%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP296-1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:25 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 50
% Syntax : Number of formulae : 406 ( 24 unt; 16 def)
% Number of atoms : 1709 ( 420 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 2575 (1272 ~;1287 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 99 !; 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(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c2)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X1,sk_c8) != sk_c6
| inverse(X1) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(X4,sk_c6) != sk_c8
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != multiply(sk_c8,X2)
| multiply(X3,sk_c8) != X2
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(reorient_equations,[],[f77]) ).
fof(f80,definition,
( spl0_1
<=> ! [X4] :
( sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f81,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_2
<=> ! [X2,X3] :
( sk_c7 != multiply(sk_c8,X2)
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f84,plain,
( ! [X2,X3] :
( sk_c7 != multiply(sk_c8,X2)
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_3
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f87,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( sk_c7 != multiply(sk_c8,sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_6
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,definition,
( spl0_7
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f101,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f78,f100,f97,f93,f90,f86,f83,f80]) ).
fof(f105,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f107,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f109,f105]) ).
fof(f114,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f115,plain,
( sk_c8 != multiply(sk_c5,sk_c6)
| spl0_10 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f74,f109,f114]) ).
fof(f119,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f121,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f109,f119]) ).
fof(f124,definition,
( spl0_12
<=> sk_c4 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f125,plain,
( sk_c4 != multiply(sk_c3,sk_c8)
| spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f126,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f70,f109,f124]) ).
fof(f129,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f131,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f68,f109,f129]) ).
fof(f133,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f66,f109,f86]) ).
fof(f135,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f137,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f135,f105]) ).
fof(f139,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f135,f114]) ).
fof(f140,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f60,f135,f119]) ).
fof(f141,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f58,f135,f124]) ).
fof(f142,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f56,f135,f129]) ).
fof(f143,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f54,f135,f86]) ).
fof(f144,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f93,f105]) ).
fof(f145,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f93,f114]) ).
fof(f149,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f93,f86]) ).
fof(f151,definition,
( spl0_15
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f153,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f151,f105]) ).
fof(f155,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f151,f114]) ).
fof(f156,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f151,f119]) ).
fof(f157,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f151,f124]) ).
fof(f158,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f151,f129]) ).
fof(f161,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f163,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f161,f105]) ).
fof(f165,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f161,f114]) ).
fof(f166,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f161,f119]) ).
fof(f167,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f161,f124]) ).
fof(f168,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f161,f129]) ).
fof(f170,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f100,f105]) ).
fof(f171,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f100,f114]) ).
fof(f172,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f100,f119]) ).
fof(f173,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f100,f124]) ).
fof(f174,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f100,f129]) ).
fof(f176,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f177,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f107]) ).
fof(f178,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f121]) ).
fof(f179,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f180,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f179,f4]) ).
fof(f187,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f116]) ).
fof(f191,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f177]) ).
fof(f192,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f191,f1]) ).
fof(f195,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f192,f116]) ).
fof(f198,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f195,f87]) ).
fof(f203,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f177,f198]) ).
fof(f204,plain,
( sk_c8 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f116,f198]) ).
fof(f228,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f187,f87]) ).
fof(f237,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f228,f204]) ).
fof(f246,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f180,f1]) ).
fof(f248,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f180,f3]) ).
fof(f249,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f180,f180]) ).
fof(f251,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f180,f237]) ).
fof(f252,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f180,f131]) ).
fof(f253,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f180,f178]) ).
fof(f256,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f180,f177]) ).
fof(f257,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_8 ),
inference(superposition,[],[f180,f192]) ).
fof(f259,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_12 ),
inference(superposition,[],[f180,f126]) ).
fof(f270,plain,
( sk_c8 = multiply(sk_c8,sk_c4)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f259,f121]) ).
fof(f275,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f251,f3]) ).
fof(f277,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f248,f249]) ).
fof(f281,plain,
( sk_c8 = multiply(sk_c8,multiply(inverse(sk_c8),sk_c7))
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f270,f252]) ).
fof(f286,plain,
( identity = multiply(identity,multiply(inverse(identity),sk_c7))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f281,f275]) ).
fof(f290,plain,
( identity = multiply(inverse(identity),sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f286,f1]) ).
fof(f292,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f290,f246]) ).
fof(f295,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f203,f292]) ).
fof(f296,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f295,f1]) ).
fof(f342,plain,
( sk_c7 != multiply(identity,sk_c6)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f95,f275]) ).
fof(f356,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f342,f1]) ).
fof(f362,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f356,f198]) ).
fof(f363,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f382,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f102,f198]) ).
fof(f384,plain,
( identity != multiply(sk_c8,identity)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f382,f292]) ).
fof(f386,plain,
( identity != sk_c8
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f384,f277]) ).
fof(f387,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f386,f275]) ).
fof(f388,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f389,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f98,f275]) ).
fof(f391,plain,
( ! [X0] :
( sk_c7 != X0
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f389,f277]) ).
fof(f393,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f391,f292]) ).
fof(f395,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f393,f275]) ).
fof(f397,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f395,f107]) ).
fof(f400,plain,
( identity != sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f397,f296]) ).
fof(f403,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f400,f198]) ).
fof(f404,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f403,f292]) ).
fof(f405,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f406,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c7)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f81,f198]) ).
fof(f407,plain,
( ! [X4] :
( sk_c8 != multiply(X4,identity)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f406,f292]) ).
fof(f408,plain,
( ! [X4] :
( sk_c8 != X4
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f407,f277]) ).
fof(f409,plain,
( ! [X4] :
( identity != X4
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f408,f275]) ).
fof(f410,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f409,f198]) ).
fof(f411,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f410,f292]) ).
fof(f428,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f411,f107]) ).
fof(f431,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f428,f296]) ).
fof(f434,plain,
( identity != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f431,f198]) ).
fof(f435,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f434,f292]) ).
fof(f436,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f437,plain,
( ! [X2,X3] :
( sk_c7 != multiply(identity,X2)
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f84,f275]) ).
fof(f438,plain,
( ! [X2,X3] :
( sk_c7 != X2
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f437,f1]) ).
fof(f439,plain,
( ! [X2,X3] :
( identity != X2
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f438,f292]) ).
fof(f440,plain,
( ! [X2,X3] :
( identity != inverse(X3)
| identity != X2
| multiply(X3,sk_c8) != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f439,f275]) ).
fof(f441,plain,
( ! [X2,X3] :
( multiply(X3,identity) != X2
| identity != inverse(X3)
| identity != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f440,f275]) ).
fof(f442,plain,
( ! [X2,X3] :
( X2 != X3
| identity != inverse(X3)
| identity != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f441,f277]) ).
fof(f449,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(equality_resolution,[],[f442]) ).
fof(f452,plain,
( identity = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f177,f296]) ).
fof(f461,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f452,f277]) ).
fof(f471,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f449,f107]) ).
fof(f474,plain,
( identity != sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f471,f461]) ).
fof(f477,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f474,f296]) ).
fof(f478,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f477]) ).
fof(f479,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f91,f275]) ).
fof(f480,plain,
( ! [X1] :
( sk_c6 != X1
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f479,f277]) ).
fof(f481,plain,
( ! [X1] :
( sk_c7 != X1
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f480,f198]) ).
fof(f482,plain,
( ! [X1] :
( identity != X1
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f481,f292]) ).
fof(f483,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f482,f275]) ).
fof(f512,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f483,f107]) ).
fof(f515,plain,
( identity != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f512,f461]) ).
fof(f518,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f515,f296]) ).
fof(f519,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f520,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f256,f277]) ).
fof(f521,plain,
( sk_c5 = inverse(multiply(sk_c8,sk_c7))
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f520,f101]) ).
fof(f525,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f111]) ).
fof(f529,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f153]) ).
fof(f531,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f180,f94]) ).
fof(f534,plain,
( multiply(sk_c8,sk_c7) = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f531,f101]) ).
fof(f622,plain,
( sk_c8 != multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| spl0_10 ),
inference(forward_demodulation,[],[f115,f257]) ).
fof(f625,plain,
( identity != sk_c8
| ~ spl0_8
| spl0_10 ),
inference(forward_demodulation,[],[f622,f3]) ).
fof(f627,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_16 ),
inference(superposition,[],[f180,f163]) ).
fof(f628,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f163]) ).
fof(f629,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f627,f153]) ).
fof(f631,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_9 ),
inference(superposition,[],[f180,f525]) ).
fof(f634,plain,
( sk_c2 = inverse(sk_c8)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f631,f277]) ).
fof(f641,plain,
( identity = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_9 ),
inference(superposition,[],[f525,f634]) ).
fof(f642,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f137,f634]) ).
fof(f643,plain,
( sk_c8 = inverse(inverse(sk_c8))
| ~ spl0_9 ),
inference(superposition,[],[f111,f634]) ).
fof(f644,plain,
( identity = sk_c6
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f642,f3]) ).
fof(f646,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_15 ),
inference(superposition,[],[f180,f529]) ).
fof(f649,plain,
( sk_c1 = inverse(sk_c8)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f646,f277]) ).
fof(f656,plain,
( sk_c7 != multiply(identity,sk_c8)
| spl0_3
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f88,f644]) ).
fof(f657,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f94,f644]) ).
fof(f659,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f177,f644]) ).
fof(f660,plain,
( ! [X0] : multiply(identity,multiply(sk_c5,X0)) = X0
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f192,f644]) ).
fof(f661,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f660,f1]) ).
fof(f662,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f659,f1]) ).
fof(f663,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f657,f277]) ).
fof(f664,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f656,f1]) ).
fof(f665,plain,
( ! [X0] : multiply(inverse(multiply(sk_c8,sk_c7)),X0) = X0
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f661,f521]) ).
fof(f666,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f664,f663]) ).
fof(f667,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f666]) ).
fof(f668,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f665,f629]) ).
fof(f669,plain,
( ! [X2,X3] :
( sk_c8 != multiply(sk_c8,X2)
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f84,f663]) ).
fof(f670,plain,
( sk_c7 = multiply(multiply(sk_c8,sk_c7),sk_c8)
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f87,f101]) ).
fof(f671,plain,
( sk_c7 = multiply(sk_c8,multiply(sk_c7,sk_c8))
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f670,f4]) ).
fof(f672,plain,
( sk_c8 = multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f671,f663]) ).
fof(f674,plain,
( multiply(sk_c8,sk_c8) = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f180,f672]) ).
fof(f677,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f674,f3]) ).
fof(f687,plain,
( sk_c6 = inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f107,f662]) ).
fof(f692,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f687,f644]) ).
fof(f697,plain,
( ! [X0] :
( sk_c8 != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != multiply(sk_c8,sk_c8) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f669,f672]) ).
fof(f703,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != multiply(sk_c8,sk_c8) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f697]) ).
fof(f706,plain,
( ! [X0] :
( identity != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f703,f677]) ).
fof(f737,plain,
( sk_c4 != multiply(multiply(inverse(sk_c8),identity),sk_c8)
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f125,f253]) ).
fof(f738,plain,
( sk_c4 != multiply(inverse(sk_c8),multiply(identity,sk_c8))
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f737,f4]) ).
fof(f739,plain,
( sk_c4 != multiply(identity,sk_c8)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f738,f668]) ).
fof(f740,plain,
( sk_c8 != sk_c4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f739,f1]) ).
fof(f741,plain,
( sk_c8 != multiply(inverse(sk_c8),sk_c7)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f740,f252]) ).
fof(f742,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f741,f534]) ).
fof(f743,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f742,f629]) ).
fof(f744,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f743]) ).
fof(f747,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f163,f649]) ).
fof(f749,plain,
( identity = sk_c7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f747,f3]) ).
fof(f756,plain,
( multiply(sk_c7,sk_c2) = multiply(sk_c1,identity)
| ~ spl0_9
| ~ spl0_16 ),
inference(superposition,[],[f628,f525]) ).
fof(f761,plain,
( sk_c1 = multiply(sk_c7,sk_c2)
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f756,f277]) ).
fof(f770,plain,
( sk_c1 = multiply(sk_c7,inverse(sk_c8))
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f761,f634]) ).
fof(f778,plain,
( sk_c1 = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f770,f663]) ).
fof(f783,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f778,f641]) ).
fof(f790,plain,
( identity = inverse(sk_c8)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f649,f783]) ).
fof(f793,plain,
( sk_c8 = inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f153,f783]) ).
fof(f794,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f793,f692]) ).
fof(f797,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f794,f625]) ).
fof(f798,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f797]) ).
fof(f855,plain,
( ! [X0] :
( identity != multiply(inverse(X0),X0)
| sk_c8 != inverse(inverse(sk_c8)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f706,f176]) ).
fof(f858,plain,
( identity != sk_c7
| sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f706,f163]) ).
fof(f862,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f858,f749]) ).
fof(f866,plain,
( ! [X0] : identity != multiply(inverse(X0),X0)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f855,f643]) ).
fof(f871,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f862,f153]) ).
fof(f872,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f871]) ).
fof(f875,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f866,f3]) ).
fof(f876,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f883,plain,
( ! [X0] :
( sk_c8 != X0
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f391,f663]) ).
fof(f885,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f883,f275]) ).
fof(f887,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f885,f275]) ).
fof(f921,plain,
( identity != sk_c6
| identity != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f887,f107]) ).
fof(f926,plain,
( identity != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f921,f644]) ).
fof(f932,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f926,f662]) ).
fof(f933,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f932]) ).
fof(f942,plain,
( ! [X0] :
( sk_c7 != multiply(X0,inverse(identity))
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f98,f793]) ).
fof(f947,plain,
( ! [X0] :
( sk_c8 != multiply(X0,inverse(identity))
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f942,f663]) ).
fof(f951,plain,
( ! [X0] :
( inverse(identity) != multiply(X0,inverse(identity))
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f947,f793]) ).
fof(f953,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| inverse(identity) != multiply(X0,inverse(identity)) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f951,f793]) ).
fof(f993,plain,
( sk_c8 != inverse(identity)
| inverse(identity) != multiply(sk_c1,inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f953,f153]) ).
fof(f1000,plain,
( inverse(identity) != multiply(sk_c1,inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f993,f793]) ).
fof(f1003,plain,
( inverse(identity) != multiply(inverse(sk_c8),inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1000,f649]) ).
fof(f1006,plain,
( inverse(identity) != multiply(identity,inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1003,f790]) ).
fof(f1010,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1006,f1]) ).
fof(f1011,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1010]) ).
fof(f1016,plain,
( ! [X4] :
( sk_c8 != multiply(X4,multiply(sk_c8,sk_c7))
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_demodulation,[],[f81,f101]) ).
fof(f1017,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1016,f629]) ).
fof(f1018,plain,
( ! [X4] :
( inverse(identity) != multiply(X4,inverse(identity))
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1017,f793]) ).
fof(f1019,plain,
( ! [X4] :
( multiply(sk_c8,sk_c7) != inverse(X4)
| inverse(identity) != multiply(X4,inverse(identity)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1018,f101]) ).
fof(f1020,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| inverse(identity) != multiply(X4,inverse(identity)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1019,f629]) ).
fof(f1021,plain,
( ! [X4] :
( inverse(X4) != inverse(identity)
| inverse(identity) != multiply(X4,inverse(identity)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1020,f793]) ).
fof(f1030,plain,
( sk_c8 != inverse(identity)
| inverse(identity) != multiply(sk_c1,inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f1021,f153]) ).
fof(f1037,plain,
( inverse(identity) != multiply(sk_c1,inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1030,f793]) ).
fof(f1040,plain,
( inverse(identity) != multiply(inverse(sk_c8),inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1037,f649]) ).
fof(f1043,plain,
( inverse(identity) != multiply(identity,inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1040,f790]) ).
fof(f1047,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1043,f1]) ).
fof(f1048,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1047]) ).
fof(f1053,plain,
( ! [X1] :
( sk_c6 != multiply(X1,inverse(identity))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f91,f793]) ).
fof(f1054,plain,
( ! [X1] :
( multiply(sk_c8,sk_c7) != multiply(X1,inverse(identity))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1053,f101]) ).
fof(f1055,plain,
( ! [X1] :
( sk_c8 != multiply(X1,inverse(identity))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1054,f629]) ).
fof(f1056,plain,
( ! [X1] :
( inverse(identity) != multiply(X1,inverse(identity))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1055,f793]) ).
fof(f1057,plain,
( ! [X1] :
( inverse(X1) != inverse(identity)
| inverse(identity) != multiply(X1,inverse(identity)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1056,f793]) ).
fof(f1061,plain,
( sk_c8 != inverse(identity)
| inverse(identity) != multiply(sk_c1,inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f1057,f153]) ).
fof(f1068,plain,
( inverse(identity) != multiply(sk_c1,inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1061,f793]) ).
fof(f1071,plain,
( inverse(identity) != multiply(inverse(sk_c8),inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1068,f649]) ).
fof(f1074,plain,
( inverse(identity) != multiply(identity,inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1071,f790]) ).
fof(f1078,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1074,f1]) ).
fof(f1079,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1078]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f103]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f112]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s7,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f133]) ).
cnf(s8,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s9,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s10,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s11,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f141]) ).
cnf(s12,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f142]) ).
cnf(s13,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s14,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f144]) ).
cnf(s15,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f145]) ).
cnf(s19,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f149]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s22,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s23,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s24,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s26,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s30,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s32,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f170]) ).
cnf(s33,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f171]) ).
cnf(s34,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f172]) ).
cnf(s35,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f173]) ).
cnf(s36,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f174]) ).
cnf(s38,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f363]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f388]) ).
cnf(s41,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f405]) ).
cnf(s43,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f436]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f478]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f519]) ).
cnf(s49,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(sat_conversion,[],[f667]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f744]) ).
cnf(s52,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f798]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f872]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(sat_conversion,[],[f876]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(sat_conversion,[],[f933]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f1011]) ).
cnf(s69,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f1048]) ).
cnf(s73,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f1079]) ).
cnf(s75,plain,
spl0_3,
inference(rat,[],[s49,s7,s13,s19]) ).
cnf(s76,plain,
spl0_7,
inference(rat,[],[s39,s32,s33,s34,s35,s36,s75]) ).
cnf(s77,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s41,s10,s11,s12,s61,s75]) ).
cnf(s78,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s52,s9,s21,s27,s77]) ).
cnf(s79,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s41,s3,s4,s5,s6,s78,s75]) ).
cnf(s80,plain,
( ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s65,s2,s8,s20,s26,s79]) ).
cnf(s81,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s80,s1,s76,s75]) ).
cnf(s82,plain,
spl0_5,
inference(rat,[],[s38,s14,s15,s75]) ).
cnf(s84,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s47,s9,s10,s11,s12,s75]) ).
cnf(s85,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s73,s24,s30,s82,s76]) ).
cnf(s86,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s51,s23,s29,s47,s85,s84,s82,s76,s75]) ).
cnf(s87,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s73,s22,s28,s82,s76]) ).
cnf(s88,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s52,s21,s27,s86,s87,s84,s82]) ).
cnf(s89,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s47,s3,s4,s5,s6,s88,s75]) ).
cnf(s90,plain,
~ spl0_4,
inference(rat,[],[s73,s2,s8,s20,s26,s89,s82,s76]) ).
cnf(s91,plain,
( spl0_14
| ~ spl0_10
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s45,s10,s11,s12,s75]) ).
cnf(s92,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s45,s4,s5,s6,s57,s91,s82,s76,s75]) ).
cnf(s93,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s52,s3,s9,s21,s27,s92,s82]) ).
cnf(s94,plain,
~ spl0_2,
inference(rat,[],[s55,s2,s8,s20,s26,s93,s75,s76,s82]) ).
cnf(s95,plain,
spl0_1,
inference(rat,[],[s81,s82,s90,s94]) ).
cnf(s96,plain,
( spl0_13
| ~ spl0_14
| ~ spl0_9 ),
inference(rat,[],[s69,s24,s30,s82,s76,s95]) ).
cnf(s97,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_9
| ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s51,s23,s29,s43,s96,s82,s76,s75,s95]) ).
cnf(s98,plain,
( ~ spl0_14
| ~ spl0_9
| ~ spl0_8
| ~ spl0_10 ),
inference(rat,[],[s69,s22,s28,s97,s95,s76,s82]) ).
cnf(s99,plain,
( spl0_14
| ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s43,s10,s11,s12,s75,s95]) ).
cnf(s100,plain,
( ~ spl0_14
| ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s43,s4,s5,s6,s98,s95,s75]) ).
cnf(s101,plain,
( ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s100,s99]) ).
cnf(s102,plain,
~ spl0_8,
inference(rat,[],[s52,s3,s9,s21,s27,s101,s82]) ).
cnf(s103,plain,
spl0_16,
inference(rat,[],[s26,s102]) ).
cnf(s104,plain,
spl0_15,
inference(rat,[],[s20,s102]) ).
cnf(s105,plain,
spl0_14,
inference(rat,[],[s8,s102]) ).
cnf(s106,plain,
spl0_9,
inference(rat,[],[s2,s102]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s69,s106,s95,s76,s82,s105,s104,s103]) ).
fof(f1084,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP296-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 09:51:26 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.45 % (2586068)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (2586078)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4066886779:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % (2586073)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=530580310_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % (2586075)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3328069865:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (2586076)dis+10_1_sil=32000:sp=arity:random_seed=667144094:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (2586077)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2003189945:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (2586079)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3037530327:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (2586074)% WARNING: option uhcvi not known.
% 0.12/0.45 % (2586078) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2586068-2586078"...
% 0.12/0.45 % TRYING [1]
% 0.12/0.45 % TRYING [2]
% 0.12/0.45 % TRYING [3]
% 0.12/0.45 % (2586078)...printing done.
% 0.12/0.45 % (2586074)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=58815444:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % TRYING [4]
% 0.12/0.45 % (2586078)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (2586078)------------------------------
% 0.12/0.46 % (2586078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (2586078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (2586078)CaDiCaL version: 2.1.3
% 0.12/0.46 % (2586078)Termination reason: Refutation
% 0.12/0.46 % (2586078)Time elapsed: 0.011 s
% 0.12/0.46 % (2586078)Peak memory usage: 12 MB
% 0.12/0.46 % (2586078)Instructions burned: 32 (million)
% 0.12/0.46 % (2586068)Success in time 0.043 s
% 0.12/0.46 % Vampire exiting
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