).
fof(f118,definition,
( spl0_13
<=> sk_c5 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f120,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f118,f93]) ).
fof(f122,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f118,f102]) ).
fof(f123,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f118,f107]) ).
fof(f124,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f118,f112]) ).
fof(f125,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f118,f74]) ).
fof(f126,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f81,f93]) ).
fof(f127,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f81,f102]) ).
fof(f128,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f81,f107]) ).
fof(f129,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f38,f81,f112]) ).
fof(f130,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f36,f81,f74]) ).
fof(f132,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f134,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f132,f93]) ).
fof(f136,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f132,f102]) ).
fof(f137,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f132,f107]) ).
fof(f138,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f132,f112]) ).
fof(f139,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f132,f74]) ).
fof(f141,definition,
( spl0_15
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f143,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f141,f93]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f141,f102]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f141,f107]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f141,f112]) ).
fof(f148,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f141,f74]) ).
fof(f149,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f88,f93]) ).
fof(f150,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f88,f102]) ).
fof(f151,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f88,f107]) ).
fof(f152,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f88,f112]) ).
fof(f153,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f88,f74]) ).
fof(f154,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f104]) ).
fof(f155,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f109]) ).
fof(f158,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f154]) ).
fof(f163,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f160,f1]) ).
fof(f164,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f158,f1]) ).
fof(f172,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f163,f95]) ).
fof(f205,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f164,f155]) ).
fof(f206,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f164,f154]) ).
fof(f207,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f164,f114]) ).
fof(f216,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f207,f109]) ).
fof(f217,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f216,f75]) ).
fof(f234,plain,
( sk_c3 = sk_c4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f206,f205]) ).
fof(f238,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f95,f234]) ).
fof(f240,plain,
( sk_c6 = multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f238,f217]) ).
fof(f262,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f240,f114]) ).
fof(f269,plain,
( sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f83,f262]) ).
fof(f276,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f269,f217]) ).
fof(f278,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f276,f172]) ).
fof(f279,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f278,f217]) ).
fof(f280,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f282,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f90,f217]) ).
fof(f284,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f282,f262]) ).
fof(f285,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f284,f172]) ).
fof(f286,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f285,f217]) ).
fof(f287,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f286]) ).
fof(f288,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f86,f262]) ).
fof(f290,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f288,f262]) ).
fof(f321,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f290,f104]) ).
fof(f324,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f321]) ).
fof(f327,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f324,f234]) ).
fof(f328,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f327,f240]) ).
fof(f329,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f330,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f69,f217]) ).
fof(f331,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f330,f104]) ).
fof(f334,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f331]) ).
fof(f337,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f334,f234]) ).
fof(f338,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f337,f240]) ).
fof(f339,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f340,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f72,f262]) ).
fof(f351,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f340,f104]) ).
fof(f356,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f351]) ).
fof(f361,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f356,f234]) ).
fof(f362,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f361,f240]) ).
fof(f363,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f364,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f79,f262]) ).
fof(f365,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f364,f217]) ).
fof(f366,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f365,f262]) ).
fof(f369,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f366,f104]) ).
fof(f374,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f369]) ).
fof(f379,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f374,f234]) ).
fof(f380,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f379,f240]) ).
fof(f381,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f384,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f99]) ).
fof(f390,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f82]) ).
fof(f392,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f89]) ).
fof(f393,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_13 ),
inference(superposition,[],[f164,f120]) ).
fof(f395,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f393,f99]) ).
fof(f396,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f395,f82]) ).
fof(f404,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f143,f396]) ).
fof(f405,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f164,f404]) ).
fof(f407,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f405,f134]) ).
fof(f408,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f407,f396]) ).
fof(f429,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f76,f396]) ).
fof(f430,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f384,f396]) ).
fof(f449,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f164,f408]) ).
fof(f451,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f449,f3]) ).
fof(f454,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f390,f396]) ).
fof(f455,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c6,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f392,f396]) ).
fof(f475,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c6),multiply(sk_c6,X0))
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f164,f454]) ).
fof(f478,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f475,f164]) ).
fof(f489,plain,
( multiply(sk_c6,identity) = multiply(sk_c5,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f455,f430]) ).
fof(f496,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f489,f451]) ).
fof(f504,plain,
( sk_c6 = multiply(sk_c5,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f496,f408]) ).
fof(f530,plain,
( sk_c6 = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f504,f478]) ).
fof(f533,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f120,f530]) ).
fof(f536,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f533,f396]) ).
fof(f538,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f536,f429]) ).
fof(f539,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f540,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f75,f396]) ).
fof(f541,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f79,f396]) ).
fof(f543,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f540,f408]) ).
fof(f544,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f541,f396]) ).
fof(f550,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f544,f543]) ).
fof(f556,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f550,f134]) ).
fof(f561,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f556,f396]) ).
fof(f565,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f561,f404]) ).
fof(f566,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f569,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f72,f396]) ).
fof(f572,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f569,f134]) ).
fof(f577,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f572,f396]) ).
fof(f581,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f577,f404]) ).
fof(f582,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f581]) ).
fof(f585,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f86,f396]) ).
fof(f586,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f585,f396]) ).
fof(f590,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f586,f134]) ).
fof(f595,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f590,f396]) ).
fof(f599,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f595,f404]) ).
fof(f600,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f599]) ).
fof(f603,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f69,f543]) ).
fof(f612,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f603,f134]) ).
fof(f617,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f612,f396]) ).
fof(f621,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f617,f404]) ).
fof(f622,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f621]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f100]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s8,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f128]) ).
cnf(s15,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s17,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s20,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s22,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s24,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s25,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f151]) ).
cnf(s30,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f152]) ).
cnf(s31,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f280]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f287]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f329]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f339]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f363]) ).
cnf(s43,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f381]) ).
cnf(s46,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f539]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f566]) ).
cnf(s51,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f582]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f600]) ).
cnf(s57,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f622]) ).
cnf(s59,plain,
spl0_3,
inference(rat,[],[s46,s6,s11,s16,s21,s26,s31]) ).
cnf(s60,plain,
spl0_7,
inference(rat,[],[s33,s27,s28,s29,s30,s59]) ).
cnf(s61,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s54,s10,s20,s25]) ).
cnf(s62,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s54,s9,s19,s24]) ).
cnf(s63,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s54,s8,s18,s23,s35,s62,s61,s59]) ).
cnf(s64,plain,
( ~ spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s35,s3,s4,s5,s63,s59]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s54,s2,s7,s17,s22,s64]) ).
cnf(s66,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s65,s1,s60,s59]) ).
cnf(s67,plain,
spl0_5,
inference(rat,[],[s32,s12,s13,s14,s15,s59]) ).
cnf(s69,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s23,s24,s25,s59]) ).
cnf(s70,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s18,s19,s20,s59]) ).
cnf(s71,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s8,s9,s10,s59]) ).
cnf(s72,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s3,s4,s5,s48,s71,s70,s69,s67,s59]) ).
cnf(s73,plain,
~ spl0_4,
inference(rat,[],[s48,s2,s7,s17,s22,s72,s59,s67]) ).
cnf(s74,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s40,s23,s24,s25,s59]) ).
cnf(s75,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s40,s18,s19,s20,s59]) ).
cnf(s76,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s40,s8,s9,s10,s59]) ).
cnf(s77,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s40,s3,s4,s5,s51,s76,s75,s74,s67,s59]) ).
cnf(s78,plain,
~ spl0_2,
inference(rat,[],[s51,s2,s7,s17,s22,s77,s67]) ).
cnf(s79,plain,
spl0_1,
inference(rat,[],[s66,s67,s73,s78]) ).
cnf(s80,plain,
( spl0_15
| ~ spl0_8 ),
inference(rat,[],[s37,s23,s24,s25,s59,s79]) ).
cnf(s81,plain,
( spl0_14
| ~ spl0_8 ),
inference(rat,[],[s37,s18,s19,s20,s59,s79]) ).
cnf(s82,plain,
( spl0_13
| ~ spl0_8 ),
inference(rat,[],[s37,s8,s9,s10,s59,s79]) ).
cnf(s83,plain,
~ spl0_8,
inference(rat,[],[s37,s3,s4,s5,s57,s82,s81,s80,s59,s79,s67]) ).
cnf(s84,plain,
spl0_15,
inference(rat,[],[s22,s83]) ).
cnf(s85,plain,
spl0_14,
inference(rat,[],[s17,s83]) ).
cnf(s86,plain,
spl0_13,
inference(rat,[],[s7,s83]) ).
cnf(s87,plain,
spl0_9,
inference(rat,[],[s2,s83]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s57,s85,s79,s67,s59,s84,s87,s86]) ).
fof(f625,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP294-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 09:48:19 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/0.83 % (2124474)Input is clausal, will run a generic CNF schedule.
% 0.44/0.83 % (2124481)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=623294406:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.44/0.83 % (2124482)lrs+10_1_sil=8000:sp=occurrence:random_seed=707030878:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.44/0.83 % (2124483)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4171792541:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.44/0.83 % (2124480)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2375994555:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.44/0.83 % (2124484)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=157507293:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.44/0.83 % (2124485)dis-21_1_sil=8000:lcm=predicate:random_seed=194371975:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.44/0.83 % (2124479)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=2956176414:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.44/0.83 % (2124485)Refutation not found, incomplete strategy
% 0.44/0.83 % (2124485)------------------------------
% 0.44/0.83 % (2124485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/0.83 % (2124485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.83 % (2124485)CaDiCaL version: 2.1.3
% 0.44/0.83 % (2124485)Termination reason: Refutation not found, incomplete strategy
% 0.44/0.83 % (2124485)Time elapsed: 0.001 s
% 0.44/0.83 % (2124485)Peak memory usage: 88 MB
% 0.44/0.83 % (2124485)Instructions burned: 1 (million)
% 0.44/0.83 % (2124482)Refutation not found, incomplete strategy
% 0.44/0.83 % (2124482)------------------------------
% 0.44/0.83 % (2124482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/0.83 % (2124482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.83 % (2124482)CaDiCaL version: 2.1.3
% 0.44/0.83 % (2124482)Termination reason: Refutation not found, incomplete strategy
% 0.44/0.83 % (2124482)Time elapsed: 0.001 s
% 0.44/0.83 % (2124482)Peak memory usage: 88 MB
% 0.44/0.83 % (2124482)Instructions burned: 3 (million)
% 0.44/0.83 % (2124484)First to succeed.
% 0.44/0.83 % (2124484)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2124474"
% 0.44/0.83 % (2124483)Instruction limit reached!
% 0.44/0.83 % (2124483)------------------------------
% 0.44/0.83 % (2124483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/0.83 % (2124483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.83 % (2124483)CaDiCaL version: 2.1.3
% 0.44/0.83 % (2124483)Termination reason: Instruction limit
% 0.44/0.83 % (2124483)Termination phase: Saturation
% 0.44/0.83 % (2124483)Time elapsed: 0.036 s
% 0.44/0.83 % (2124483)Peak memory usage: 89 MB
% 0.44/0.83 % (2124483)Instructions burned: 114 (million)
% 0.44/0.83 % (2124482)------------------------------
% 0.44/0.83 % (2124482)------------------------------
% 0.44/0.83 % (2124485)------------------------------
% 0.44/0.83 % (2124485)------------------------------
% 0.44/0.83 % (2124484)Refutation found. Thanks to Tanya!
% 0.44/0.83 % SZS status Unsatisfiable for theBenchmark
% 0.44/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.93 % (2124484)------------------------------
% 2.39/0.93 % (2124484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/0.93 % (2124484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.93 % (2124484)CaDiCaL version: 2.1.3
% 2.39/0.93 % (2124484)Termination reason: Refutation
% 2.39/0.93 % (2124484)Time elapsed: 0.008 s
% 2.39/0.93 % (2124484)Peak memory usage: 89 MB
% 2.39/0.93 % (2124484)Instructions burned: 22 (million)
% 2.39/0.93 % (2124484)------------------------------
% 2.39/0.93 % (2124484)------------------------------
% 2.39/0.93 % (2124474)Success in time 0.305 s
% 2.39/0.93 % Vampire exiting
%------------------------------------------------------------------------------