%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n015.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 10:17:24 AM UTC 2026
% Result : Unsatisfiable 0.33s 0.47s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 49
% Syntax : Number of formulae : 312 ( 22 unt; 15 def)
% Number of atoms : 1114 ( 297 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1532 ( 730 ~; 787 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 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/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',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(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f155]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f172,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f163,f95]) ).
fof(f189,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f168,f114]) ).
fof(f198,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f164,f3]) ).
fof(f199,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f164,f164]) ).
fof(f203,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f164,f75]) ).
fof(f204,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f164,f172]) ).
fof(f205,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f164,f155]) ).
fof(f217,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f203,f204]) ).
fof(f220,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f198,f199]) ).
fof(f229,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f189,f217]) ).
fof(f231,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f75,f189]) ).
fof(f233,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f164,f189]) ).
fof(f235,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f233,f3]) ).
fof(f237,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f235,f217]) ).
fof(f268,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_3
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f83,f231]) ).
fof(f269,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f268,f217]) ).
fof(f273,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f269,f229]) ).
fof(f274,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f279,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f90,f231]) ).
fof(f281,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f279,f217]) ).
fof(f282,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f281,f229]) ).
fof(f283,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f284,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f86,f217]) ).
fof(f286,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f284,f217]) ).
fof(f292,plain,
( sk_c7 != sk_c6
| sk_c6 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f286,f114]) ).
fof(f294,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f292,f217]) ).
fof(f298,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f294,f109]) ).
fof(f299,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f300,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f69,f231]) ).
fof(f302,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f205,f237]) ).
fof(f304,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f302,f3]) ).
fof(f306,plain,
( sk_c6 = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f304,f237]) ).
fof(f313,plain,
( sk_c7 != sk_c6
| sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f300,f114]) ).
fof(f315,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f313,f217]) ).
fof(f319,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f315,f109]) ).
fof(f320,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f321,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f72,f217]) ).
fof(f322,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f109,f306]) ).
fof(f339,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f321,f3]) ).
fof(f345,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f339,f237]) ).
fof(f351,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f345,f322]) ).
fof(f354,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f351,f322]) ).
fof(f355,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f356,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f79,f217]) ).
fof(f357,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,[],[f356,f231]) ).
fof(f358,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f357,f217]) ).
fof(f373,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f358,f3]) ).
fof(f379,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f373,f237]) ).
fof(f385,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f379,f322]) ).
fof(f388,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f385,f322]) ).
fof(f389,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f393,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f99]) ).
fof(f415,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f164,f89]) ).
fof(f419,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_13 ),
inference(superposition,[],[f164,f120]) ).
fof(f422,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f419,f99]) ).
fof(f424,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f422,f82]) ).
fof(f426,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_15 ),
inference(superposition,[],[f164,f143]) ).
fof(f429,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f426,f134]) ).
fof(f434,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f89,f424]) ).
fof(f446,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f76,f424]) ).
fof(f447,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f393,f424]) ).
fof(f453,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f415,f424]) ).
fof(f456,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f429,f424]) ).
fof(f460,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f434,f456]) ).
fof(f461,plain,
( sk_c6 != sk_c5
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f446,f456]) ).
fof(f463,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f461,f460]) ).
fof(f464,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f463]) ).
fof(f469,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f79,f424]) ).
fof(f475,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f469,f460]) ).
fof(f476,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f475,f424]) ).
fof(f507,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f453,f460]) ).
fof(f508,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f507,f3]) ).
fof(f513,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f164,f447]) ).
fof(f516,plain,
( sk_c2 = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f513,f220]) ).
fof(f525,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f476,f3]) ).
fof(f532,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f525,f508]) ).
fof(f535,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f532,f516]) ).
fof(f538,plain,
( sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f535,f99]) ).
fof(f540,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f538,f424]) ).
fof(f541,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f542,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f86,f424]) ).
fof(f543,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f542,f424]) ).
fof(f554,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f543,f3]) ).
fof(f561,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f554,f508]) ).
fof(f564,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f561,f516]) ).
fof(f567,plain,
( sk_c7 != sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f564,f99]) ).
fof(f569,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f567,f424]) ).
fof(f570,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f569]) ).
fof(f571,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f72,f424]) ).
fof(f574,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f571,f3]) ).
fof(f581,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f574,f508]) ).
fof(f584,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f581,f516]) ).
fof(f587,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f584,f99]) ).
fof(f589,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f587,f424]) ).
fof(f590,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f591,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f69,f460]) ).
fof(f598,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f591,f3]) ).
fof(f605,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f598,f508]) ).
fof(f608,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f605,f516]) ).
fof(f611,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f608,f99]) ).
fof(f613,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f611,f424]) ).
fof(f614,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f613]) ).
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,[],[f274]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f283]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f299]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f320]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f355]) ).
cnf(s43,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f389]) ).
cnf(s46,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f464]) ).
cnf(s49,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f541]) ).
cnf(s50,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f570]) ).
cnf(s51,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f590]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f614]) ).
cnf(s53,plain,
spl0_3,
inference(rat,[],[s46,s6,s11,s16,s21,s26,s31]) ).
cnf(s54,plain,
spl0_7,
inference(rat,[],[s33,s27,s28,s29,s30,s53]) ).
cnf(s55,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s50,s10,s20,s25,s54]) ).
cnf(s56,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s50,s9,s19,s24,s54]) ).
cnf(s57,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s50,s8,s18,s23,s34,s56,s55,s54,s53]) ).
cnf(s58,plain,
( ~ spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s34,s3,s4,s5,s57,s53]) ).
cnf(s59,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s50,s2,s7,s17,s22,s58,s54]) ).
cnf(s60,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s59,s1,s54,s53]) ).
cnf(s61,plain,
spl0_5,
inference(rat,[],[s32,s12,s13,s14,s15,s53]) ).
cnf(s63,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s23,s24,s25,s53]) ).
cnf(s64,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s18,s19,s20,s53]) ).
cnf(s65,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s8,s9,s10,s53]) ).
cnf(s66,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s43,s3,s4,s5,s49,s65,s64,s63,s54,s61,s53]) ).
cnf(s67,plain,
~ spl0_4,
inference(rat,[],[s49,s2,s7,s17,s22,s66,s61,s54]) ).
cnf(s68,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s39,s23,s24,s25,s53]) ).
cnf(s69,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s39,s18,s19,s20,s53]) ).
cnf(s70,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s39,s8,s9,s10,s53]) ).
cnf(s71,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s39,s3,s4,s5,s51,s70,s69,s68,s54,s61,s53]) ).
cnf(s72,plain,
~ spl0_2,
inference(rat,[],[s51,s2,s7,s17,s22,s71,s61,s54]) ).
cnf(s73,plain,
spl0_1,
inference(rat,[],[s60,s61,s67,s72]) ).
cnf(s74,plain,
( spl0_15
| ~ spl0_8 ),
inference(rat,[],[s35,s23,s24,s25,s53,s73]) ).
cnf(s75,plain,
( spl0_14
| ~ spl0_8 ),
inference(rat,[],[s35,s18,s19,s20,s53,s73]) ).
cnf(s76,plain,
( spl0_13
| ~ spl0_8 ),
inference(rat,[],[s35,s8,s9,s10,s53,s73]) ).
cnf(s77,plain,
~ spl0_8,
inference(rat,[],[s35,s3,s4,s5,s52,s76,s75,s74,s53,s73,s61,s54]) ).
cnf(s78,plain,
spl0_15,
inference(rat,[],[s22,s77]) ).
cnf(s79,plain,
spl0_14,
inference(rat,[],[s17,s77]) ).
cnf(s80,plain,
spl0_13,
inference(rat,[],[s7,s77]) ).
cnf(s81,plain,
spl0_9,
inference(rat,[],[s2,s77]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s52,s79,s73,s54,s61,s78,s81,s80]) ).
fof(f615,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP294-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:51:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.46 % (1413581)Will run a generic schedule for satisfiability detection.
% 0.33/0.46 % (1413592)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3631708692:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.46 % (1413587)% WARNING: option uhcvi not known.
% 0.33/0.46 % (1413586)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=566579374_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.46 % (1413588)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=61485147:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.46 % (1413589)dis+10_1_sil=32000:sp=arity:random_seed=3184141494:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.46 % (1413590)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1544252587:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.46 % (1413591)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3604892927:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.46 % (1413587)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2922484093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.47 % TRYING [1]
% 0.33/0.47 % TRYING [2]
% 0.33/0.47 % TRYING [3]
% 0.33/0.47 % TRYING [4]
% 0.33/0.47 % (1413590) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1413581-1413590"...
% 0.33/0.47 % (1413591) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1413581-1413591"...
% 0.33/0.47 % (1413589) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1413581-1413589"...
% 0.33/0.47 % (1413590)...printing done.
% 0.33/0.47 % (1413592) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1413581-1413592"...
% 0.33/0.47 % (1413590)Refutation found. Thanks to Tanya!
% 0.33/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.33/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.47 % (1413590)------------------------------
% 0.33/0.47 % (1413590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (1413590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (1413590)CaDiCaL version: 2.1.3
% 0.33/0.47 % (1413590)Termination reason: Refutation
% 0.33/0.47 % (1413590)Time elapsed: 0.014 s
% 0.33/0.47 % (1413590)Peak memory usage: 12 MB
% 0.33/0.47 % (1413590)Instructions burned: 20 (million)
% 0.33/0.47 % (1413581)Success in time 0.05 s
% 0.33/0.47 % Vampire exiting
%------------------------------------------------------------------------------