%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:18 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 55
% Syntax : Number of formulae : 480 ( 21 unt; 18 def)
% Number of atoms : 2073 ( 494 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 3162 (1569 ~;1575 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = inverse(sk_c2)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f52]) ).
fof(f56,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f62]) ).
fof(f66,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(X2,sk_c6) != sk_c8
| inverse(X2) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f74]) ).
fof(f77,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f78,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f81,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_3
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_3 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl0_4
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f88,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f91,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_6
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f95,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_7
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f98,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f75,f97,f94,f90,f87,f83,f80,f77]) ).
fof(f101,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f107,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f73,f105,f101]) ).
fof(f110,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f71,f105,f110]) ).
fof(f115,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f117,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f69,f105,f115]) ).
fof(f120,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f122,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f67,f105,f120]) ).
fof(f126,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f128,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f63,f126,f101]) ).
fof(f130,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f61,f126,f110]) ).
fof(f131,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f59,f126,f115]) ).
fof(f132,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f57,f126,f120]) ).
fof(f134,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f53,f90,f101]) ).
fof(f135,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f51,f90,f110]) ).
fof(f136,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f49,f90,f115]) ).
fof(f137,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f47,f90,f120]) ).
fof(f138,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f45,f90,f83]) ).
fof(f140,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f142,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f43,f140,f101]) ).
fof(f144,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f41,f140,f110]) ).
fof(f145,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f140,f115]) ).
fof(f146,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f140,f120]) ).
fof(f147,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f140,f83]) ).
fof(f149,definition,
( spl0_15
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f150,plain,
( sk_c6 != multiply(sk_c2,sk_c7)
| spl0_15 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f33,f149,f101]) ).
fof(f153,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f31,f149,f110]) ).
fof(f154,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f29,f149,f115]) ).
fof(f155,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f149,f120]) ).
fof(f156,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f149,f83]) ).
fof(f158,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f159,plain,
( sk_c8 != inverse(sk_c1)
| spl0_16 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f160,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f23,f158,f101]) ).
fof(f162,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f21,f158,f110]) ).
fof(f163,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f19,f158,f115]) ).
fof(f164,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f17,f158,f120]) ).
fof(f165,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f15,f158,f83]) ).
fof(f167,definition,
( spl0_17
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f168,plain,
( multiply(sk_c1,sk_c8) != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f169,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f13,f167,f101]) ).
fof(f171,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f11,f167,f110]) ).
fof(f172,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f9,f167,f115]) ).
fof(f173,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f7,f167,f120]) ).
fof(f174,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f5,f167,f83]) ).
fof(f175,plain,
( sk_c7 != multiply(multiply(sk_c7,sk_c8),sk_c8)
| ~ spl0_3
| spl0_5 ),
inference(forward_demodulation,[],[f92,f84]) ).
fof(f176,plain,
( sk_c7 = multiply(sk_c5,multiply(sk_c7,sk_c8))
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f103,f84]) ).
fof(f177,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c8,sk_c8))
| ~ spl0_3
| spl0_5 ),
inference(forward_demodulation,[],[f175,f4]) ).
fof(f179,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f112]) ).
fof(f180,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_12 ),
inference(superposition,[],[f3,f122]) ).
fof(f181,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f181,f4]) ).
fof(f186,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f179]) ).
fof(f187,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(sk_c8,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f117]) ).
fof(f188,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(multiply(sk_c7,sk_c8),X0))
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f4,f176]) ).
fof(f189,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c7,multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f188,f4]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f186,f1]) ).
fof(f194,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f180]) ).
fof(f195,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f194,f1]) ).
fof(f210,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f195,f117]) ).
fof(f211,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f195,f187]) ).
fof(f212,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c4,X0)) = multiply(sk_c5,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f189,f195]) ).
fof(f219,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f182,f3]) ).
fof(f220,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f182,f182]) ).
fof(f224,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_10 ),
inference(superposition,[],[f182,f190]) ).
fof(f235,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(multiply(sk_c8,sk_c8)),X0)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f224,f210]) ).
fof(f237,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f219,f220]) ).
fof(f245,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c5,multiply(multiply(sk_c8,sk_c8),sk_c8))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f176,f210]) ).
fof(f249,plain,
( ! [X0] : multiply(multiply(sk_c8,sk_c8),X0) = multiply(sk_c5,multiply(multiply(sk_c8,sk_c8),multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f189,f210]) ).
fof(f252,plain,
( ! [X0] : multiply(multiply(sk_c8,sk_c8),X0) = multiply(inverse(multiply(sk_c8,sk_c8)),multiply(multiply(sk_c8,sk_c8),multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f235]) ).
fof(f256,plain,
( multiply(sk_c8,sk_c8) = multiply(inverse(multiply(sk_c8,sk_c8)),multiply(multiply(sk_c8,sk_c8),sk_c8))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f235]) ).
fof(f259,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(multiply(sk_c8,sk_c8),X0)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f252,f182]) ).
fof(f263,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f256,f182]) ).
fof(f264,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f259,f4]) ).
fof(f301,plain,
( sk_c7 != multiply(sk_c7,sk_c8)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f177,f263]) ).
fof(f303,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f182,f263]) ).
fof(f305,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f303,f3]) ).
fof(f307,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f301,f211]) ).
fof(f309,plain,
( sk_c7 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f307,f264]) ).
fof(f311,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f309,f210]) ).
fof(f312,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f313,plain,
( ! [X2] :
( sk_c8 != multiply(X2,multiply(sk_c7,sk_c8))
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f88,f84]) ).
fof(f314,plain,
( sk_c7 = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f91,f305]) ).
fof(f315,plain,
( ! [X2] :
( sk_c8 != multiply(X2,multiply(sk_c8,multiply(sk_c8,sk_c8)))
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f313,f211]) ).
fof(f316,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f314,f237]) ).
fof(f317,plain,
( ! [X2] :
( sk_c8 != multiply(X2,multiply(sk_c8,sk_c8))
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f315,f264]) ).
fof(f318,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f316,f210]) ).
fof(f319,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c8)
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f317,f263]) ).
fof(f320,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f318,f263]) ).
fof(f321,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f319,f305]) ).
fof(f322,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f320,f305]) ).
fof(f323,plain,
( ! [X2] :
( identity != X2
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f321,f237]) ).
fof(f324,plain,
( ! [X2] :
( multiply(sk_c7,sk_c8) != inverse(X2)
| identity != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f323,f84]) ).
fof(f325,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c8,multiply(sk_c8,sk_c8))
| identity != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f324,f211]) ).
fof(f326,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c8,sk_c8)
| identity != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f325,f264]) ).
fof(f327,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| identity != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f326,f263]) ).
fof(f328,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f327,f305]) ).
fof(f340,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f180,f305]) ).
fof(f341,plain,
( sk_c7 = multiply(sk_c5,multiply(sk_c7,identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f176,f305]) ).
fof(f342,plain,
( sk_c7 = multiply(sk_c7,multiply(sk_c4,identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f341,f212]) ).
fof(f343,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f340,f1]) ).
fof(f346,plain,
( sk_c7 = multiply(sk_c8,multiply(sk_c8,multiply(sk_c4,identity)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f342,f211]) ).
fof(f349,plain,
( sk_c7 = multiply(sk_c8,multiply(sk_c4,identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f346,f264]) ).
fof(f352,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f349,f195]) ).
fof(f361,plain,
( identity != sk_c8
| identity != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f328,f122]) ).
fof(f362,plain,
( identity != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f361,f305]) ).
fof(f364,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f362,f343]) ).
fof(f365,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f370,plain,
( multiply(sk_c7,sk_c8) = inverse(sk_c3)
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f107,f84]) ).
fof(f372,plain,
( sk_c8 = multiply(sk_c3,multiply(sk_c7,sk_c8))
| ~ spl0_3
| ~ spl0_13 ),
inference(forward_demodulation,[],[f128,f84]) ).
fof(f374,plain,
( sk_c7 = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f169,f160]) ).
fof(f378,plain,
( sk_c7 = multiply(sk_c6,inverse(sk_c1))
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f91,f160]) ).
fof(f379,plain,
( ! [X2] :
( inverse(sk_c1) != multiply(X2,multiply(sk_c7,inverse(sk_c1)))
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16 ),
inference(forward_demodulation,[],[f313,f160]) ).
fof(f380,plain,
( inverse(sk_c3) = multiply(sk_c7,inverse(sk_c1))
| ~ spl0_3
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f370,f160]) ).
fof(f382,plain,
( inverse(sk_c1) = multiply(sk_c3,multiply(sk_c7,inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f372,f160]) ).
fof(f385,plain,
( sk_c7 = multiply(multiply(sk_c7,sk_c8),inverse(sk_c1))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f378,f84]) ).
fof(f386,plain,
( ! [X2] :
( inverse(sk_c1) != multiply(X2,multiply(multiply(sk_c1,inverse(sk_c1)),inverse(sk_c1)))
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f379,f374]) ).
fof(f387,plain,
( inverse(sk_c3) = multiply(multiply(sk_c1,inverse(sk_c1)),inverse(sk_c1))
| ~ spl0_3
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f380,f374]) ).
fof(f389,plain,
( inverse(sk_c1) = multiply(sk_c3,multiply(multiply(sk_c1,inverse(sk_c1)),inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f382,f374]) ).
fof(f391,plain,
( sk_c7 = multiply(sk_c7,multiply(sk_c8,inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f385,f4]) ).
fof(f392,plain,
( ! [X2] :
( inverse(sk_c1) != multiply(X2,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))))
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f386,f4]) ).
fof(f393,plain,
( inverse(sk_c3) = multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f387,f4]) ).
fof(f395,plain,
( inverse(sk_c1) = multiply(sk_c3,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f389,f4]) ).
fof(f397,plain,
( sk_c7 = multiply(sk_c7,multiply(inverse(sk_c1),inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f391,f160]) ).
fof(f398,plain,
( ! [X2] :
( multiply(sk_c7,sk_c8) != inverse(X2)
| inverse(sk_c1) != multiply(X2,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f392,f84]) ).
fof(f399,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(multiply(sk_c1,inverse(sk_c1)),multiply(inverse(sk_c1),inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f397,f374]) ).
fof(f400,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c7,inverse(sk_c1))
| inverse(sk_c1) != multiply(X2,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f398,f160]) ).
fof(f401,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c1,multiply(inverse(sk_c1),multiply(inverse(sk_c1),inverse(sk_c1))))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f399,f4]) ).
fof(f402,plain,
( ! [X2] :
( inverse(X2) != multiply(multiply(sk_c1,inverse(sk_c1)),inverse(sk_c1))
| inverse(sk_c1) != multiply(X2,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f400,f374]) ).
fof(f403,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))
| inverse(sk_c1) != multiply(X2,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f402,f4]) ).
fof(f407,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f3,f142]) ).
fof(f408,plain,
( identity = multiply(multiply(sk_c1,inverse(sk_c1)),sk_c2)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f407,f374]) ).
fof(f412,plain,
( identity = multiply(sk_c1,multiply(inverse(sk_c1),sk_c2))
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f408,f4]) ).
fof(f497,plain,
( multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))) = multiply(inverse(sk_c3),inverse(sk_c1))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f182,f395]) ).
fof(f500,plain,
( multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))) = multiply(multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))),inverse(sk_c1))
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f497,f393]) ).
fof(f502,plain,
( multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))) = multiply(sk_c1,multiply(multiply(inverse(sk_c1),inverse(sk_c1)),inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f500,f4]) ).
fof(f503,plain,
( multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))) = multiply(sk_c1,multiply(inverse(sk_c1),multiply(inverse(sk_c1),inverse(sk_c1))))
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f502,f4]) ).
fof(f504,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f503,f401]) ).
fof(f519,plain,
( multiply(inverse(sk_c1),sk_c2) = multiply(inverse(sk_c1),identity)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f182,f412]) ).
fof(f522,plain,
( inverse(sk_c1) = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f519,f237]) ).
fof(f530,plain,
( identity = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f412,f522]) ).
fof(f531,plain,
( sk_c2 = multiply(inverse(inverse(sk_c1)),inverse(sk_c1))
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f182,f522]) ).
fof(f533,plain,
( identity = sk_c2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f531,f3]) ).
fof(f538,plain,
( multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))) != multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1)))
| inverse(sk_c1) != multiply(sk_c3,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f403,f393]) ).
fof(f539,plain,
( inverse(sk_c1) != multiply(sk_c3,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f538]) ).
fof(f540,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f539,f395]) ).
fof(f541,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f564,definition,
( spl0_18
<=> identity = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f565,plain,
( identity = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f566,plain,
( identity != inverse(sk_c1)
| spl0_18 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f572,plain,
( ! [X4] :
( inverse(X4) != multiply(sk_c1,inverse(sk_c1))
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f78,f374]) ).
fof(f573,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f572,f530]) ).
fof(f574,plain,
( ! [X4] :
( sk_c7 != multiply(X4,multiply(sk_c7,sk_c8))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f573,f84]) ).
fof(f575,plain,
( ! [X4] :
( sk_c7 != multiply(X4,multiply(sk_c7,inverse(sk_c1)))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f574,f160]) ).
fof(f576,plain,
( ! [X4] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X4,multiply(multiply(sk_c1,inverse(sk_c1)),inverse(sk_c1)))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f575,f374]) ).
fof(f577,plain,
( ! [X4] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X4,multiply(sk_c1,multiply(inverse(sk_c1),inverse(sk_c1))))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f576,f4]) ).
fof(f578,plain,
( ! [X4] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X4,multiply(sk_c1,inverse(sk_c1)))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f577,f504]) ).
fof(f579,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f578,f530]) ).
fof(f580,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f579,f237]) ).
fof(f584,plain,
( sk_c7 = inverse(identity)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f142,f533]) ).
fof(f591,plain,
( identity != sk_c7
| identity != sk_c2
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f580,f142]) ).
fof(f594,plain,
( identity != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f591,f533]) ).
fof(f598,plain,
( identity != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f594,f374]) ).
fof(f601,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f598,f530]) ).
fof(f602,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f607,plain,
( ! [X3] :
( inverse(sk_c1) != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f81,f160]) ).
fof(f608,plain,
( ! [X3] :
( sk_c8 != multiply(X3,multiply(sk_c1,inverse(sk_c1)))
| inverse(sk_c1) != inverse(X3) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f607,f374]) ).
fof(f609,plain,
( ! [X3] :
( sk_c8 != multiply(X3,identity)
| inverse(sk_c1) != inverse(X3) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f608,f530]) ).
fof(f610,plain,
( ! [X3] :
( sk_c8 != X3
| inverse(sk_c1) != inverse(X3) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f609,f237]) ).
fof(f611,plain,
( ! [X3] :
( inverse(sk_c1) != inverse(X3)
| inverse(sk_c1) != X3 )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f610,f160]) ).
fof(f615,plain,
( inverse(identity) = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f374,f584]) ).
fof(f616,plain,
( identity = inverse(identity)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f615,f530]) ).
fof(f625,plain,
( sk_c7 != inverse(sk_c1)
| inverse(sk_c1) != sk_c2
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f611,f142]) ).
fof(f630,plain,
( inverse(sk_c1) != multiply(sk_c1,inverse(sk_c1))
| inverse(sk_c1) != sk_c2
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f625,f374]) ).
fof(f822,plain,
( identity != inverse(sk_c1)
| inverse(sk_c1) != sk_c2
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f630,f530]) ).
fof(f960,plain,
( inverse(sk_c1) != sk_c2
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f822,f565]) ).
fof(f964,plain,
( identity != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f960,f533]) ).
fof(f968,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f964,f565]) ).
fof(f969,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f968]) ).
fof(f973,plain,
( ! [X1] :
( sk_c6 != multiply(X1,multiply(sk_c1,inverse(sk_c1)))
| sk_c7 != inverse(X1) )
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f95,f374]) ).
fof(f974,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f973,f530]) ).
fof(f975,plain,
( ! [X1] :
( sk_c6 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f974,f237]) ).
fof(f976,plain,
( ! [X1] :
( multiply(sk_c7,sk_c8) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f975,f84]) ).
fof(f977,plain,
( ! [X1] :
( multiply(sk_c7,inverse(sk_c1)) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f976,f160]) ).
fof(f978,plain,
( ! [X1] :
( multiply(sk_c7,identity) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f977,f565]) ).
fof(f979,plain,
( ! [X1] :
( sk_c7 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f978,f237]) ).
fof(f980,plain,
( ! [X1] :
( multiply(sk_c1,inverse(sk_c1)) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f979,f374]) ).
fof(f981,plain,
( ! [X1] :
( identity != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f980,f530]) ).
fof(f982,plain,
( ! [X1] :
( inverse(X1) != multiply(sk_c1,inverse(sk_c1))
| identity != X1 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f981,f374]) ).
fof(f983,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f982,f530]) ).
fof(f986,plain,
( identity != sk_c7
| identity != sk_c2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f983,f142]) ).
fof(f992,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f986,f533]) ).
fof(f994,plain,
( identity != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f992,f374]) ).
fof(f997,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f994,f530]) ).
fof(f998,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f997]) ).
fof(f999,plain,
( ! [X0] :
( sk_c7 != multiply(X0,inverse(sk_c1))
| inverse(X0) != sk_c8 )
| ~ spl0_7
| ~ spl0_16 ),
inference(forward_demodulation,[],[f98,f160]) ).
fof(f1000,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f999,f565]) ).
fof(f1001,plain,
( ! [X0] :
( sk_c7 != X0
| inverse(X0) != sk_c8 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1000,f237]) ).
fof(f1002,plain,
( ! [X0] :
( multiply(sk_c1,inverse(sk_c1)) != X0
| inverse(X0) != sk_c8 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1001,f374]) ).
fof(f1003,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c8 )
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1002,f530]) ).
fof(f1004,plain,
( ! [X0] :
( inverse(X0) != inverse(sk_c1)
| identity != X0 )
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1003,f160]) ).
fof(f1005,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1004,f565]) ).
fof(f1020,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f565]) ).
fof(f1021,plain,
( identity = sk_c1
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1020,f1]) ).
fof(f1058,plain,
( identity != sk_c7
| identity != sk_c2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1005,f142]) ).
fof(f1065,plain,
( identity != sk_c7
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1058,f533]) ).
fof(f1069,plain,
( identity != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1065,f374]) ).
fof(f1072,plain,
( $false
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1069,f530]) ).
fof(f1073,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1072]) ).
fof(f1074,plain,
( sk_c6 != multiply(sk_c7,inverse(sk_c1))
| spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f85,f160]) ).
fof(f1076,plain,
( sk_c6 = multiply(sk_c2,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f151,f374]) ).
fof(f1082,plain,
( sk_c6 != multiply(sk_c7,identity)
| spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1074,f565]) ).
fof(f1084,plain,
( sk_c6 = multiply(sk_c2,identity)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1076,f530]) ).
fof(f1088,plain,
( sk_c7 != sk_c6
| spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1082,f237]) ).
fof(f1089,plain,
( sk_c6 = sk_c2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1084,f237]) ).
fof(f1092,plain,
( sk_c6 != multiply(sk_c1,inverse(sk_c1))
| spl0_3
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1088,f374]) ).
fof(f1093,plain,
( identity = sk_c6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1089,f533]) ).
fof(f1095,plain,
( identity != sk_c6
| spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1092,f530]) ).
fof(f1096,plain,
( $false
| spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1095,f1093]) ).
fof(f1097,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1096]) ).
fof(f1098,plain,
( sk_c7 = multiply(identity,inverse(sk_c1))
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f378,f1093]) ).
fof(f1101,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1098,f1]) ).
fof(f1104,plain,
( inverse(sk_c1) = inverse(identity)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1101,f584]) ).
fof(f1106,plain,
( identity = inverse(sk_c1)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1104,f616]) ).
fof(f1108,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f1106,f566]) ).
fof(f1109,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f1108]) ).
fof(f1112,plain,
( inverse(sk_c1) = multiply(inverse(sk_c1),inverse(sk_c1))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f263,f160]) ).
fof(f1114,plain,
( sk_c7 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f103,f322]) ).
fof(f1119,plain,
( sk_c7 = multiply(inverse(sk_c1),inverse(sk_c1))
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f210,f160]) ).
fof(f1120,plain,
( sk_c8 = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f122,f343]) ).
fof(f1121,plain,
( sk_c6 != multiply(sk_c2,multiply(sk_c1,inverse(sk_c1)))
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f150,f374]) ).
fof(f1126,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1114,f237]) ).
fof(f1131,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1119,f1112]) ).
fof(f1133,plain,
( sk_c6 != multiply(sk_c2,identity)
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1121,f530]) ).
fof(f1144,plain,
( sk_c6 != sk_c2
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1133,f237]) ).
fof(f1151,plain,
( identity != sk_c6
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1144,f533]) ).
fof(f1159,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1151,f322]) ).
fof(f1160,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1159]) ).
fof(f1167,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1120,f305]) ).
fof(f1171,plain,
( identity = inverse(sk_c1)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1131,f352]) ).
fof(f1176,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f1171,f566]) ).
fof(f1177,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f1176]) ).
fof(f1185,plain,
( identity != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_16 ),
inference(forward_demodulation,[],[f159,f305]) ).
fof(f1186,plain,
( identity = multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f169,f352]) ).
fof(f1189,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f81,f305]) ).
fof(f1192,plain,
( identity = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f112,f352]) ).
fof(f1199,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1126,f352]) ).
fof(f1200,plain,
( identity = multiply(sk_c1,identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1186,f305]) ).
fof(f1203,plain,
( ! [X3] :
( sk_c8 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1189,f352]) ).
fof(f1210,plain,
( identity = sk_c1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1200,f237]) ).
fof(f1213,plain,
( ! [X3] :
( sk_c8 != X3
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1203,f237]) ).
fof(f1217,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1213,f305]) ).
fof(f1257,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1185,f1210]) ).
fof(f1258,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1257,f1167]) ).
fof(f1259,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1258]) ).
fof(f1274,plain,
( identity != identity
| identity != identity
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1217,f1167]) ).
fof(f1277,plain,
( identity != identity
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(duplicate_literal_removal,[],[f1274]) ).
fof(f1278,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1277]) ).
fof(f1279,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1278]) ).
fof(f1285,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f95,f352]) ).
fof(f1286,plain,
( ! [X1] :
( sk_c6 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1285,f237]) ).
fof(f1287,plain,
( ! [X1] :
( identity != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1286,f322]) ).
fof(f1288,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1287,f352]) ).
fof(f1312,plain,
( identity != identity
| identity != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1288,f1192]) ).
fof(f1313,plain,
( identity != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1312]) ).
fof(f1317,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1313,f1199]) ).
fof(f1318,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1317]) ).
fof(f1322,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f98,f305]) ).
fof(f1324,plain,
( ! [X0] :
( sk_c7 != X0
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1322,f237]) ).
fof(f1326,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1324,f352]) ).
fof(f1327,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1326,f305]) ).
fof(f1366,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f78,f352]) ).
fof(f1367,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1366,f322]) ).
fof(f1368,plain,
( ! [X4] :
( sk_c7 != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1367,f237]) ).
fof(f1369,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1368,f352]) ).
fof(f1373,plain,
( identity != identity
| identity != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1369,f1192]) ).
fof(f1374,plain,
( identity != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1373]) ).
fof(f1378,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1374,f1199]) ).
fof(f1379,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1378]) ).
fof(f1386,plain,
( identity != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(forward_demodulation,[],[f168,f352]) ).
fof(f1391,plain,
( identity != multiply(sk_c1,identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(forward_demodulation,[],[f1386,f305]) ).
fof(f1393,plain,
( identity != sk_c1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(forward_demodulation,[],[f1391,f237]) ).
fof(f1395,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1393,f1021]) ).
fof(f1396,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1395]) ).
fof(f1399,plain,
( identity != identity
| identity != identity
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1327,f1167]) ).
fof(f1402,plain,
( identity != identity
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(duplicate_literal_removal,[],[f1399]) ).
fof(f1403,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1402]) ).
fof(f1404,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1403]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f99]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f108]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f118]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f123]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s8,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s10,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s12,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f134]) ).
cnf(s13,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f135]) ).
cnf(s14,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s15,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f138]) ).
cnf(s17,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f144]) ).
cnf(s19,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s20,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s22,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f152]) ).
cnf(s23,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f153]) ).
cnf(s24,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s25,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s27,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f161]) ).
cnf(s28,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f162]) ).
cnf(s29,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f163]) ).
cnf(s30,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s31,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f170]) ).
cnf(s33,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f171]) ).
cnf(s34,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f172]) ).
cnf(s35,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f173]) ).
cnf(s36,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f174]) ).
cnf(s37,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f312]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f365]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f541]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f602]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f969]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f998]) ).
cnf(s60,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s61,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1097]) ).
cnf(s62,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f1109]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1160]) ).
cnf(s70,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f1177]) ).
cnf(s75,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1259]) ).
cnf(s76,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1279]) ).
cnf(s80,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1318]) ).
cnf(s86,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1379]) ).
cnf(s90,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1396]) ).
cnf(s91,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1404]) ).
cnf(s94,plain,
spl0_3,
inference(rat,[],[s61,s62,s16,s21,s26,s31,s36]) ).
cnf(s95,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s60,s62,s17,s22,s27,s32]) ).
cnf(s96,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s62,s60]) ).
cnf(s97,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s91,s33,s34,s35,s94]) ).
cnf(s98,plain,
( spl0_16
| ~ spl0_17
| ~ spl0_8 ),
inference(rat,[],[s75,s28,s29,s30,s94]) ).
cnf(s99,plain,
( ~ spl0_14
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s67,s23,s24,s25,s96,s98,s97,s95,s94]) ).
cnf(s100,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s91,s18,s19,s20,s99,s95,s94]) ).
cnf(s101,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s62,s55,s94]) ).
cnf(s102,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_8
| ~ spl0_14
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s70,s90,s33,s34,s35,s101,s94]) ).
cnf(s103,plain,
( spl0_16
| ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s80,s28,s29,s30,s94]) ).
cnf(s104,plain,
( ~ spl0_16
| ~ spl0_8
| ~ spl0_5
| ~ spl0_14
| ~ spl0_6 ),
inference(rat,[],[s80,s23,s24,s25,s102,s94]) ).
cnf(s105,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s104,s103]) ).
cnf(s106,plain,
( ~ spl0_14
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s62,s55,s22,s27,s32,s105,s94]) ).
cnf(s107,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s80,s17,s18,s19,s20,s106,s94]) ).
cnf(s108,plain,
( spl0_7
| ~ spl0_5
| spl0_1
| spl0_4
| spl0_2 ),
inference(rat,[],[s107,s1,s94]) ).
cnf(s109,plain,
( ~ spl0_5
| spl0_4
| spl0_2
| spl0_1 ),
inference(rat,[],[s108,s100]) ).
cnf(s110,plain,
spl0_5,
inference(rat,[],[s37,s12,s13,s14,s15,s94]) ).
cnf(s113,plain,
( spl0_10
| ~ spl0_16
| ~ spl0_4 ),
inference(rat,[],[s40,s3,s8,s33,s94]) ).
cnf(s114,plain,
( spl0_11
| ~ spl0_17
| ~ spl0_16
| ~ spl0_4 ),
inference(rat,[],[s40,s4,s9,s94]) ).
cnf(s115,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s40,s5,s10,s38,s114,s113,s94]) ).
cnf(s116,plain,
( ~ spl0_16
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s38,s34,s35,s115,s113,s94]) ).
cnf(s117,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s38,s28,s29,s30,s116,s94]) ).
cnf(s118,plain,
~ spl0_4,
inference(rat,[],[s40,s2,s7,s27,s32,s117,s94]) ).
cnf(s119,plain,
( spl0_11
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s52,s62,s19,s24,s34,s110]) ).
cnf(s120,plain,
( spl0_12
| ~ spl0_17
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s62,s52,s20,s25,s110]) ).
cnf(s121,plain,
( ~ spl0_17
| ~ spl0_8
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s62,s52,s18,s23,s76,s120,s119,s110,s94]) ).
cnf(s122,plain,
( ~ spl0_8
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s76,s33,s35,s121,s119,s94]) ).
cnf(s123,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s62,s52,s17,s22,s32,s122,s110]) ).
cnf(s124,plain,
~ spl0_2,
inference(rat,[],[s76,s27,s28,s29,s30,s123,s94]) ).
cnf(s125,plain,
spl0_1,
inference(rat,[],[s109,s118,s110,s124]) ).
cnf(s126,plain,
( spl0_11
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s42,s4,s9,s19,s125,s94,s110]) ).
cnf(s127,plain,
( spl0_12
| ~ spl0_14
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s42,s5,s10,s125,s94,s110]) ).
cnf(s128,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s42,s3,s8,s86,s127,s126,s125,s94,s110]) ).
cnf(s129,plain,
( ~ spl0_17
| ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s86,s18,s20,s128,s126,s94,s110,s125]) ).
cnf(s130,plain,
( ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s86,s33,s34,s35,s129,s125,s110,s94]) ).
cnf(s131,plain,
~ spl0_16,
inference(rat,[],[s42,s2,s7,s17,s32,s130,s125,s94,s110]) ).
cnf(s132,plain,
spl0_12,
inference(rat,[],[s30,s131]) ).
cnf(s133,plain,
spl0_11,
inference(rat,[],[s29,s131]) ).
cnf(s134,plain,
spl0_10,
inference(rat,[],[s28,s131]) ).
cnf(s135,plain,
spl0_8,
inference(rat,[],[s27,s131]) ).
cnf(s138,plain,
$false,
inference(rat,[],[s86,s135,s125,s110,s94,s133,s132,s134]) ).
fof(f1410,plain,
$false,
inference(avatar_sat_refutation,[],[s138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:46:45 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49 % (1411110)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (1411120)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1251527794:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (1411116)% WARNING: option uhcvi not known.
% 0.18/0.49 % (1411116)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=360856908:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (1411115)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2409066934_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (1411119)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=120033868:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (1411117)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3505868247:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (1411118)dis+10_1_sil=32000:sp=arity:random_seed=2218559642:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (1411121)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=784779577:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % TRYING [1]
% 0.18/0.49 % TRYING [2]
% 0.18/0.49 % (1411120) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1411110-1411120"...
% 0.18/0.49 % TRYING [3]
% 0.18/0.49 % TRYING [4]
% 0.18/0.49 % (1411120)...printing done.
% 0.18/0.49 % (1411120)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (1411120)------------------------------
% 0.18/0.50 % (1411120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (1411120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (1411120)CaDiCaL version: 2.1.3
% 0.18/0.50 % (1411120)Termination reason: Refutation
% 0.18/0.50 % (1411120)Time elapsed: 0.015 s
% 0.18/0.50 % (1411120)Peak memory usage: 12 MB
% 0.18/0.50 % (1411120)Instructions burned: 44 (million)
% 0.18/0.50 % (1411110)Success in time 0.057 s
% 0.18/0.50 % Vampire exiting
%------------------------------------------------------------------------------