%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP359-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:44 AM UTC 2026
% Result : Unsatisfiable 2.30s 1.16s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 48
% Syntax : Number of formulae : 300 ( 17 unt; 14 def)
% Number of atoms : 1000 ( 302 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1299 ( 599 ~; 686 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,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_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,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_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,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_20) ).
fof(f44,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
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(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
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_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl0_4
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( sk_c6 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_5
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f68,f84,f80,f70,f76,f73,f70]) ).
fof(f89,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f91,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f95,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f93,f89]) ).
fof(f98,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f100,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f62,f93,f98]) ).
fof(f103,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f93,f103]) ).
fof(f108,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f110,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f93,f108]) ).
fof(f113,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f115,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f93,f113]) ).
fof(f117,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f54,f93,f76]) ).
fof(f119,definition,
( spl0_12
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f121,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f119,f89]) ).
fof(f123,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f119,f98]) ).
fof(f124,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f119,f103]) ).
fof(f125,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f119,f108]) ).
fof(f126,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f44,f119,f113]) ).
fof(f127,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f42,f119,f76]) ).
fof(f129,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f131,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f129,f89]) ).
fof(f133,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f129,f98]) ).
fof(f134,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f129,f103]) ).
fof(f135,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f129,f108]) ).
fof(f136,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f129,f113]) ).
fof(f137,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f129,f76]) ).
fof(f138,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f28,f80,f89]) ).
fof(f139,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f26,f80,f98]) ).
fof(f140,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f24,f80,f103]) ).
fof(f141,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f22,f80,f108]) ).
fof(f142,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f20,f80,f113]) ).
fof(f143,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f18,f80,f76]) ).
fof(f144,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f84,f89]) ).
fof(f145,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f84,f98]) ).
fof(f146,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f84,f103]) ).
fof(f147,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f84,f108]) ).
fof(f148,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f84,f113]) ).
fof(f149,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f84,f76]) ).
fof(f150,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f91]) ).
fof(f151,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f110]) ).
fof(f154,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f105]) ).
fof(f157,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f115]) ).
fof(f158,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f100]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f154,f1]) ).
fof(f162,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f150]) ).
fof(f163,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f162,f1]) ).
fof(f166,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f163,f100]) ).
fof(f172,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f166,f105]) ).
fof(f180,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f157,f172]) ).
fof(f184,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f158,f77]) ).
fof(f194,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f184,f172]) ).
fof(f206,plain,
( identity = multiply(sk_c3,identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f180,f151]) ).
fof(f223,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f159,f156]) ).
fof(f225,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f159,f151]) ).
fof(f227,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f159,f105]) ).
fof(f228,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_6 ),
inference(superposition,[],[f159,f150]) ).
fof(f229,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f159,f115]) ).
fof(f242,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f229,f172]) ).
fof(f243,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f227,f172]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f223,f172]) ).
fof(f248,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f110]) ).
fof(f249,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f243,f3]) ).
fof(f250,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f246,f159]) ).
fof(f252,plain,
( sk_c5 = multiply(sk_c3,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f206,f249]) ).
fof(f261,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f159,f248]) ).
fof(f263,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f261,f3]) ).
fof(f271,plain,
( sk_c5 = multiply(inverse(sk_c3),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f159,f252]) ).
fof(f274,plain,
( sk_c5 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f271,f110]) ).
fof(f275,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f105]) ).
fof(f276,plain,
( sk_c8 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f275,f172]) ).
fof(f285,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f225,f249]) ).
fof(f286,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f285,f276]) ).
fof(f287,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f286,f3]) ).
fof(f288,plain,
( sk_c8 = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f263]) ).
fof(f289,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f110,f288]) ).
fof(f300,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f228,f249]) ).
fof(f301,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f300,f276]) ).
fof(f302,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f301,f3]) ).
fof(f303,plain,
( sk_c5 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f302,f249]) ).
fof(f304,plain,
( sk_c8 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f276]) ).
fof(f317,plain,
( sk_c6 != sk_c8
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f82,f289]) ).
fof(f330,plain,
( sk_c8 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f194,f250]) ).
fof(f331,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f330,f304]) ).
fof(f333,plain,
( multiply(sk_c4,sk_c8) = multiply(sk_c5,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f158,f331]) ).
fof(f337,plain,
( sk_c6 = multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f333,f250]) ).
fof(f339,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f337,f304]) ).
fof(f342,plain,
( sk_c6 = sk_c8
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f339,f248]) ).
fof(f343,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f342,f317]) ).
fof(f344,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f345,plain,
( sk_c6 = sk_c8
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f81,f289]) ).
fof(f346,plain,
( sk_c8 != multiply(sk_c8,sk_c6)
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f86,f172]) ).
fof(f347,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f346,f331]) ).
fof(f348,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f349,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f71,f172]) ).
fof(f355,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f349,f91]) ).
fof(f356,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c3,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f349,f110]) ).
fof(f359,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c3,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f356]) ).
fof(f360,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f355]) ).
fof(f362,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f359,f115]) ).
fof(f363,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f360,f163]) ).
fof(f364,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f367,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f362,f77]) ).
fof(f368,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f367,f345]) ).
fof(f369,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f370,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f74,f172]) ).
fof(f371,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f370,f91]) ).
fof(f376,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f371]) ).
fof(f381,plain,
( sk_c8 != sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f376,f100]) ).
fof(f382,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f381,f276]) ).
fof(f383,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f388,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_7 ),
inference(superposition,[],[f3,f95]) ).
fof(f390,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f159,f85]) ).
fof(f391,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f85]) ).
fof(f392,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f159,f121]) ).
fof(f394,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f392,f95]) ).
fof(f404,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f71,f95]) ).
fof(f405,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f404]) ).
fof(f408,plain,
( sk_c7 != multiply(sk_c8,sk_c2)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f405,f121]) ).
fof(f416,definition,
( spl0_15
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f417,plain,
( sk_c6 = sk_c8
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f420,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f408,f131]) ).
fof(f421,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f423,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f159,f388]) ).
fof(f426,plain,
( sk_c1 = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f423,f81]) ).
fof(f450,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f394,f131]) ).
fof(f453,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f159,f394]) ).
fof(f455,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f453,f3]) ).
fof(f466,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f78,f450]) ).
fof(f590,plain,
( sk_c1 = multiply(sk_c6,sk_c2)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f426,f455]) ).
fof(f619,plain,
( multiply(sk_c8,sk_c2) = multiply(sk_c7,sk_c1)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f391,f590]) ).
fof(f623,plain,
( multiply(sk_c8,sk_c2) = multiply(sk_c8,sk_c1)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f619,f450]) ).
fof(f624,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f623,f388]) ).
fof(f625,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f624,f131]) ).
fof(f626,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f625,f450]) ).
fof(f627,plain,
( sk_c8 = sk_c2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f626,f455]) ).
fof(f666,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f390,f450]) ).
fof(f667,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f666,f3]) ).
fof(f668,plain,
( sk_c6 = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f667,f626]) ).
fof(f671,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f668,f129,f119,f93,f84,f80,f416]) ).
fof(f676,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f85,f417]) ).
fof(f677,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f676,f450]) ).
fof(f719,plain,
( sk_c6 != sk_c8
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f466,f677]) ).
fof(f720,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f719,f417]) ).
fof(f721,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f720]) ).
fof(f722,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f74,f450]) ).
fof(f728,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f722,f95]) ).
fof(f729,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f728]) ).
fof(f732,plain,
( sk_c8 != sk_c2
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f729,f121]) ).
fof(f737,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f732,f627]) ).
fof(f738,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f737]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f116]) ).
cnf(s8,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f117]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s10,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f123]) ).
cnf(s11,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f124]) ).
cnf(s12,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f125]) ).
cnf(s13,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f126]) ).
cnf(s14,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s15,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s16,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f133]) ).
cnf(s17,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f134]) ).
cnf(s18,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s19,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s20,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s21,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f138]) ).
cnf(s22,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f139]) ).
cnf(s23,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f140]) ).
cnf(s24,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f141]) ).
cnf(s25,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f142]) ).
cnf(s26,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f143]) ).
cnf(s27,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f144]) ).
cnf(s28,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f145]) ).
cnf(s29,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f146]) ).
cnf(s30,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f147]) ).
cnf(s31,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f148]) ).
cnf(s32,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f149]) ).
cnf(s34,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f344]) ).
cnf(s35,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f348]) ).
cnf(s36,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f364]) ).
cnf(s38,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f369]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f383]) ).
cnf(s43,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f421]) ).
cnf(s48,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f671]) ).
cnf(s49,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f721]) ).
cnf(s51,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f738]) ).
cnf(s54,plain,
spl0_3,
inference(rat,[],[s49,s48,s8,s14,s20,s26,s32]) ).
cnf(s55,plain,
spl0_5,
inference(rat,[],[s35,s27,s28,s29,s30,s31,s54]) ).
cnf(s56,plain,
spl0_4,
inference(rat,[],[s34,s21,s22,s23,s24,s25,s54]) ).
cnf(s57,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s51,s13,s19,s56,s55]) ).
cnf(s58,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s51,s12,s18,s56,s55]) ).
cnf(s59,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s51,s11,s17,s56,s55]) ).
cnf(s60,plain,
( ~ spl0_7
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s51,s10,s16,s41,s59,s58,s57,s56,s55]) ).
cnf(s61,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s41,s4,s5,s6,s7,s60]) ).
cnf(s62,plain,
~ spl0_2,
inference(rat,[],[s51,s3,s9,s15,s61,s56,s55]) ).
cnf(s63,plain,
spl0_1,
inference(rat,[],[s2,s54,s55,s56,s62]) ).
cnf(s64,plain,
( spl0_9
| ~ spl0_7 ),
inference(rat,[],[s43,s11,s17,s63]) ).
cnf(s65,plain,
( ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s43,s10,s16,s36,s64,s63]) ).
cnf(s66,plain,
~ spl0_6,
inference(rat,[],[s38,s4,s5,s6,s7,s65,s54,s56,s63]) ).
cnf(s67,plain,
spl0_13,
inference(rat,[],[s15,s66]) ).
cnf(s68,plain,
spl0_12,
inference(rat,[],[s9,s66]) ).
cnf(s69,plain,
spl0_7,
inference(rat,[],[s3,s66]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s43,s63,s69,s67,s68]) ).
fof(f743,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP359-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:55:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.30/1.16 % (3263025)Input is clausal, will run a generic CNF schedule.
% 2.30/1.16 % (3263035)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=109767579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.30/1.16 % (3263035)First to succeed.
% 2.30/1.16 % (3263035)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3263025"
% 2.30/1.16 % (3263030)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1051026978:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.30/1.16 % (3263032)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2005029176:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.30/1.16 % (3263033)lrs+10_1_sil=8000:sp=occurrence:random_seed=1761282462:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.30/1.16 % (3263031)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2677218655:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.30/1.16 % (3263034)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=755773918:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.30/1.16 % (3263033)Refutation not found, incomplete strategy
% 2.30/1.16 % (3263033)------------------------------
% 2.30/1.16 % (3263033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (3263033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (3263033)CaDiCaL version: 2.1.3
% 2.30/1.16 % (3263033)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.16 % (3263033)Time elapsed: 0.004 s
% 2.30/1.16 % (3263033)Peak memory usage: 88 MB
% 2.30/1.16 % (3263033)Instructions burned: 4 (million)
% 2.30/1.16 % (3263036)dis-21_1_sil=8000:lcm=predicate:random_seed=3055861775:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.30/1.16 % (3263036)Refutation not found, incomplete strategy
% 2.30/1.16 % (3263036)------------------------------
% 2.30/1.16 % (3263036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (3263036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (3263036)CaDiCaL version: 2.1.3
% 2.30/1.16 % (3263036)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.16 % (3263036)Time elapsed: 0.002 s
% 2.30/1.16 % (3263036)Peak memory usage: 88 MB
% 2.30/1.16 % (3263036)Instructions burned: 2 (million)
% 2.30/1.16 % (3263034)Instruction limit reached!
% 2.30/1.16 % (3263034)------------------------------
% 2.30/1.16 % (3263034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (3263034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (3263034)CaDiCaL version: 2.1.3
% 2.30/1.16 % (3263034)Termination reason: Instruction limit
% 2.30/1.16 % (3263034)Termination phase: Saturation
% 2.30/1.16 % (3263034)Time elapsed: 0.067 s
% 2.30/1.16 % (3263034)Peak memory usage: 89 MB
% 2.30/1.16 % (3263034)Instructions burned: 114 (million)
% 2.30/1.16 % (3263035)Refutation found. Thanks to Tanya!
% 2.30/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.30/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.26 % (3263035)------------------------------
% 2.63/1.26 % (3263035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.26 % (3263035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.26 % (3263035)CaDiCaL version: 2.1.3
% 2.63/1.26 % (3263035)Termination reason: Refutation
% 2.63/1.26 % (3263035)Time elapsed: 0.010 s
% 2.63/1.26 % (3263035)Peak memory usage: 89 MB
% 2.63/1.26 % (3263035)Instructions burned: 26 (million)
% 2.63/1.26 % (3263035)------------------------------
% 2.63/1.26 % (3263035)------------------------------
% 2.63/1.26 % (3263025)Success in time 0.303 s
% 2.63/1.26 % Vampire exiting
%------------------------------------------------------------------------------