%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP358-1 : 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 : n017.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 10:17:35 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 47
% Syntax : Number of formulae : 403 ( 21 unt; 15 def)
% Number of atoms : 1764 ( 457 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 2709 (1348 ~;1346 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 125 !; 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_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl0_4
<=> ! [X0,X1] :
( sk_c7 != multiply(sk_c8,X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( ! [X0,X1] :
( sk_c7 != multiply(sk_c8,X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_5
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( sk_c6 != inverse(sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| spl0_6 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f66,f84,f80,f77,f74,f71,f68]) ).
fof(f89,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f91,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f93,f89]) ).
fof(f98,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f100,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f93,f98]) ).
fof(f103,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f93,f103]) ).
fof(f108,definition,
( spl0_11
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f110,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f93,f108]) ).
fof(f113,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c8 != inverse(sk_c3)
| spl0_12 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f93,f113]) ).
fof(f118,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f93,f118]) ).
fof(f123,definition,
( spl0_14
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f125,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f123,f89]) ).
fof(f127,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f123,f98]) ).
fof(f128,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f123,f103]) ).
fof(f129,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f123,f108]) ).
fof(f130,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f123,f113]) ).
fof(f131,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f123,f118]) ).
fof(f133,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f135,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f133,f89]) ).
fof(f137,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f133,f98]) ).
fof(f138,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f133,f103]) ).
fof(f139,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f133,f108]) ).
fof(f140,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f133,f113]) ).
fof(f141,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f133,f118]) ).
fof(f142,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f80,f89]) ).
fof(f143,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f80,f98]) ).
fof(f144,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f80,f103]) ).
fof(f145,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f22,f80,f108]) ).
fof(f148,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f84,f89]) ).
fof(f149,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f84,f98]) ).
fof(f150,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f84,f103]) ).
fof(f151,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f84,f108]) ).
fof(f152,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f84,f113]) ).
fof(f153,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f84,f118]) ).
fof(f155,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f100]) ).
fof(f156,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f105]) ).
fof(f157,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f115]) ).
fof(f158,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f158,f4]) ).
fof(f169,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f155]) ).
fof(f170,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f169,f1]) ).
fof(f179,plain,
( sk_c8 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f170,f91]) ).
fof(f190,plain,
( sk_c6 != inverse(multiply(sk_c6,sk_c6))
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f82,f179]) ).
fof(f206,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f159,f3]) ).
fof(f207,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f159,f159]) ).
fof(f208,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f159,f156]) ).
fof(f214,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f159,f110]) ).
fof(f223,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f214,f105]) ).
fof(f227,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f206,f207]) ).
fof(f235,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f159,f223]) ).
fof(f237,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f235,f3]) ).
fof(f295,plain,
( identity != inverse(multiply(identity,identity))
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f190,f237]) ).
fof(f297,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f155,f237]) ).
fof(f298,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f1]) ).
fof(f300,plain,
( identity != inverse(identity)
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f295,f1]) ).
fof(f321,plain,
( sk_c6 = multiply(identity,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f91,f298]) ).
fof(f322,plain,
( sk_c6 = inverse(identity)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f100,f298]) ).
fof(f323,plain,
( identity = inverse(identity)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f322,f237]) ).
fof(f324,plain,
( sk_c6 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f321,f1]) ).
fof(f328,plain,
( $false
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f323,f300]) ).
fof(f329,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f330,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f324,f237]) ).
fof(f337,plain,
( multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c6)
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f86,f179]) ).
fof(f339,plain,
( multiply(identity,identity) != multiply(sk_c7,identity)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f337,f237]) ).
fof(f341,plain,
( sk_c7 != multiply(identity,identity)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f339,f227]) ).
fof(f342,plain,
( identity != sk_c7
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f341,f1]) ).
fof(f345,plain,
( sk_c7 = multiply(sk_c3,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f120,f330]) ).
fof(f346,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f157,f330]) ).
fof(f353,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f346,f1]) ).
fof(f354,plain,
( sk_c7 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f345,f227]) ).
fof(f359,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f354,f353]) ).
fof(f363,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f359,f342]) ).
fof(f364,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f371,plain,
( ! [X0,X1] :
( sk_c7 != multiply(multiply(sk_c6,sk_c6),X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f78,f179]) ).
fof(f373,plain,
( ! [X0,X1] :
( sk_c7 != multiply(sk_c6,multiply(sk_c6,X0))
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f371,f4]) ).
fof(f375,plain,
( ! [X0,X1] :
( sk_c7 != multiply(identity,multiply(identity,X0))
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f373,f237]) ).
fof(f376,plain,
( ! [X0,X1] :
( multiply(identity,X0) != sk_c7
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f375,f1]) ).
fof(f377,plain,
( ! [X0,X1] :
( identity != multiply(identity,X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f376,f359]) ).
fof(f378,plain,
( ! [X0,X1] :
( identity != X0
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f377,f1]) ).
fof(f379,plain,
( ! [X0,X1] :
( inverse(X1) != multiply(sk_c6,sk_c6)
| identity != X0
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f378,f179]) ).
fof(f380,plain,
( ! [X0,X1] :
( inverse(X1) != multiply(identity,identity)
| identity != X0
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f379,f237]) ).
fof(f381,plain,
( ! [X0,X1] :
( identity != inverse(X1)
| identity != X0
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f380,f1]) ).
fof(f382,plain,
( ! [X0,X1] :
( multiply(X1,multiply(sk_c6,sk_c6)) != X0
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f381,f179]) ).
fof(f383,plain,
( ! [X0,X1] :
( multiply(X1,multiply(identity,identity)) != X0
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f382,f237]) ).
fof(f384,plain,
( ! [X0,X1] :
( multiply(X1,identity) != X0
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f383,f1]) ).
fof(f385,plain,
( ! [X0,X1] :
( X0 != X1
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f384,f227]) ).
fof(f386,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(equality_resolution,[],[f385]) ).
fof(f403,plain,
( identity != sk_c7
| identity != sk_c4
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f386,f105]) ).
fof(f406,plain,
( identity != sk_c4
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f403,f359]) ).
fof(f410,plain,
( identity != multiply(inverse(sk_c7),identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f406,f208]) ).
fof(f413,plain,
( identity != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f410,f227]) ).
fof(f414,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f413,f359]) ).
fof(f415,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f414,f323]) ).
fof(f416,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f417,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f237]) ).
fof(f418,plain,
( ! [X4] :
( sk_c6 != multiply(X4,multiply(sk_c6,sk_c6))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f417,f179]) ).
fof(f419,plain,
( ! [X4] :
( identity != multiply(X4,multiply(identity,identity))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f418,f237]) ).
fof(f420,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f419,f1]) ).
fof(f421,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f420,f227]) ).
fof(f424,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f156,f359]) ).
fof(f427,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f424,f1]) ).
fof(f441,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f421,f100]) ).
fof(f442,plain,
( identity != sk_c7
| identity != sk_c4
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f421,f105]) ).
fof(f445,plain,
( identity != sk_c4
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f442,f359]) ).
fof(f446,plain,
( identity != sk_c5
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f441,f237]) ).
fof(f449,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f445,f427]) ).
fof(f450,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f451,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f446,f298]) ).
fof(f452,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f453,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f72,f359]) ).
fof(f454,plain,
( ! [X3] :
( sk_c6 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f453,f227]) ).
fof(f455,plain,
( ! [X3] :
( identity != X3
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f454,f237]) ).
fof(f456,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f455,f359]) ).
fof(f474,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f456,f100]) ).
fof(f479,plain,
( identity != sk_c5
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f474,f237]) ).
fof(f484,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f479,f298]) ).
fof(f485,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f486,plain,
( ! [X2] :
( sk_c7 != multiply(X2,multiply(sk_c6,sk_c6))
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f75,f179]) ).
fof(f487,plain,
( ! [X2] :
( sk_c7 != multiply(X2,multiply(identity,identity))
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f486,f237]) ).
fof(f488,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f487,f1]) ).
fof(f489,plain,
( ! [X2] :
( sk_c7 != X2
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f488,f227]) ).
fof(f490,plain,
( ! [X2] :
( identity != X2
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f489,f359]) ).
fof(f491,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c6,sk_c6)
| identity != X2 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f490,f179]) ).
fof(f492,plain,
( ! [X2] :
( inverse(X2) != multiply(identity,identity)
| identity != X2 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f491,f237]) ).
fof(f493,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f492,f1]) ).
fof(f504,plain,
( identity != sk_c8
| identity != sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f493,f115]) ).
fof(f512,plain,
( identity != sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f504,f330]) ).
fof(f517,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f512,f353]) ).
fof(f518,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f544,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_8 ),
inference(superposition,[],[f3,f95]) ).
fof(f573,plain,
( multiply(sk_c7,sk_c6) != inverse(sk_c3)
| ~ spl0_6
| spl0_12 ),
inference(forward_demodulation,[],[f114,f85]) ).
fof(f576,plain,
( identity = multiply(multiply(sk_c7,sk_c6),sk_c1)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f544,f85]) ).
fof(f581,plain,
( identity = multiply(sk_c7,multiply(sk_c6,sk_c1))
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f576,f4]) ).
fof(f588,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f81]) ).
fof(f589,plain,
( identity = multiply(sk_c6,multiply(sk_c7,sk_c6))
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f588,f85]) ).
fof(f594,plain,
( sk_c6 = inverse(multiply(sk_c7,sk_c6))
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f81,f85]) ).
fof(f599,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f159,f125]) ).
fof(f600,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(sk_c2,X0)
| ~ spl0_14 ),
inference(superposition,[],[f4,f125]) ).
fof(f601,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c1,multiply(multiply(sk_c7,sk_c6),X0))
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f600,f85]) ).
fof(f602,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f599,f95]) ).
fof(f603,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c1,multiply(sk_c7,multiply(sk_c6,X0)))
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f601,f4]) ).
fof(f604,plain,
( sk_c7 = sk_c8
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f602,f135]) ).
fof(f607,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f159,f135]) ).
fof(f610,plain,
( sk_c2 = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f607,f81]) ).
fof(f617,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f81,f604]) ).
fof(f618,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f85,f604]) ).
fof(f620,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f125,f604]) ).
fof(f624,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f620,f610]) ).
fof(f626,plain,
( multiply(inverse(sk_c7),sk_c7) = multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f624,f617]) ).
fof(f627,plain,
( identity = multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f626,f3]) ).
fof(f649,plain,
( sk_c7 != sk_c2
| sk_c8 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f75,f125]) ).
fof(f651,plain,
( sk_c7 != sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f649,f95]) ).
fof(f659,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f651,f610]) ).
fof(f666,plain,
( sk_c7 != multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f659,f617]) ).
fof(f672,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f666,f3]) ).
fof(f696,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f159,f618]) ).
fof(f697,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f4,f618]) ).
fof(f698,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c7,multiply(inverse(sk_c7),X0))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f697,f617]) ).
fof(f699,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f696,f3]) ).
fof(f703,plain,
( identity = multiply(sk_c7,multiply(inverse(sk_c7),sk_c1))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f581,f617]) ).
fof(f710,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f703,f698]) ).
fof(f721,plain,
( identity = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f617,f699]) ).
fof(f734,plain,
( identity = multiply(identity,multiply(sk_c7,identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f589,f699]) ).
fof(f737,plain,
( multiply(sk_c7,sk_c6) = multiply(inverse(sk_c6),identity)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f159,f589]) ).
fof(f740,plain,
( multiply(sk_c7,sk_c6) = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f737,f227]) ).
fof(f743,plain,
( identity = multiply(sk_c7,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f734,f1]) ).
fof(f745,plain,
( multiply(sk_c7,inverse(sk_c7)) = inverse(inverse(sk_c7))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f740,f617]) ).
fof(f746,plain,
( inverse(identity) = multiply(sk_c7,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f745,f721]) ).
fof(f835,plain,
( multiply(sk_c1,multiply(sk_c7,identity)) = multiply(sk_c2,multiply(sk_c7,sk_c6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f603,f589]) ).
fof(f836,plain,
( multiply(sk_c1,identity) = multiply(sk_c2,sk_c1)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f603,f581]) ).
fof(f844,plain,
( multiply(sk_c1,multiply(sk_c7,identity)) = multiply(sk_c2,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f835,f618]) ).
fof(f854,plain,
( multiply(sk_c1,multiply(sk_c7,identity)) = multiply(multiply(sk_c6,sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f844,f610]) ).
fof(f864,plain,
( multiply(sk_c1,multiply(sk_c7,identity)) = multiply(sk_c6,multiply(sk_c7,sk_c7))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f854,f4]) ).
fof(f945,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f743,f227]) ).
fof(f946,plain,
( sk_c7 = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f746,f227]) ).
fof(f950,plain,
( multiply(sk_c1,identity) = multiply(multiply(sk_c6,sk_c7),sk_c1)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f836,f610]) ).
fof(f955,plain,
( multiply(sk_c1,multiply(sk_c7,identity)) = multiply(inverse(sk_c7),multiply(sk_c7,sk_c7))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f864,f617]) ).
fof(f965,plain,
( multiply(sk_c1,identity) = multiply(sk_c6,multiply(sk_c7,sk_c1))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f950,f4]) ).
fof(f970,plain,
( sk_c7 = multiply(sk_c1,multiply(sk_c7,identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f955,f159]) ).
fof(f972,plain,
( multiply(sk_c6,identity) = multiply(sk_c1,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f965,f710]) ).
fof(f977,plain,
( sk_c7 = multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f970,f227]) ).
fof(f979,plain,
( sk_c1 = multiply(sk_c6,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f972,f227]) ).
fof(f984,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f977,f627]) ).
fof(f985,plain,
( sk_c6 = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f979,f227]) ).
fof(f989,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f984,f672]) ).
fof(f990,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f989]) ).
fof(f991,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f985,f617]) ).
fof(f994,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f991,f721]) ).
fof(f996,plain,
( ! [X3] :
( multiply(X3,sk_c7) != inverse(sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f72,f617]) ).
fof(f997,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f946,f945]) ).
fof(f998,plain,
( ! [X3] :
( identity != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f996,f721]) ).
fof(f999,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f998,f945]) ).
fof(f1000,plain,
( ! [X3] :
( identity != X3
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f999,f227]) ).
fof(f1001,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1000,f945]) ).
fof(f1006,plain,
( sk_c8 = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f95,f994]) ).
fof(f1007,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1006,f997]) ).
fof(f1032,plain,
( sk_c7 = multiply(sk_c3,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f120,f1007]) ).
fof(f1040,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1032,f227]) ).
fof(f1047,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1040,f945]) ).
fof(f1055,plain,
( identity != sk_c6
| identity != multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1001,f594]) ).
fof(f1060,plain,
( identity != multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1055,f699]) ).
fof(f1065,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1060,f618]) ).
fof(f1066,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1065,f945]) ).
fof(f1067,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1066]) ).
fof(f1068,plain,
( ! [X0,X1] :
( sk_c7 != multiply(multiply(sk_c7,sk_c6),X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f78,f85]) ).
fof(f1069,plain,
( ! [X0,X1] :
( sk_c7 != multiply(sk_c7,multiply(sk_c6,X0))
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1068,f4]) ).
fof(f1070,plain,
( ! [X0,X1] :
( sk_c7 != multiply(sk_c7,multiply(inverse(sk_c7),X0))
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1069,f617]) ).
fof(f1071,plain,
( ! [X0,X1] :
( sk_c7 != multiply(sk_c7,X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1070,f698]) ).
fof(f1072,plain,
( ! [X0,X1] :
( identity != multiply(identity,X0)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1071,f945]) ).
fof(f1073,plain,
( ! [X0,X1] :
( identity != X0
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1072,f1]) ).
fof(f1074,plain,
( ! [X0,X1] :
( multiply(sk_c7,sk_c6) != inverse(X1)
| identity != X0
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1073,f85]) ).
fof(f1075,plain,
( ! [X0,X1] :
( sk_c7 != inverse(X1)
| identity != X0
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1074,f618]) ).
fof(f1076,plain,
( ! [X0,X1] :
( identity != inverse(X1)
| identity != X0
| multiply(X1,sk_c8) != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1075,f945]) ).
fof(f1077,plain,
( ! [X0,X1] :
( multiply(X1,multiply(sk_c7,sk_c6)) != X0
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1076,f85]) ).
fof(f1078,plain,
( ! [X0,X1] :
( multiply(X1,sk_c7) != X0
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1077,f618]) ).
fof(f1079,plain,
( ! [X0,X1] :
( multiply(X1,identity) != X0
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1078,f945]) ).
fof(f1080,plain,
( ! [X0,X1] :
( X0 != X1
| identity != inverse(X1)
| identity != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1079,f227]) ).
fof(f1082,plain,
( multiply(sk_c7,sk_c6) != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f573,f1047]) ).
fof(f1087,plain,
( identity != multiply(sk_c7,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1082,f997]) ).
fof(f1090,plain,
( identity != sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1087,f618]) ).
fof(f1092,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1090,f945]) ).
fof(f1093,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1092]) ).
fof(f1160,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(equality_resolution,[],[f1080]) ).
fof(f1162,plain,
( identity != sk_c6
| identity != multiply(sk_c7,sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1160,f594]) ).
fof(f1167,plain,
( identity != multiply(sk_c7,sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1162,f699]) ).
fof(f1172,plain,
( identity != sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1167,f618]) ).
fof(f1173,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1172,f945]) ).
fof(f1174,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1173]) ).
fof(f1175,plain,
( ! [X4] :
( inverse(X4) != inverse(sk_c7)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f69,f617]) ).
fof(f1176,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1175,f721]) ).
fof(f1177,plain,
( ! [X4] :
( sk_c6 != multiply(X4,multiply(sk_c7,sk_c6))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1176,f85]) ).
fof(f1178,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1177,f618]) ).
fof(f1179,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1178,f945]) ).
fof(f1180,plain,
( ! [X4] :
( sk_c6 != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1179,f227]) ).
fof(f1181,plain,
( ! [X4] :
( inverse(sk_c7) != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1180,f617]) ).
fof(f1182,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1181,f721]) ).
fof(f1199,plain,
( identity != sk_c6
| identity != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1182,f594]) ).
fof(f1206,plain,
( identity != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1199,f699]) ).
fof(f1213,plain,
( identity != sk_c7
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1206,f618]) ).
fof(f1214,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1213,f945]) ).
fof(f1215,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1214]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f101]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f111]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s8,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s9,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s10,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s11,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s12,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s13,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s14,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f136]) ).
cnf(s15,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f137]) ).
cnf(s16,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f138]) ).
cnf(s17,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s18,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f140]) ).
cnf(s19,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f141]) ).
cnf(s20,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f142]) ).
cnf(s21,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f143]) ).
cnf(s22,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f145]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f151]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f152]) ).
cnf(s31,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f153]) ).
cnf(s32,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f329]) ).
cnf(s33,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f364]) ).
cnf(s36,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f416]) ).
cnf(s38,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f450]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f452]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f485]) ).
cnf(s46,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f518]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f990]) ).
cnf(s60,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f1067]) ).
cnf(s61,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f1093]) ).
cnf(s65,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f1174]) ).
cnf(s69,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f1215]) ).
cnf(s70,plain,
spl0_5,
inference(rat,[],[s32,s20,s21,s22,s23]) ).
cnf(s71,plain,
spl0_6,
inference(rat,[],[s33,s26,s27,s28,s29,s30,s31]) ).
cnf(s72,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s36,s3,s4,s5,s6,s7]) ).
cnf(s73,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s65,s13,s19,s70,s71]) ).
cnf(s74,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_8 ),
inference(rat,[],[s61,s12,s18,s70,s71]) ).
cnf(s75,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s65,s11,s17,s70,s71]) ).
cnf(s76,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s65,s10,s16,s70,s71]) ).
cnf(s77,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s65,s9,s15,s36,s76,s75,s74,s73,s72,s71,s70]) ).
cnf(s78,plain,
~ spl0_4,
inference(rat,[],[s65,s2,s8,s14,s77,s70,s71]) ).
cnf(s79,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s57,s13,s19,s70,s71]) ).
cnf(s80,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s57,s11,s17,s70,s71]) ).
cnf(s81,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s57,s10,s16,s70,s71]) ).
cnf(s82,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s57,s9,s15,s46,s81,s80,s74,s79,s70,s71]) ).
cnf(s83,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s46,s3,s4,s5,s6,s7,s82]) ).
cnf(s84,plain,
~ spl0_3,
inference(rat,[],[s57,s2,s8,s14,s83,s70,s71]) ).
cnf(s85,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s60,s13,s19,s70,s71]) ).
cnf(s86,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s60,s11,s17,s70,s71]) ).
cnf(s87,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s60,s10,s16,s70,s71]) ).
cnf(s88,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s60,s9,s15,s42,s87,s86,s74,s85,s70,s71]) ).
cnf(s89,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s42,s3,s4,s5,s6,s7,s88]) ).
cnf(s90,plain,
~ spl0_2,
inference(rat,[],[s60,s2,s8,s14,s89,s70,s71]) ).
cnf(s91,plain,
spl0_1,
inference(rat,[],[s1,s70,s78,s71,s84,s90]) ).
cnf(s92,plain,
( spl0_11
| ~ spl0_8 ),
inference(rat,[],[s69,s11,s17,s70,s71,s91]) ).
cnf(s93,plain,
( spl0_10
| ~ spl0_8 ),
inference(rat,[],[s69,s10,s16,s70,s71,s91]) ).
cnf(s94,plain,
( ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s69,s9,s15,s39,s93,s92,s70,s71,s91]) ).
cnf(s95,plain,
~ spl0_7,
inference(rat,[],[s38,s3,s4,s5,s6,s7,s94,s91]) ).
cnf(s96,plain,
spl0_15,
inference(rat,[],[s14,s95]) ).
cnf(s97,plain,
spl0_14,
inference(rat,[],[s8,s95]) ).
cnf(s98,plain,
spl0_8,
inference(rat,[],[s2,s95]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s69,s91,s71,s70,s98,s97,s96]) ).
fof(f1216,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:51:05 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.47 % (2299951)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2299961)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=407134141:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2299957)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2299956)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4202192982_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2299957)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1434888872:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2299958)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=858747627:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2299959)dis+10_1_sil=32000:sp=arity:random_seed=3937848257:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2299960)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3828798657:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2299962)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1187706985:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % (2299961) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2299951-2299961"...
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2299961)...printing done.
% 0.17/0.47 % (2299961)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2299961)------------------------------
% 0.17/0.48 % (2299961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2299961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2299961)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2299961)Termination reason: Refutation
% 0.17/0.48 % (2299961)Time elapsed: 0.013 s
% 0.17/0.48 % (2299961)Peak memory usage: 12 MB
% 0.17/0.48 % (2299961)Instructions burned: 35 (million)
% 0.17/0.48 % (2299951)Success in time 0.039 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------