%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP317-1 : 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 : 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 10:17:28 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 60
% Syntax : Number of formulae : 430 ( 26 unt; 19 def)
% Number of atoms : 1651 ( 462 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2371 (1150 ~;1202 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 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_c8,sk_c9) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f75]) ).
fof(f83,negated_conjecture,
( inverse(sk_c4) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( inverse(sk_c4) = sk_c3
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f83]) ).
fof(f87,negated_conjecture,
( inverse(sk_c4) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( inverse(sk_c4) = sk_c3
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f95,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f95]) ).
fof(f99,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f99]) ).
fof(f107,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f108,plain,
( sk_c3 = multiply(sk_c4,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f107]) ).
fof(f111,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f112,plain,
( sk_c3 = multiply(sk_c4,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f111]) ).
fof(f113,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| inverse(X2) != X3
| inverse(X3) != sk_c9
| multiply(X2,sk_c9) != X3
| multiply(sk_c8,sk_c7) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(X5,sk_c9) != sk_c7
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| inverse(X2) != X3
| sk_c9 != inverse(X3)
| multiply(X2,sk_c9) != X3
| sk_c9 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(sk_c8)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f113]) ).
fof(f116,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f117,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f120,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_3
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f123,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( sk_c7 != inverse(sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl0_4
<=> sk_c9 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f127,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( sk_c9 != multiply(sk_c8,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f130,definition,
( spl0_5
<=> ! [X2,X3] :
( inverse(X2) != X3
| multiply(X2,sk_c9) != X3
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f131,plain,
( ! [X2,X3] :
( inverse(X2) != X3
| multiply(X2,sk_c9) != X3
| sk_c9 != inverse(X3) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl0_6
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f135,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| spl0_6 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,definition,
( spl0_7
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f138,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl0_8
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f141,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f142,plain,
( multiply(sk_c8,sk_c9) != sk_c7
| spl0_8 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_2
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f114,f140,f137,f133,f119,f130,f126,f122,f119,f116]) ).
fof(f145,definition,
( spl0_9
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f147,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f149,definition,
( spl0_10
<=> sk_c3 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f151,plain,
( sk_c3 = multiply(sk_c4,sk_c9)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f112,f149,f145]) ).
fof(f154,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f156,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f159,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f161,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_12
| spl0_10 ),
inference(avatar_split_clause,[],[f108,f149,f159]) ).
fof(f164,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f165,plain,
( sk_c9 != multiply(sk_c5,sk_c8)
| spl0_13 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f171,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f173,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f100,f171,f145]) ).
fof(f176,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f96,f171,f159]) ).
fof(f181,definition,
( spl0_15
<=> inverse(sk_c4) = sk_c3 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f183,plain,
( inverse(sk_c4) = sk_c3
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f88,f181,f145]) ).
fof(f186,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f84,f181,f159]) ).
fof(f191,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f193,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f76,f191,f145]) ).
fof(f195,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f74,f191,f154]) ).
fof(f196,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f72,f191,f159]) ).
fof(f197,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f70,f191,f164]) ).
fof(f198,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f68,f191,f122]) ).
fof(f199,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f66,f191,f126]) ).
fof(f201,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f203,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f201,f145]) ).
fof(f205,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f62,f201,f154]) ).
fof(f206,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f60,f201,f159]) ).
fof(f207,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f58,f201,f164]) ).
fof(f208,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f56,f201,f122]) ).
fof(f209,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f54,f201,f126]) ).
fof(f210,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f52,f133,f145]) ).
fof(f211,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f50,f133,f154]) ).
fof(f212,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f48,f133,f159]) ).
fof(f213,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f46,f133,f164]) ).
fof(f217,definition,
( spl0_18
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f219,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f220,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f40,f217,f145]) ).
fof(f221,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f38,f217,f154]) ).
fof(f222,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f36,f217,f159]) ).
fof(f224,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f217,f122]) ).
fof(f225,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f217,f126]) ).
fof(f227,definition,
( spl0_19
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f229,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f28,f227,f145]) ).
fof(f231,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f26,f227,f154]) ).
fof(f232,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f24,f227,f159]) ).
fof(f234,plain,
( spl0_3
| spl0_19 ),
inference(avatar_split_clause,[],[f20,f227,f122]) ).
fof(f235,plain,
( spl0_4
| spl0_19 ),
inference(avatar_split_clause,[],[f18,f227,f126]) ).
fof(f236,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f16,f140,f145]) ).
fof(f237,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f14,f140,f154]) ).
fof(f238,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f12,f140,f159]) ).
fof(f240,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f140,f122]) ).
fof(f241,plain,
( spl0_4
| spl0_8 ),
inference(avatar_split_clause,[],[f6,f140,f126]) ).
fof(f242,plain,
( sk_c9 = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f127,f123]) ).
fof(f243,plain,
( multiply(sk_c8,sk_c9) != inverse(sk_c8)
| ~ spl0_3
| spl0_8 ),
inference(forward_demodulation,[],[f142,f123]) ).
fof(f244,plain,
( inverse(sk_c8) = multiply(sk_c6,sk_c9)
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_demodulation,[],[f156,f123]) ).
fof(f245,plain,
( inverse(sk_c8) != multiply(sk_c8,multiply(sk_c8,inverse(sk_c8)))
| ~ spl0_3
| ~ spl0_4
| spl0_8 ),
inference(forward_demodulation,[],[f243,f242]) ).
fof(f246,plain,
( inverse(sk_c8) = multiply(sk_c6,multiply(sk_c8,inverse(sk_c8)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f244,f242]) ).
fof(f247,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f249,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f161]) ).
fof(f250,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f251,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f250,f4]) ).
fof(f258,plain,
( ! [X0] : multiply(sk_c6,multiply(multiply(sk_c8,inverse(sk_c8)),X0)) = multiply(inverse(sk_c8),X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f4,f246]) ).
fof(f259,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = multiply(sk_c6,multiply(sk_c8,multiply(inverse(sk_c8),X0)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f4]) ).
fof(f265,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f249]) ).
fof(f266,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f265,f1]) ).
fof(f270,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f266,f166]) ).
fof(f273,plain,
( sk_c8 = multiply(sk_c8,multiply(sk_c8,inverse(sk_c8)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f270,f242]) ).
fof(f287,plain,
( identity = multiply(sk_c6,multiply(sk_c8,identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f259,f3]) ).
fof(f296,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f251,f3]) ).
fof(f297,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f251,f251]) ).
fof(f298,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_12 ),
inference(superposition,[],[f251,f249]) ).
fof(f300,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = multiply(sk_c5,X0)
| ~ spl0_12 ),
inference(superposition,[],[f251,f266]) ).
fof(f301,plain,
( multiply(sk_c8,inverse(sk_c8)) = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f251,f273]) ).
fof(f313,plain,
( identity = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f301,f3]) ).
fof(f314,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f296,f297]) ).
fof(f324,plain,
( ! [X0] : multiply(sk_c8,multiply(multiply(inverse(sk_c8),identity),X0)) = X0
| ~ spl0_12 ),
inference(superposition,[],[f266,f298]) ).
fof(f326,plain,
( sk_c9 = multiply(multiply(inverse(sk_c8),identity),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f166,f298]) ).
fof(f329,plain,
( sk_c9 = multiply(inverse(sk_c8),multiply(identity,sk_c8))
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f326,f4]) ).
fof(f331,plain,
( ! [X0] : multiply(sk_c8,multiply(inverse(sk_c8),multiply(identity,X0))) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f324,f4]) ).
fof(f333,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f329,f1]) ).
fof(f334,plain,
( ! [X0] : multiply(sk_c8,multiply(inverse(sk_c8),X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f331,f1]) ).
fof(f336,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f333,f3]) ).
fof(f343,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c9,sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f247,f147]) ).
fof(f361,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(multiply(sk_c8,inverse(sk_c8)),sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f343,f242]) ).
fof(f367,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c8,multiply(inverse(sk_c8),sk_c6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f361,f4]) ).
fof(f370,plain,
( ! [X0] : multiply(inverse(X0),X0) = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f367,f334]) ).
fof(f381,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f3,f370]) ).
fof(f386,plain,
( ! [X0] : inverse(sk_c8) = multiply(multiply(inverse(X0),X0),multiply(sk_c8,inverse(sk_c8)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f246,f370]) ).
fof(f387,plain,
( ! [X0] : sk_c9 = inverse(multiply(inverse(X0),X0))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f147,f370]) ).
fof(f388,plain,
( ! [X0] : inverse(sk_c8) = multiply(inverse(X0),multiply(X0,multiply(sk_c8,inverse(sk_c8))))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f386,f4]) ).
fof(f394,plain,
( inverse(sk_c8) = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f388,f251]) ).
fof(f399,plain,
( identity = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f394,f313]) ).
fof(f407,plain,
( sk_c9 = inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f147,f381]) ).
fof(f408,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f407,f336]) ).
fof(f414,plain,
( identity = multiply(identity,multiply(sk_c8,identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f287,f381]) ).
fof(f422,plain,
( identity = multiply(sk_c8,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f414,f1]) ).
fof(f425,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f422,f314]) ).
fof(f430,plain,
( inverse(identity) != multiply(identity,multiply(identity,inverse(identity)))
| ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f245,f425]) ).
fof(f450,plain,
( inverse(identity) != multiply(identity,inverse(identity))
| ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f430,f1]) ).
fof(f459,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f450,f1]) ).
fof(f460,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f471,plain,
( sk_c8 != multiply(sk_c9,inverse(sk_c8))
| ~ spl0_3
| spl0_6 ),
inference(forward_demodulation,[],[f135,f123]) ).
fof(f473,plain,
( sk_c8 != multiply(sk_c9,identity)
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f471,f399]) ).
fof(f475,plain,
( sk_c8 != sk_c9
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f473,f314]) ).
fof(f477,plain,
( sk_c8 != multiply(sk_c8,inverse(sk_c8))
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f475,f242]) ).
fof(f479,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f477,f313]) ).
fof(f481,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f479,f425]) ).
fof(f482,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f484,plain,
( ! [X0] :
( sk_c8 != multiply(X0,multiply(sk_c8,inverse(sk_c8)))
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f138,f242]) ).
fof(f486,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f484,f313]) ).
fof(f488,plain,
( ! [X0] :
( sk_c8 != X0
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f486,f314]) ).
fof(f490,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f488,f425]) ).
fof(f491,plain,
( ! [X0] :
( inverse(X0) != multiply(sk_c8,inverse(sk_c8))
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f490,f242]) ).
fof(f492,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f491,f313]) ).
fof(f494,plain,
( identity != sk_c9
| identity != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f492,f147]) ).
fof(f497,plain,
( identity != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f494,f336]) ).
fof(f500,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f497,f381]) ).
fof(f501,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f500]) ).
fof(f502,plain,
( ! [X5] :
( sk_c7 != multiply(X5,multiply(sk_c8,inverse(sk_c8)))
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f117,f242]) ).
fof(f503,plain,
( ! [X5] :
( sk_c7 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f502,f313]) ).
fof(f504,plain,
( ! [X5] :
( sk_c7 != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f503,f314]) ).
fof(f505,plain,
( ! [X5] :
( inverse(sk_c8) != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f504,f123]) ).
fof(f506,plain,
( ! [X5] :
( identity != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f505,f399]) ).
fof(f507,plain,
( ! [X5] :
( inverse(X5) != multiply(sk_c8,inverse(sk_c8))
| identity != X5 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f506,f242]) ).
fof(f508,plain,
( ! [X5] :
( identity != inverse(X5)
| identity != X5 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f507,f313]) ).
fof(f528,plain,
( identity != sk_c9
| identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f508,f147]) ).
fof(f531,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f528,f336]) ).
fof(f534,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f531,f381]) ).
fof(f535,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f536,plain,
( ! [X4] :
( sk_c9 != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f120,f425]) ).
fof(f537,plain,
( ! [X4] :
( sk_c9 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f536,f314]) ).
fof(f538,plain,
( ! [X4] :
( multiply(sk_c8,inverse(sk_c8)) != X4
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f537,f242]) ).
fof(f539,plain,
( ! [X4] :
( identity != X4
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f538,f313]) ).
fof(f540,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f539,f425]) ).
fof(f561,plain,
( identity != sk_c9
| identity != sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f540,f147]) ).
fof(f568,plain,
( identity != sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f561,f336]) ).
fof(f571,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f568,f381]) ).
fof(f572,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f571]) ).
fof(f573,plain,
( ! [X2,X3] :
( multiply(X2,multiply(sk_c8,inverse(sk_c8))) != X3
| inverse(X2) != X3
| sk_c9 != inverse(X3) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f131,f242]) ).
fof(f574,plain,
( ! [X2,X3] :
( multiply(X2,identity) != X3
| inverse(X2) != X3
| sk_c9 != inverse(X3) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f573,f313]) ).
fof(f575,plain,
( ! [X2,X3] :
( X2 != X3
| inverse(X2) != X3
| sk_c9 != inverse(X3) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f574,f314]) ).
fof(f576,plain,
( ! [X2,X3] :
( inverse(X3) != multiply(sk_c8,inverse(sk_c8))
| X2 != X3
| inverse(X2) != X3 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f575,f242]) ).
fof(f577,plain,
( ! [X2,X3] :
( identity != inverse(X3)
| X2 != X3
| inverse(X2) != X3 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f576,f313]) ).
fof(f587,plain,
( ! [X0] :
( identity != identity
| identity != X0
| identity != inverse(X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f577,f408]) ).
fof(f592,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f587]) ).
fof(f1183,plain,
( ! [X0] :
( identity != sk_c9
| identity != multiply(inverse(X0),X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f592,f387]) ).
fof(f1196,plain,
( ! [X0] : identity != multiply(inverse(X0),X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1183,f336]) ).
fof(f1202,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1196,f3]) ).
fof(f1203,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1202]) ).
fof(f1248,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_16 ),
inference(superposition,[],[f3,f193]) ).
fof(f1275,plain,
( sk_c9 != multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| spl0_13 ),
inference(forward_demodulation,[],[f165,f300]) ).
fof(f1276,plain,
( sk_c9 = inverse(inverse(sk_c4))
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f173,f183]) ).
fof(f1278,plain,
( identity != sk_c9
| ~ spl0_12
| spl0_13 ),
inference(forward_demodulation,[],[f1275,f3]) ).
fof(f1279,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f219]) ).
fof(f1289,plain,
( multiply(sk_c8,sk_c9) != inverse(sk_c8)
| spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f124,f141]) ).
fof(f1291,plain,
( inverse(sk_c4) = multiply(sk_c4,sk_c9)
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f183,f151]) ).
fof(f1297,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f251,f203]) ).
fof(f1299,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1297,f193]) ).
fof(f1312,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_16 ),
inference(superposition,[],[f251,f1248]) ).
fof(f1315,plain,
( inverse(sk_c8) = sk_c2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1312,f314]) ).
fof(f1321,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f203,f1315]) ).
fof(f1323,plain,
( identity = sk_c9
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1321,f3]) ).
fof(f1324,plain,
( $false
| ~ spl0_12
| spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1323,f1278]) ).
fof(f1325,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1324]) ).
fof(f1327,plain,
( sk_c8 = multiply(sk_c1,identity)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f229,f1323]) ).
fof(f1330,plain,
( sk_c8 = sk_c1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1327,f314]) ).
fof(f1335,plain,
( sk_c9 = inverse(sk_c8)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f219,f1330]) ).
fof(f1336,plain,
( identity = inverse(sk_c8)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1335,f1323]) ).
fof(f1337,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1279,f1323]) ).
fof(f1338,plain,
( identity = multiply(sk_c9,sk_c8)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f1279,f1330]) ).
fof(f1343,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1338,f1323]) ).
fof(f1344,plain,
( identity = sk_c1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1337,f1]) ).
fof(f1346,plain,
( identity = sk_c8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1343,f1]) ).
fof(f1367,plain,
( inverse(sk_c8) != multiply(sk_c8,identity)
| spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1289,f1323]) ).
fof(f1368,plain,
( sk_c8 != inverse(sk_c8)
| spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1367,f314]) ).
fof(f1369,plain,
( identity != sk_c8
| spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1368,f1336]) ).
fof(f1370,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1369,f1346]) ).
fof(f1371,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1370]) ).
fof(f1372,plain,
( ! [X5] :
( sk_c7 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f117,f1323]) ).
fof(f1374,plain,
( ! [X5] :
( sk_c7 != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1372,f314]) ).
fof(f1375,plain,
( ! [X5] :
( multiply(sk_c8,sk_c9) != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1374,f141]) ).
fof(f1376,plain,
( ! [X5] :
( sk_c8 != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1375,f1299]) ).
fof(f1377,plain,
( ! [X5] :
( identity != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1376,f1346]) ).
fof(f1378,plain,
( ! [X5] :
( identity != inverse(X5)
| identity != X5 )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1377,f1323]) ).
fof(f1391,plain,
( identity != sk_c8
| identity != sk_c2
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f1378,f193]) ).
fof(f1392,plain,
( identity != sk_c2
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1391,f1346]) ).
fof(f1395,plain,
( identity != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1392,f1315]) ).
fof(f1399,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1395,f1336]) ).
fof(f1400,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1399]) ).
fof(f1403,plain,
( sk_c9 != multiply(sk_c8,multiply(sk_c8,sk_c9))
| spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f128,f141]) ).
fof(f1406,plain,
( sk_c9 != multiply(sk_c8,sk_c8)
| spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1403,f1299]) ).
fof(f1408,plain,
( sk_c9 != multiply(identity,identity)
| spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1406,f1346]) ).
fof(f1410,plain,
( identity != sk_c9
| spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1408,f1]) ).
fof(f1411,plain,
( $false
| spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1410,f1323]) ).
fof(f1412,plain,
( spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1411]) ).
fof(f1414,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c9 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f138,f1323]) ).
fof(f1417,plain,
( ! [X0] :
( sk_c8 != X0
| inverse(X0) != sk_c9 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1414,f314]) ).
fof(f1419,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c9 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1417,f1346]) ).
fof(f1421,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1419,f1323]) ).
fof(f1453,plain,
( identity != sk_c9
| identity != sk_c1
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f1421,f219]) ).
fof(f1457,plain,
( identity != sk_c1
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1453,f1323]) ).
fof(f1463,plain,
( $false
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1457,f1344]) ).
fof(f1464,plain,
( ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1463]) ).
fof(f1468,plain,
( ! [X2,X3] :
( multiply(X2,identity) != X3
| inverse(X2) != X3
| sk_c9 != inverse(X3) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f131,f1323]) ).
fof(f1469,plain,
( ! [X2,X3] :
( X2 != X3
| inverse(X2) != X3
| sk_c9 != inverse(X3) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1468,f314]) ).
fof(f1470,plain,
( ! [X2,X3] :
( identity != inverse(X3)
| X2 != X3
| inverse(X2) != X3 )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1469,f1323]) ).
fof(f1481,plain,
( ! [X0] :
( identity != sk_c9
| inverse(sk_c4) != X0
| inverse(X0) != inverse(sk_c4) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1470,f1276]) ).
fof(f1490,plain,
( ! [X0] :
( inverse(sk_c4) != X0
| inverse(X0) != inverse(sk_c4) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1481,f1323]) ).
fof(f1494,plain,
( ! [X0] :
( multiply(sk_c4,sk_c9) != X0
| inverse(X0) != inverse(sk_c4) )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1490,f1291]) ).
fof(f1497,plain,
( ! [X0] :
( multiply(sk_c4,identity) != X0
| inverse(X0) != inverse(sk_c4) )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1494,f1323]) ).
fof(f1500,plain,
( ! [X0] :
( sk_c4 != X0
| inverse(X0) != inverse(sk_c4) )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1497,f314]) ).
fof(f1503,plain,
( ! [X0] :
( inverse(X0) != multiply(sk_c4,sk_c9)
| sk_c4 != X0 )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1500,f1291]) ).
fof(f1504,plain,
( ! [X0] :
( inverse(X0) != multiply(sk_c4,identity)
| sk_c4 != X0 )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1503,f1323]) ).
fof(f1505,plain,
( ! [X0] :
( inverse(X0) != sk_c4
| sk_c4 != X0 )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1504,f314]) ).
fof(f1520,plain,
( sk_c9 = inverse(multiply(sk_c4,sk_c9))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1276,f1291]) ).
fof(f1530,plain,
( identity = inverse(multiply(sk_c4,identity))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1520,f1323]) ).
fof(f1535,plain,
( identity = inverse(sk_c4)
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1530,f314]) ).
fof(f1543,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f1535]) ).
fof(f1546,plain,
( ! [X0] : multiply(identity,multiply(sk_c4,X0)) = X0
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f251,f1535]) ).
fof(f1549,plain,
( ! [X0] : multiply(sk_c4,X0) = X0
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1546,f1]) ).
fof(f1552,plain,
( identity = sk_c4
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1543,f1]) ).
fof(f1575,plain,
( sk_c9 != sk_c4
| sk_c4 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1505,f1276]) ).
fof(f1584,plain,
( identity != sk_c9
| sk_c4 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1575,f1552]) ).
fof(f1586,plain,
( sk_c4 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1584,f1323]) ).
fof(f1589,plain,
( sk_c4 != multiply(sk_c4,sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1586,f1291]) ).
fof(f1590,plain,
( sk_c9 != sk_c4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1589,f1549]) ).
fof(f1591,plain,
( identity != sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1590,f1552]) ).
fof(f1592,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1591,f1323]) ).
fof(f1593,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1592]) ).
fof(f1594,plain,
( ! [X4] :
( sk_c9 != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f120,f1346]) ).
fof(f1595,plain,
( ! [X4] :
( sk_c9 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1594,f314]) ).
fof(f1596,plain,
( ! [X4] :
( identity != X4
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1595,f1323]) ).
fof(f1597,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1596,f1346]) ).
fof(f1613,plain,
( identity != sk_c9
| identity != sk_c1
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f1597,f219]) ).
fof(f1627,plain,
( identity != sk_c1
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1613,f1323]) ).
fof(f1636,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1627,f1344]) ).
fof(f1637,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1636]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f143]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f152]) ).
cnf(s5,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f162]) ).
cnf(s9,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f174]) ).
cnf(s11,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f176]) ).
cnf(s15,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f184]) ).
cnf(s17,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f186]) ).
cnf(s21,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f194]) ).
cnf(s22,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s23,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f196]) ).
cnf(s24,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f197]) ).
cnf(s25,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s26,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f199]) ).
cnf(s27,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s28,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s29,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s30,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s31,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s32,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f209]) ).
cnf(s33,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f210]) ).
cnf(s34,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f211]) ).
cnf(s35,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f212]) ).
cnf(s36,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f213]) ).
cnf(s39,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f220]) ).
cnf(s40,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s41,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s43,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f224]) ).
cnf(s44,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f225]) ).
cnf(s45,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s46,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f231]) ).
cnf(s47,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f232]) ).
cnf(s49,plain,
( spl0_3
| spl0_19 ),
inference(sat_conversion,[],[f234]) ).
cnf(s50,plain,
( spl0_4
| spl0_19 ),
inference(sat_conversion,[],[f235]) ).
cnf(s51,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f236]) ).
cnf(s52,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f237]) ).
cnf(s53,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f238]) ).
cnf(s55,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f240]) ).
cnf(s56,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f241]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f460]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f482]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f501]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f535]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f572]) ).
cnf(s71,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1203]) ).
cnf(s75,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1325]) ).
cnf(s77,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1371]) ).
cnf(s79,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1400]) ).
cnf(s80,plain,
( spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1412]) ).
cnf(s83,plain,
( ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1464]) ).
cnf(s86,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1593]) ).
cnf(s92,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1637]) ).
cnf(s95,plain,
spl0_3,
inference(rat,[],[s77,s25,s31,s43,s49,s55]) ).
cnf(s96,plain,
spl0_4,
inference(rat,[],[s80,s26,s32,s44,s50,s56]) ).
cnf(s97,plain,
spl0_8,
inference(rat,[],[s58,s51,s52,s53,s95,s96]) ).
cnf(s98,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_7
| ~ spl0_9 ),
inference(rat,[],[s75,s24,s30,s61,s96,s95]) ).
cnf(s99,plain,
( spl0_12
| ~ spl0_7 ),
inference(rat,[],[s83,s23,s29,s41,s47]) ).
cnf(s100,plain,
( spl0_11
| ~ spl0_7 ),
inference(rat,[],[s83,s22,s28,s40,s46]) ).
cnf(s101,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_7 ),
inference(rat,[],[s83,s21,s27,s39,s45,s98]) ).
cnf(s102,plain,
~ spl0_7,
inference(rat,[],[s101,s100,s99]) ).
cnf(s103,plain,
spl0_6,
inference(rat,[],[s59,s33,s34,s35,s36,s95,s96]) ).
cnf(s104,plain,
( ~ spl0_12
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s75,s24,s30,s71,s96,s95]) ).
cnf(s105,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s86,s5,s11,s17,s23,s29]) ).
cnf(s106,plain,
( ~ spl0_12
| ~ spl0_5 ),
inference(rat,[],[s86,s3,s9,s15,s21,s27,s104]) ).
cnf(s107,plain,
~ spl0_5,
inference(rat,[],[s106,s105]) ).
cnf(s108,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_12
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s92,s40,s46,s66,s75,s95,s96]) ).
cnf(s109,plain,
( spl0_17
| ~ spl0_12
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s66,s28,s30,s95,s96]) ).
cnf(s110,plain,
( ~ spl0_17
| ~ spl0_12
| ~ spl0_2
| ~ spl0_9 ),
inference(rat,[],[s66,s22,s24,s108,s96,s95]) ).
cnf(s111,plain,
( ~ spl0_12
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s110,s109]) ).
cnf(s112,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s92,s23,s29,s41,s47]) ).
cnf(s113,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s92,s21,s27,s39,s45,s111]) ).
cnf(s114,plain,
~ spl0_2,
inference(rat,[],[s113,s112]) ).
cnf(s115,plain,
spl0_1,
inference(rat,[],[s2,s97,s102,s95,s103,s96,s107,s114]) ).
cnf(s116,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_12
| ~ spl0_9 ),
inference(rat,[],[s79,s40,s46,s63,s75,s97,s115,s95,s96]) ).
cnf(s117,plain,
( spl0_16
| ~ spl0_12
| ~ spl0_9 ),
inference(rat,[],[s63,s22,s24,s95,s96,s115]) ).
cnf(s118,plain,
( ~ spl0_16
| ~ spl0_12
| ~ spl0_9 ),
inference(rat,[],[s63,s28,s30,s116,s115,s96,s95]) ).
cnf(s119,plain,
( ~ spl0_12
| ~ spl0_9 ),
inference(rat,[],[s118,s117]) ).
cnf(s120,plain,
spl0_12,
inference(rat,[],[s79,s23,s29,s41,s47,s97,s115]) ).
cnf(s121,plain,
~ spl0_9,
inference(rat,[],[s119,s120]) ).
cnf(s122,plain,
spl0_19,
inference(rat,[],[s45,s121]) ).
cnf(s123,plain,
spl0_18,
inference(rat,[],[s39,s121]) ).
cnf(s124,plain,
spl0_17,
inference(rat,[],[s27,s121]) ).
cnf(s125,plain,
spl0_16,
inference(rat,[],[s21,s121]) ).
cnf(s129,plain,
$false,
inference(rat,[],[s79,s125,s124,s115,s97,s122,s123]) ).
fof(f1642,plain,
$false,
inference(avatar_sat_refutation,[],[s129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:52:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.46 % (2587313)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (2587323)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3437112934:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (2587318)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=386188142_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (2587320)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2680218420:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (2587321)dis+10_1_sil=32000:sp=arity:random_seed=4283376706:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (2587322)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=523272459:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (2587324)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1437914434:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (2587319)% WARNING: option uhcvi not known.
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % (2587323) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2587313-2587323"...
% 0.10/0.46 % (2587319)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1308174119:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (2587323)...printing done.
% 0.10/0.46 % TRYING [4]
% 0.10/0.46 % (2587323)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2587323)------------------------------
% 0.15/0.47 % (2587323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2587323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2587323)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2587323)Termination reason: Refutation
% 0.15/0.47 % (2587323)Time elapsed: 0.015 s
% 0.15/0.47 % (2587323)Peak memory usage: 12 MB
% 0.15/0.47 % (2587323)Instructions burned: 44 (million)
% 0.15/0.47 % (2587313)Success in time 0.044 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------