%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 10:17:25 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 48
% Syntax : Number of formulae : 328 ( 19 unt; 15 def)
% Number of atoms : 1255 ( 323 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1794 ( 867 ~; 912 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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 : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/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/sandbox/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,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = inverse(sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = 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
| inverse(sk_c7) != sk_c5
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/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_c5 != inverse(sk_c7)
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| 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 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ 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_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f82,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( sk_c5 != inverse(sk_c7)
| 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(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_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c6 = 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_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f109,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ 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 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c7 = inverse(sk_c3)
| ~ 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_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f120,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ 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(f154,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f104]) ).
fof(f155,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f114]) ).
fof(f158,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f159,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f75]) ).
fof(f160,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f154]) ).
fof(f161,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f109]) ).
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(f173,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f163,f95]) ).
fof(f176,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f161,f75]) ).
fof(f177,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c3,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f161,f154]) ).
fof(f200,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_12 ),
inference(superposition,[],[f164,f155]) ).
fof(f207,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f164,f109]) ).
fof(f216,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f207,f114]) ).
fof(f217,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f159,f216]) ).
fof(f220,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f217,f173]) ).
fof(f227,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f164,f220]) ).
fof(f229,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f227,f3]) ).
fof(f235,plain,
( sk_c5 != inverse(identity)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f83,f229]) ).
fof(f239,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f200,f229]) ).
fof(f240,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f216,f229]) ).
fof(f242,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f240,f1]) ).
fof(f243,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f239,f3]) ).
fof(f275,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f176,f216]) ).
fof(f276,plain,
( identity = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f275,f242]) ).
fof(f293,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f276,f243]) ).
fof(f294,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f293,f1]) ).
fof(f310,plain,
( multiply(sk_c7,sk_c4) = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f177,f243]) ).
fof(f311,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f310,f1]) ).
fof(f312,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f311,f229]) ).
fof(f313,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f312,f1]) ).
fof(f318,plain,
( sk_c6 = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f104,f313]) ).
fof(f319,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f318,f242]) ).
fof(f354,plain,
( identity != sk_c5
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f235,f319]) ).
fof(f355,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f354,f294]) ).
fof(f356,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f358,plain,
( identity != multiply(sk_c7,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f90,f294]) ).
fof(f360,plain,
( identity != multiply(sk_c7,identity)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f358,f242]) ).
fof(f361,plain,
( identity != multiply(identity,identity)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f360,f229]) ).
fof(f362,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f361,f1]) ).
fof(f363,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f364,plain,
( ! [X0] :
( sk_c6 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f86,f229]) ).
fof(f366,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f364,f242]) ).
fof(f368,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f366,f229]) ).
fof(f375,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c7))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f368,f200]) ).
fof(f381,plain,
( identity != inverse(inverse(sk_c7))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f375,f243]) ).
fof(f387,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f381,f229]) ).
fof(f393,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f387,f319]) ).
fof(f396,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f393,f319]) ).
fof(f397,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f396]) ).
fof(f398,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f69,f242]) ).
fof(f399,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f398,f294]) ).
fof(f400,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f399,f242]) ).
fof(f406,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f400,f200]) ).
fof(f412,plain,
( identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f406,f243]) ).
fof(f418,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f412,f229]) ).
fof(f424,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f418,f319]) ).
fof(f427,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f424,f319]) ).
fof(f428,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f429,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f72,f229]) ).
fof(f430,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f429,f242]) ).
fof(f431,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f430,f229]) ).
fof(f438,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c7))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f431,f200]) ).
fof(f444,plain,
( identity != inverse(inverse(sk_c7))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f438,f243]) ).
fof(f450,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f444,f229]) ).
fof(f456,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f450,f319]) ).
fof(f459,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f456,f319]) ).
fof(f460,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f461,plain,
( ! [X1] :
( sk_c5 != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f79,f242]) ).
fof(f462,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f461,f294]) ).
fof(f463,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f462,f242]) ).
fof(f470,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c7))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f463,f200]) ).
fof(f476,plain,
( identity != inverse(inverse(sk_c7))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f470,f243]) ).
fof(f482,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f476,f229]) ).
fof(f488,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f482,f319]) ).
fof(f491,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f488,f319]) ).
fof(f492,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f491]) ).
fof(f496,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f3,f82]) ).
fof(f499,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f99]) ).
fof(f504,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f134]) ).
fof(f682,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_13 ),
inference(superposition,[],[f164,f120]) ).
fof(f684,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f682,f99]) ).
fof(f685,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_15 ),
inference(superposition,[],[f164,f143]) ).
fof(f687,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f685,f134]) ).
fof(f699,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f164,f684]) ).
fof(f701,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f699,f3]) ).
fof(f714,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f496,f701]) ).
fof(f718,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f714,f1]) ).
fof(f736,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f504,f718]) ).
fof(f741,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f736,f1]) ).
fof(f749,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f687,f718]) ).
fof(f750,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f749,f1]) ).
fof(f751,plain,
( sk_c5 != multiply(identity,sk_c7)
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f76,f750]) ).
fof(f756,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f499,f750]) ).
fof(f763,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f756,f1]) ).
fof(f768,plain,
( sk_c7 != sk_c5
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f751,f1]) ).
fof(f773,plain,
( identity != sk_c7
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f768,f701]) ).
fof(f776,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f773,f718]) ).
fof(f777,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f776]) ).
fof(f779,plain,
( ! [X0] :
( sk_c6 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f86,f718]) ).
fof(f781,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f779,f750]) ).
fof(f783,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f781,f718]) ).
fof(f784,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f783,f1]) ).
fof(f789,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f784]) ).
fof(f793,plain,
( sk_c6 = inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f99,f763]) ).
fof(f794,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f793,f750]) ).
fof(f803,plain,
( sk_c7 = inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f134,f741]) ).
fof(f804,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f803,f718]) ).
fof(f808,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f804,f789]) ).
fof(f809,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f808]) ).
fof(f812,plain,
( ! [X1] :
( sk_c5 != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f79,f750]) ).
fof(f813,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f812,f701]) ).
fof(f814,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f813,f750]) ).
fof(f815,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f814,f1]) ).
fof(f820,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f815]) ).
fof(f821,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f794,f820]) ).
fof(f822,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f821]) ).
fof(f823,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f72,f718]) ).
fof(f824,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f823,f750]) ).
fof(f825,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f824,f718]) ).
fof(f826,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f825,f1]) ).
fof(f831,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f826]) ).
fof(f832,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f794,f831]) ).
fof(f833,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f832]) ).
fof(f834,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f69,f750]) ).
fof(f835,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f834,f701]) ).
fof(f836,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f835,f750]) ).
fof(f837,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f836,f1]) ).
fof(f842,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f837]) ).
fof(f843,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f794,f842]) ).
fof(f844,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f843]) ).
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(s32,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f356]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f363]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f397]) ).
cnf(s43,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f428]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f460]) ).
cnf(s53,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f492]) ).
cnf(s56,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f777]) ).
cnf(s57,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f809]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f822]) ).
cnf(s59,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f833]) ).
cnf(s60,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f844]) ).
cnf(s61,plain,
spl0_3,
inference(rat,[],[s56,s6,s11,s16,s21,s26]) ).
cnf(s62,plain,
spl0_7,
inference(rat,[],[s33,s27,s28,s29,s30,s61]) ).
cnf(s63,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s10,s20,s25]) ).
cnf(s64,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s9,s19,s24]) ).
cnf(s65,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s8,s18,s23,s38,s64,s63,s61]) ).
cnf(s66,plain,
( ~ spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s38,s3,s4,s5,s65,s61]) ).
cnf(s67,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s57,s2,s7,s17,s22,s66]) ).
cnf(s68,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s67,s1,s62,s61]) ).
cnf(s69,plain,
spl0_5,
inference(rat,[],[s32,s12,s13,s14,s15,s61]) ).
cnf(s71,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s23,s24,s25,s61]) ).
cnf(s72,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s18,s19,s20,s61]) ).
cnf(s73,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s8,s9,s10,s61]) ).
cnf(s74,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s3,s4,s5,s58,s73,s72,s71,s69,s61]) ).
cnf(s75,plain,
~ spl0_4,
inference(rat,[],[s58,s2,s7,s17,s22,s74,s69]) ).
cnf(s76,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s48,s23,s24,s25,s61]) ).
cnf(s77,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s48,s18,s19,s20,s61]) ).
cnf(s78,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s48,s8,s9,s10,s61]) ).
cnf(s79,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s48,s3,s4,s5,s59,s78,s77,s76,s69,s61]) ).
cnf(s80,plain,
~ spl0_2,
inference(rat,[],[s59,s2,s7,s17,s22,s79,s69]) ).
cnf(s81,plain,
spl0_1,
inference(rat,[],[s68,s69,s75,s80]) ).
cnf(s82,plain,
( spl0_15
| ~ spl0_8 ),
inference(rat,[],[s43,s23,s24,s25,s61,s81]) ).
cnf(s83,plain,
( spl0_14
| ~ spl0_8 ),
inference(rat,[],[s43,s18,s19,s20,s61,s81]) ).
cnf(s84,plain,
( spl0_13
| ~ spl0_8 ),
inference(rat,[],[s43,s8,s9,s10,s61,s81]) ).
cnf(s85,plain,
~ spl0_8,
inference(rat,[],[s43,s3,s4,s5,s60,s84,s83,s82,s61,s81,s69]) ).
cnf(s86,plain,
spl0_15,
inference(rat,[],[s22,s85]) ).
cnf(s87,plain,
spl0_14,
inference(rat,[],[s17,s85]) ).
cnf(s88,plain,
spl0_13,
inference(rat,[],[s7,s85]) ).
cnf(s89,plain,
spl0_9,
inference(rat,[],[s2,s85]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s60,s87,s81,s69,s86,s89,s88]) ).
fof(f845,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:48:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % (555391)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (555399)dis+10_1_sil=32000:sp=arity:random_seed=1235039520:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (555398)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2214307250:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (555396)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3411708734_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (555400)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3938129310:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (555401)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1848172952:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (555402)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1382259675:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % (555399) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-555391-555399"...
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % (555399)...printing done.
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % (555399)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (555399)------------------------------
% 0.09/0.45 % (555399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (555399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (555399)CaDiCaL version: 2.1.3
% 0.09/0.45 % (555399)Termination reason: Refutation
% 0.09/0.45 % (555399)Time elapsed: 0.010 s
% 0.09/0.45 % (555399)Peak memory usage: 12 MB
% 0.09/0.45 % (555399)Instructions burned: 29 (million)
% 0.09/0.45 % (555391)Success in time 0.037 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------