%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP324-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 10:17:29 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 52
% Syntax : Number of formulae : 338 ( 22 unt; 24 def)
% Number of atoms : 996 ( 308 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1248 ( 590 ~; 634 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X4,sk_c7) != sk_c6
| inverse(X4) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != inverse(sk_c8)
| sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != inverse(sk_c8)
| sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) ),
inference(equality_resolution,[],[f78]) ).
fof(f81,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_2
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( sk_c6 != inverse(sk_c8)
| spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,definition,
( spl0_4
<=> sk_c6 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f95,definition,
( spl0_5
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f96,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_6
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f99,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_7
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f102,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f79,f101,f98,f95,f91,f88,f84,f81]) ).
fof(f106,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f112,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f110,f106]) ).
fof(f115,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c5,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f117,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f74,f110,f115]) ).
fof(f119,plain,
( spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f110,f84]) ).
fof(f121,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f123,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f126,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f130,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f66,f110,f91]) ).
fof(f132,definition,
( spl0_13
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f64,f132,f106]) ).
fof(f136,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f62,f132,f115]) ).
fof(f137,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f60,f132,f84]) ).
fof(f140,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f132,f91]) ).
fof(f142,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f142,f106]) ).
fof(f146,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f142,f115]) ).
fof(f147,plain,
( spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f142,f84]) ).
fof(f150,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f142,f91]) ).
fof(f152,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f154,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f152,f106]) ).
fof(f156,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f152,f115]) ).
fof(f157,plain,
( spl0_2
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f152,f84]) ).
fof(f160,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f152,f91]) ).
fof(f162,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f162,f106]) ).
fof(f166,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f162,f115]) ).
fof(f167,plain,
( spl0_2
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f162,f84]) ).
fof(f170,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f18,f162,f91]) ).
fof(f173,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f101,f84]) ).
fof(f174,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f101,f121]) ).
fof(f175,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f101,f126]) ).
fof(f176,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f101,f91]) ).
fof(f177,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f3,f85]) ).
fof(f181,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_4 ),
inference(superposition,[],[f4,f92]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f181,f1]) ).
fof(f189,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_2 ),
inference(superposition,[],[f4,f177]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c8,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f189,f1]) ).
fof(f200,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f190,f92]) ).
fof(f230,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f187,f117]) ).
fof(f231,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f187,f128]) ).
fof(f239,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f231,f123]) ).
fof(f240,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f230,f108]) ).
fof(f245,plain,
( sk_c8 = sk_c6
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f239,f92]) ).
fof(f249,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f187,f239]) ).
fof(f251,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f3]) ).
fof(f256,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f187,f240]) ).
fof(f258,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f256,f3]) ).
fof(f275,plain,
( sk_c6 != multiply(identity,sk_c8)
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f103,f251]) ).
fof(f287,plain,
( sk_c8 != sk_c6
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f275,f1]) ).
fof(f290,plain,
( $false
| ~ spl0_4
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f287,f245]) ).
fof(f291,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f360,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f177,f258]) ).
fof(f362,plain,
( sk_c7 = multiply(identity,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f200,f258]) ).
fof(f370,plain,
( identity = sk_c7
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f362,f1]) ).
fof(f372,plain,
( identity = sk_c8
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f360,f1]) ).
fof(f387,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f112]) ).
fof(f395,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f187,f134]) ).
fof(f397,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f395,f112]) ).
fof(f428,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f187,f144]) ).
fof(f431,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f187,f164]) ).
fof(f433,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f431,f154]) ).
fof(f443,plain,
( sk_c7 != multiply(sk_c8,sk_c3)
| sk_c8 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f96,f134]) ).
fof(f447,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| sk_c8 != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f96,f183]) ).
fof(f448,plain,
( identity != sk_c7
| sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f447,f177]) ).
fof(f450,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f443,f144]) ).
fof(f461,definition,
( spl0_21
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f463,plain,
( sk_c8 != inverse(sk_c7)
| spl0_21 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f470,definition,
( spl0_23
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f471,plain,
( identity = sk_c7
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f473,plain,
( ~ spl0_21
| ~ spl0_23
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f448,f95,f91,f84,f470,f461]) ).
fof(f475,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f450,f112]) ).
fof(f476,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f482,plain,
( sk_c8 != sk_c6
| sk_c7 != inverse(sk_c8)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f99,f92]) ).
fof(f484,plain,
( sk_c8 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f99,f164]) ).
fof(f488,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f484]) ).
fof(f494,definition,
( spl0_25
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f495,plain,
( identity = sk_c8
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f496,plain,
( identity != sk_c8
| spl0_25 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f499,definition,
( spl0_26
<=> sk_c7 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f500,plain,
( sk_c7 = inverse(identity)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f501,plain,
( sk_c7 != inverse(identity)
| spl0_26 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f503,definition,
( spl0_27
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f504,plain,
( sk_c7 = sk_c8
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f505,plain,
( sk_c7 != sk_c8
| spl0_27 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f507,plain,
( $false
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f488,f154]) ).
fof(f508,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f509,plain,
( sk_c7 != sk_c6
| sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f482,f85]) ).
fof(f515,definition,
( spl0_29
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f516,plain,
( sk_c7 = sk_c6
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f517,plain,
( sk_c7 != sk_c6
| spl0_29 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f519,plain,
( sk_c7 = sk_c8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f397,f144]) ).
fof(f520,plain,
( spl0_27
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f519,f142,f132,f110,f503]) ).
fof(f524,plain,
( sk_c7 != sk_c3
| sk_c8 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f89,f134]) ).
fof(f527,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,sk_c8))
| sk_c8 != inverse(multiply(X0,X1)) )
| ~ spl0_3 ),
inference(superposition,[],[f89,f4]) ).
fof(f530,plain,
( sk_c7 != sk_c3
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f524,f112]) ).
fof(f534,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_2
| ~ spl0_27 ),
inference(superposition,[],[f85,f504]) ).
fof(f536,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[],[f92,f504]) ).
fof(f545,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_9
| ~ spl0_27 ),
inference(superposition,[],[f387,f504]) ).
fof(f546,plain,
( sk_c7 != inverse(sk_c7)
| spl0_21
| ~ spl0_27 ),
inference(forward_demodulation,[],[f463,f504]) ).
fof(f549,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| spl0_21
| ~ spl0_27 ),
inference(superposition,[],[f546,f534]) ).
fof(f552,plain,
( ~ spl0_29
| ~ spl0_2
| spl0_21
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f549,f503,f461,f84,f515]) ).
fof(f571,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f433,f504]) ).
fof(f627,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,sk_c7))
| sk_c8 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_27 ),
inference(forward_demodulation,[],[f527,f504]) ).
fof(f628,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,sk_c7))
| sk_c7 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_27 ),
inference(forward_demodulation,[],[f627,f504]) ).
fof(f640,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(multiply(sk_c6,sk_c8))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_27 ),
inference(superposition,[],[f628,f190]) ).
fof(f650,plain,
( sk_c7 != inverse(multiply(sk_c6,sk_c8))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f640]) ).
fof(f658,plain,
( sk_c7 != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_27 ),
inference(forward_demodulation,[],[f650,f177]) ).
fof(f668,plain,
( ~ spl0_26
| ~ spl0_2
| ~ spl0_3
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f658,f503,f88,f84,f499]) ).
fof(f708,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(superposition,[],[f536,f571]) ).
fof(f715,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(superposition,[],[f187,f571]) ).
fof(f717,plain,
( identity = sk_c7
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f715,f3]) ).
fof(f734,plain,
( sk_c6 != inverse(sk_c7)
| spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f86,f504]) ).
fof(f742,plain,
( spl0_29
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f708,f503,f162,f152,f91,f515]) ).
fof(f747,plain,
( spl0_23
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f717,f503,f162,f152,f470]) ).
fof(f752,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_14
| ~ spl0_27 ),
inference(forward_demodulation,[],[f428,f504]) ).
fof(f773,plain,
( identity = sk_c3
| ~ spl0_14
| ~ spl0_27 ),
inference(forward_demodulation,[],[f752,f3]) ).
fof(f786,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_9
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[],[f545,f471]) ).
fof(f794,plain,
( sk_c6 != inverse(identity)
| spl0_2
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[],[f734,f471]) ).
fof(f795,plain,
( sk_c7 != inverse(identity)
| spl0_2
| ~ spl0_23
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_demodulation,[],[f794,f516]) ).
fof(f800,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f786,f1]) ).
fof(f821,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_27 ),
inference(superposition,[],[f530,f773]) ).
fof(f824,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f821,f471]) ).
fof(f825,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f824]) ).
fof(f831,plain,
( sk_c8 = inverse(identity)
| ~ spl0_9
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[],[f112,f800]) ).
fof(f843,plain,
( sk_c7 = inverse(identity)
| ~ spl0_9
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f831,f504]) ).
fof(f846,plain,
( $false
| ~ spl0_9
| ~ spl0_23
| spl0_26
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f843,f501]) ).
fof(f847,plain,
( ~ spl0_9
| ~ spl0_23
| spl0_26
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f846]) ).
fof(f848,plain,
( identity = inverse(identity)
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f500,f471]) ).
fof(f849,plain,
( identity != inverse(identity)
| spl0_2
| ~ spl0_23
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_demodulation,[],[f795,f471]) ).
fof(f854,plain,
( sk_c6 = multiply(sk_c7,identity)
| ~ spl0_7
| ~ spl0_25 ),
inference(superposition,[],[f102,f495]) ).
fof(f868,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f854,f471]) ).
fof(f873,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f868,f1]) ).
fof(f901,plain,
( $false
| spl0_2
| ~ spl0_23
| ~ spl0_26
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f849,f848]) ).
fof(f902,plain,
( spl0_2
| ~ spl0_23
| ~ spl0_26
| ~ spl0_27
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f901]) ).
fof(f903,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f82,f471]) ).
fof(f933,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_29 ),
inference(forward_demodulation,[],[f903,f516]) ).
fof(f952,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_29 ),
inference(forward_demodulation,[],[f933,f471]) ).
fof(f961,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_29 ),
inference(forward_demodulation,[],[f952,f471]) ).
fof(f966,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_23
| ~ spl0_29 ),
inference(superposition,[],[f961,f1]) ).
fof(f970,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_23
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f966]) ).
fof(f976,plain,
( sk_c6 != multiply(sk_c8,identity)
| spl0_4
| ~ spl0_23 ),
inference(forward_demodulation,[],[f93,f471]) ).
fof(f980,plain,
( sk_c6 != multiply(sk_c7,identity)
| spl0_4
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f976,f504]) ).
fof(f983,plain,
( sk_c6 != multiply(identity,identity)
| spl0_4
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f980,f471]) ).
fof(f985,plain,
( identity != sk_c6
| spl0_4
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f983,f1]) ).
fof(f1009,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f873,f985]) ).
fof(f1010,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1009]) ).
fof(f1086,plain,
( identity != inverse(identity)
| ~ spl0_23
| spl0_26 ),
inference(forward_demodulation,[],[f501,f471]) ).
fof(f1149,plain,
( identity != sk_c7
| spl0_25
| ~ spl0_27 ),
inference(forward_demodulation,[],[f496,f504]) ).
fof(f1150,plain,
( spl0_25
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f372,f115,f106,f84,f494]) ).
fof(f1155,plain,
( $false
| ~ spl0_23
| spl0_25
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1149,f471]) ).
fof(f1156,plain,
( ~ spl0_23
| spl0_25
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1155]) ).
fof(f1165,plain,
( identity != sk_c6
| sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_23 ),
inference(forward_demodulation,[],[f509,f471]) ).
fof(f1187,plain,
( sk_c7 != sk_c6
| identity != sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1165,f504]) ).
fof(f1198,plain,
( identity != sk_c6
| identity != sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1187,f471]) ).
fof(f1199,plain,
( identity != sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_23
| ~ spl0_27 ),
inference(duplicate_literal_removal,[],[f1198]) ).
fof(f1203,definition,
( spl0_34
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1204,plain,
( identity = sk_c6
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1211,plain,
( ~ spl0_34
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_23
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1199,f503,f470,f98,f91,f84,f1203]) ).
fof(f1213,definition,
( spl0_36
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f1221,plain,
( ~ spl0_36
| ~ spl0_1
| ~ spl0_23
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f970,f515,f470,f81,f1213]) ).
fof(f1224,plain,
( sk_c6 = multiply(sk_c7,identity)
| ~ spl0_7
| ~ spl0_25 ),
inference(superposition,[],[f102,f495]) ).
fof(f1234,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1224,f471]) ).
fof(f1237,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1234,f1]) ).
fof(f1239,plain,
( spl0_34
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1237,f494,f470,f101,f1203]) ).
fof(f1260,plain,
( identity != sk_c7
| spl0_29
| ~ spl0_34 ),
inference(forward_demodulation,[],[f517,f1204]) ).
fof(f1263,plain,
( $false
| ~ spl0_23
| spl0_29
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1260,f471]) ).
fof(f1264,plain,
( ~ spl0_23
| spl0_29
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[],[f1263]) ).
fof(f1271,plain,
( spl0_23
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f370,f115,f106,f91,f84,f470]) ).
fof(f1327,plain,
( ~ spl0_36
| ~ spl0_23
| spl0_26 ),
inference(avatar_split_clause,[],[f1086,f499,f470,f1213]) ).
fof(f1331,plain,
( identity != sk_c7
| ~ spl0_25
| spl0_27 ),
inference(forward_demodulation,[],[f505,f495]) ).
fof(f1337,plain,
( sk_c6 = inverse(identity)
| ~ spl0_2
| ~ spl0_25 ),
inference(forward_demodulation,[],[f85,f495]) ).
fof(f1361,plain,
( ~ spl0_23
| ~ spl0_25
| spl0_27 ),
inference(avatar_split_clause,[],[f1331,f503,f494,f470]) ).
fof(f1367,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_25
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1337,f1204]) ).
fof(f1378,plain,
( spl0_36
| ~ spl0_2
| ~ spl0_25
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1367,f1203,f494,f84,f1213]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f130]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s16,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s22,plain,
( spl0_2
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s25,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s26,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s28,plain,
( spl0_2
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s31,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f170]) ).
cnf(s34,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f173]) ).
cnf(s35,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f174]) ).
cnf(s36,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f175]) ).
cnf(s37,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f176]) ).
cnf(s38,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f291]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f473]) ).
cnf(s49,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f476]) ).
cnf(s52,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f508]) ).
cnf(s54,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_27 ),
inference(sat_conversion,[],[f520]) ).
cnf(s58,plain,
( ~ spl0_2
| spl0_21
| ~ spl0_27
| ~ spl0_29 ),
inference(sat_conversion,[],[f552]) ).
cnf(s61,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f668]) ).
cnf(s66,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| spl0_29 ),
inference(sat_conversion,[],[f742]) ).
cnf(s69,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_23
| ~ spl0_27 ),
inference(sat_conversion,[],[f747]) ).
cnf(s72,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(sat_conversion,[],[f825]) ).
cnf(s76,plain,
( ~ spl0_9
| ~ spl0_23
| spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f847]) ).
cnf(s79,plain,
( spl0_2
| ~ spl0_23
| ~ spl0_26
| ~ spl0_27
| ~ spl0_29 ),
inference(sat_conversion,[],[f902]) ).
cnf(s84,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_23
| ~ spl0_25
| ~ spl0_27 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s86,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| spl0_25 ),
inference(sat_conversion,[],[f1150]) ).
cnf(s91,plain,
( ~ spl0_23
| spl0_25
| ~ spl0_27 ),
inference(sat_conversion,[],[f1156]) ).
cnf(s94,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_23
| ~ spl0_27
| ~ spl0_34 ),
inference(sat_conversion,[],[f1211]) ).
cnf(s97,plain,
( ~ spl0_1
| ~ spl0_23
| ~ spl0_29
| ~ spl0_36 ),
inference(sat_conversion,[],[f1221]) ).
cnf(s100,plain,
( ~ spl0_7
| ~ spl0_23
| ~ spl0_25
| spl0_34 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s107,plain,
( ~ spl0_23
| spl0_29
| ~ spl0_34 ),
inference(sat_conversion,[],[f1264]) ).
cnf(s109,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| spl0_23 ),
inference(sat_conversion,[],[f1271]) ).
cnf(s128,plain,
( ~ spl0_23
| spl0_26
| ~ spl0_36 ),
inference(sat_conversion,[],[f1327]) ).
cnf(s133,plain,
( ~ spl0_23
| ~ spl0_25
| spl0_27 ),
inference(sat_conversion,[],[f1361]) ).
cnf(s137,plain,
( ~ spl0_2
| ~ spl0_25
| ~ spl0_34
| spl0_36 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s141,plain,
spl0_2,
inference(rat,[],[s79,s66,s76,s84,s91,s69,s54,s4,s10,s16,s22,s28,s34]) ).
cnf(s142,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s38,s35,s36]) ).
cnf(s143,plain,
( ~ spl0_25
| ~ spl0_23
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s94,s100,s133,s142,s141]) ).
cnf(s144,plain,
( spl0_10
| ~ spl0_6 ),
inference(rat,[],[s52,s21,s27]) ).
cnf(s145,plain,
( spl0_8
| ~ spl0_6 ),
inference(rat,[],[s52,s20,s26]) ).
cnf(s146,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s143,s86,s109,s145,s144,s141]) ).
cnf(s147,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s107,s58,s100,s133,s47,s86,s109,s142,s141]) ).
cnf(s148,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s49,s3,s9,s15]) ).
cnf(s149,plain,
( ~ spl0_10
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s49,s2,s8,s14,s147]) ).
cnf(s150,plain,
( spl0_6
| ~ spl0_7
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s149,s148,s1,s141]) ).
cnf(s152,plain,
spl0_4,
inference(rat,[],[s84,s91,s69,s54,s7,s13,s19,s25,s31,s37]) ).
cnf(s153,plain,
spl0_7,
inference(rat,[],[s142,s152]) ).
cnf(s154,plain,
~ spl0_6,
inference(rat,[],[s146,s152]) ).
cnf(s155,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s128,s137,s61,s100,s133,s86,s109,s141,s153,s152]) ).
cnf(s156,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s69,s72,s54,s2,s8,s14,s20,s26]) ).
cnf(s157,plain,
( ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s69,s72,s54,s3,s9,s15,s21,s27,s155]) ).
cnf(s158,plain,
~ spl0_3,
inference(rat,[],[s157,s156]) ).
cnf(s159,plain,
spl0_1,
inference(rat,[],[s150,s152,s158,s153,s154]) ).
cnf(s160,plain,
( ~ spl0_25
| ~ spl0_23 ),
inference(rat,[],[s97,s107,s137,s100,s153,s141,s159]) ).
cnf(s161,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(rat,[],[s160,s86,s109,s152,s141]) ).
cnf(s162,plain,
( ~ spl0_27
| ~ spl0_23 ),
inference(rat,[],[s160,s91]) ).
cnf(s163,plain,
( ~ spl0_27
| ~ spl0_15
| ~ spl0_16 ),
inference(rat,[],[s162,s69]) ).
cnf(s164,plain,
spl0_8,
inference(rat,[],[s163,s54,s2,s8,s14,s20,s26]) ).
cnf(s165,plain,
~ spl0_10,
inference(rat,[],[s161,s164]) ).
cnf(s166,plain,
spl0_16,
inference(rat,[],[s27,s165]) ).
cnf(s167,plain,
spl0_15,
inference(rat,[],[s21,s165]) ).
cnf(s168,plain,
spl0_14,
inference(rat,[],[s15,s165]) ).
cnf(s169,plain,
spl0_13,
inference(rat,[],[s9,s165]) ).
cnf(s170,plain,
spl0_9,
inference(rat,[],[s3,s165]) ).
cnf(s172,plain,
~ spl0_27,
inference(rat,[],[s163,s166,s167]) ).
cnf(s173,plain,
$false,
inference(rat,[],[s54,s168,s170,s172,s169]) ).
fof(f1383,plain,
$false,
inference(avatar_sat_refutation,[],[s173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP324-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:51:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % (989186)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (989194)dis+10_1_sil=32000:sp=arity:random_seed=14942726:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (989192)% WARNING: option uhcvi not known.
% 0.18/0.46 % (989191)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=137384632_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.46 % (989192)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=467416185:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.46 % (989193)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3233636843:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.46 % (989195)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3009136106:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.46 % (989197)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2712991661:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.46 % (989196)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=402103523:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % TRYING [1]
% 0.18/0.47 % TRYING [2]
% 0.18/0.47 % TRYING [3]
% 0.18/0.47 % (989194) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-989186-989194"...
% 0.18/0.47 % (989194)...printing done.
% 0.18/0.47 % TRYING [4]
% 0.18/0.47 % (989194)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (989194)------------------------------
% 0.18/0.47 % (989194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (989194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (989194)CaDiCaL version: 2.1.3
% 0.18/0.47 % (989194)Termination reason: Refutation
% 0.18/0.47 % (989194)Time elapsed: 0.015 s
% 0.18/0.47 % (989194)Peak memory usage: 12 MB
% 0.18/0.47 % (989194)Instructions burned: 45 (million)
% 0.18/0.47 % (989186)Success in time 0.046 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------