%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP336-1 : 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 10:17:31 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 56
% Syntax : Number of formulae : 374 ( 19 unt; 20 def)
% Number of atoms : 1237 ( 368 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1647 ( 784 ~; 843 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 61 !; 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_c9,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f87]) ).
fof(f91,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f94,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f93]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c10
| multiply(X1,X2) != sk_c9
| inverse(X1) != X2
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,X6) != sk_c9
| inverse(X5) != X6
| multiply(X6,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| multiply(X1,X2) != sk_c9
| inverse(X1) != X2
| sk_c9 != multiply(X2,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c9 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c9 != multiply(X6,sk_c8) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c9 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c9 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f102]) ).
fof(f104,plain,
! [X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) ),
inference(equality_resolution,[],[f103]) ).
fof(f106,definition,
( spl0_1
<=> ! [X5] :
( sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f107,plain,
( ! [X5] :
( sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,definition,
( spl0_2
<=> ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f110,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_3
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f113,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl0_4
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f117,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_5
<=> ! [X1] :
( sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f120,plain,
( ! [X1] :
( sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_6
<=> multiply(sk_c9,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f123,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( multiply(sk_c9,sk_c10) != sk_c8
| spl0_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f104,f122,f109,f119,f116,f112,f109,f106]) ).
fof(f131,definition,
( spl0_8
<=> sk_c9 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f133,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f136,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f138,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f141,definition,
( spl0_10
<=> sk_c9 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f143,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f146,definition,
( spl0_11
<=> sk_c10 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f147,plain,
( sk_c10 != multiply(sk_c5,sk_c9)
| spl0_11 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f94,f131,f146]) ).
fof(f151,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f153,plain,
( sk_c10 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f92,f131,f151]) ).
fof(f157,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f159,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f88,f131,f157]) ).
fof(f162,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f163,plain,
( sk_c9 != multiply(sk_c4,sk_c10)
| spl0_14 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f164,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f86,f131,f162]) ).
fof(f167,definition,
( spl0_15
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f169,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f173,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f78,f167,f146]) ).
fof(f174,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f76,f167,f151]) ).
fof(f175,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f74,f167,f112]) ).
fof(f176,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f72,f167,f157]) ).
fof(f177,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f70,f167,f162]) ).
fof(f179,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f181,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f185,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f62,f179,f146]) ).
fof(f186,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f60,f179,f151]) ).
fof(f187,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f58,f179,f112]) ).
fof(f188,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f56,f179,f157]) ).
fof(f189,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f179,f162]) ).
fof(f191,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f192,plain,
( sk_c10 != multiply(sk_c1,sk_c9)
| spl0_17 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f193,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f197,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f46,f191,f146]) ).
fof(f198,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f44,f191,f151]) ).
fof(f199,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f42,f191,f112]) ).
fof(f200,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f40,f191,f157]) ).
fof(f201,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f38,f191,f162]) ).
fof(f203,definition,
( spl0_18
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f207,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f34,f203,f136]) ).
fof(f208,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f203,f141]) ).
fof(f209,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f203,f146]) ).
fof(f211,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f26,f203,f112]) ).
fof(f212,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f24,f203,f157]) ).
fof(f213,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f203,f162]) ).
fof(f215,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f122,f136]) ).
fof(f216,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f122,f141]) ).
fof(f217,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f122,f146]) ).
fof(f218,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f122,f151]) ).
fof(f219,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f122,f112]) ).
fof(f220,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f122,f157]) ).
fof(f221,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f122,f162]) ).
fof(f222,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f3,f138]) ).
fof(f223,plain,
( identity = multiply(sk_c10,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f153]) ).
fof(f224,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f159]) ).
fof(f226,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f229,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c10,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f164]) ).
fof(f234,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f226,f1]) ).
fof(f236,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f222]) ).
fof(f237,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f236,f1]) ).
fof(f238,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c5,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f223]) ).
fof(f239,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c5,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f238,f1]) ).
fof(f245,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f237,f143]) ).
fof(f248,plain,
( multiply(sk_c9,sk_c8) = multiply(sk_c4,sk_c9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f229,f113]) ).
fof(f260,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f239,f148]) ).
fof(f297,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f234,f245]) ).
fof(f299,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f234,f164]) ).
fof(f301,plain,
( sk_c8 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_3 ),
inference(superposition,[],[f234,f113]) ).
fof(f303,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_13 ),
inference(superposition,[],[f234,f224]) ).
fof(f304,plain,
( sk_c5 = multiply(inverse(sk_c10),identity)
| ~ spl0_12 ),
inference(superposition,[],[f234,f223]) ).
fof(f310,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f299,f159]) ).
fof(f312,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f297,f3]) ).
fof(f321,plain,
( sk_c8 != multiply(identity,sk_c10)
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f124,f312]) ).
fof(f322,plain,
( sk_c10 != sk_c8
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f321,f1]) ).
fof(f330,plain,
( sk_c8 = multiply(inverse(sk_c10),identity)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f301,f312]) ).
fof(f341,plain,
( sk_c4 = sk_c5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f304,f303]) ).
fof(f345,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f148,f341]) ).
fof(f347,plain,
( sk_c10 = multiply(sk_c4,identity)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f345,f312]) ).
fof(f357,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f330,f303]) ).
fof(f384,plain,
( multiply(sk_c4,identity) = multiply(identity,sk_c8)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f248,f312]) ).
fof(f385,plain,
( sk_c8 = multiply(sk_c4,identity)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f384,f1]) ).
fof(f386,plain,
( sk_c10 = sk_c8
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f385,f347]) ).
fof(f387,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f386,f322]) ).
fof(f388,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f390,plain,
( sk_c8 = multiply(identity,sk_c10)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f123,f312]) ).
fof(f391,plain,
( sk_c10 = sk_c8
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f390,f1]) ).
fof(f423,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f205]) ).
fof(f431,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f234,f181]) ).
fof(f433,plain,
( sk_c3 = multiply(sk_c3,sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f431,f169]) ).
fof(f434,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_17 ),
inference(superposition,[],[f234,f193]) ).
fof(f435,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c9,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f193]) ).
fof(f436,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f434,f205]) ).
fof(f439,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f117,f164]) ).
fof(f445,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f439]) ).
fof(f448,definition,
( spl0_21
<=> sk_c10 = inverse(inverse(sk_c10)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f450,plain,
( sk_c10 != inverse(inverse(sk_c10))
| spl0_21 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f452,definition,
( spl0_22
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f453,plain,
( identity = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f461,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f445,f159]) ).
fof(f462,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f476,plain,
( sk_c1 = multiply(inverse(sk_c10),identity)
| ~ spl0_18 ),
inference(superposition,[],[f234,f423]) ).
fof(f479,plain,
( sk_c4 = sk_c1
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f476,f303]) ).
fof(f512,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f234,f310]) ).
fof(f514,plain,
( identity = sk_c9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f512,f3]) ).
fof(f518,plain,
( spl0_22
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f514,f162,f157,f452]) ).
fof(f519,plain,
( sk_c8 = multiply(identity,sk_c10)
| ~ spl0_6
| ~ spl0_22 ),
inference(superposition,[],[f123,f453]) ).
fof(f521,plain,
( sk_c10 = multiply(sk_c1,identity)
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f193,f453]) ).
fof(f527,plain,
( sk_c10 = multiply(sk_c4,identity)
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f521,f479]) ).
fof(f529,plain,
( sk_c10 = sk_c8
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f519,f1]) ).
fof(f539,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f113,f529]) ).
fof(f540,plain,
( ! [X1] :
( identity != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10) )
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[],[f120,f453]) ).
fof(f541,plain,
( ! [X1] :
( identity != multiply(inverse(X1),sk_c10)
| identity != multiply(X1,inverse(X1)) )
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[],[f540,f453]) ).
fof(f542,plain,
( identity != multiply(sk_c10,sk_c10)
| identity != multiply(sk_c4,sk_c10)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f541,f159]) ).
fof(f543,plain,
( identity != multiply(sk_c10,sk_c10)
| identity != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f541,f153]) ).
fof(f545,plain,
( identity != multiply(sk_c3,sk_c10)
| identity != multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f541,f169]) ).
fof(f548,plain,
( identity != sk_c9
| identity != multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f545,f133]) ).
fof(f550,plain,
( identity != sk_c9
| identity != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f543,f260]) ).
fof(f551,plain,
( identity != sk_c9
| identity != multiply(sk_c4,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f542,f260]) ).
fof(f552,plain,
( identity != multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f548,f453]) ).
fof(f554,plain,
( identity != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f550,f453]) ).
fof(f555,plain,
( identity != multiply(sk_c4,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f551,f453]) ).
fof(f556,plain,
( identity != sk_c9
| ~ spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f552,f181]) ).
fof(f558,plain,
( identity != multiply(sk_c4,sk_c10)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f554,f341]) ).
fof(f559,plain,
( identity != sk_c9
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f555,f164]) ).
fof(f560,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f556,f453]) ).
fof(f561,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f563,plain,
( identity != sk_c9
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f558,f164]) ).
fof(f564,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f559,f453]) ).
fof(f565,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f564]) ).
fof(f568,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f563,f453]) ).
fof(f569,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f570,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| sk_c10 != inverse(X4) )
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f110,f453]) ).
fof(f572,plain,
( sk_c10 != sk_c4
| sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_2
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f570,f303]) ).
fof(f583,definition,
( spl0_27
<=> sk_c10 = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f584,plain,
( sk_c10 = sk_c4
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f599,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,multiply(identity,X0))
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f435,f453]) ).
fof(f600,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,X0)
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f599,f1]) ).
fof(f601,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c4,X0)
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f600,f479]) ).
fof(f602,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(superposition,[],[f570,f527]) ).
fof(f605,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f602]) ).
fof(f608,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f605,f159]) ).
fof(f609,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f610,plain,
( ! [X5] :
( identity != multiply(X5,inverse(X5))
| sk_c9 != multiply(inverse(X5),sk_c8) )
| ~ spl0_1
| ~ spl0_22 ),
inference(forward_demodulation,[],[f107,f453]) ).
fof(f611,plain,
( ! [X5] :
( sk_c9 != multiply(inverse(X5),sk_c10)
| identity != multiply(X5,inverse(X5)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f610,f529]) ).
fof(f612,plain,
( ! [X5] :
( identity != multiply(inverse(X5),sk_c10)
| identity != multiply(X5,inverse(X5)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f611,f453]) ).
fof(f614,plain,
( identity != multiply(sk_c10,sk_c10)
| identity != multiply(sk_c5,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f612,f153]) ).
fof(f616,plain,
( identity != multiply(sk_c3,sk_c10)
| identity != multiply(sk_c2,sk_c3)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f612,f169]) ).
fof(f619,plain,
( identity != sk_c9
| identity != multiply(sk_c2,sk_c3)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f616,f133]) ).
fof(f621,plain,
( identity != sk_c9
| identity != multiply(sk_c5,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f614,f260]) ).
fof(f623,plain,
( identity != multiply(sk_c2,sk_c3)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f619,f453]) ).
fof(f625,plain,
( identity != multiply(sk_c5,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f621,f453]) ).
fof(f627,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f623,f181]) ).
fof(f629,plain,
( identity != multiply(sk_c4,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f625,f341]) ).
fof(f631,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f627,f453]) ).
fof(f632,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f631]) ).
fof(f634,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f629,f164]) ).
fof(f639,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f634,f453]) ).
fof(f640,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f639]) ).
fof(f641,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f114,f529]) ).
fof(f643,plain,
( sk_c10 != multiply(sk_c5,identity)
| spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f147,f453]) ).
fof(f644,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f436,f453]) ).
fof(f645,plain,
( identity != multiply(sk_c10,sk_c10)
| spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f641,f453]) ).
fof(f646,plain,
( sk_c10 != multiply(sk_c4,identity)
| spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f643,f341]) ).
fof(f647,plain,
( $false
| spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f646,f527]) ).
fof(f648,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f647]) ).
fof(f669,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f163,f601]) ).
fof(f670,plain,
( identity != multiply(sk_c10,sk_c10)
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f669,f453]) ).
fof(f690,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f644,f645]) ).
fof(f691,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f693,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f234,f433]) ).
fof(f695,plain,
( identity = sk_c9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f693,f3]) ).
fof(f703,plain,
( spl0_22
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f695,f179,f167,f452]) ).
fof(f717,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f539,f453]) ).
fof(f720,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f717,f670]) ).
fof(f721,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f720]) ).
fof(f726,plain,
( sk_c10 = multiply(sk_c5,identity)
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f148,f453]) ).
fof(f737,plain,
( sk_c10 != multiply(sk_c1,identity)
| spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f192,f453]) ).
fof(f738,plain,
( sk_c10 != multiply(sk_c4,identity)
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f737,f479]) ).
fof(f760,plain,
( sk_c10 = multiply(sk_c4,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f726,f341]) ).
fof(f765,plain,
( sk_c10 = sk_c4
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f357,f391]) ).
fof(f768,plain,
( ~ spl0_21
| ~ spl0_27
| ~ spl0_2
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f572,f452,f157,f109,f583,f448]) ).
fof(f769,plain,
( spl0_27
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f765,f157,f141,f136,f122,f112,f583]) ).
fof(f771,plain,
( $false
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f760,f738]) ).
fof(f772,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f771]) ).
fof(f773,plain,
( sk_c10 = multiply(sk_c1,identity)
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f193,f453]) ).
fof(f793,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,multiply(identity,X0))
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f4,f773]) ).
fof(f794,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,X0)
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f793,f1]) ).
fof(f796,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f570,f773]) ).
fof(f806,plain,
( ! [X3] :
( identity != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f117,f453]) ).
fof(f925,plain,
( identity != multiply(sk_c10,sk_c10)
| sk_c10 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f806,f794]) ).
fof(f930,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f925,f717]) ).
fof(f932,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f930,f205]) ).
fof(f933,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f932]) ).
fof(f934,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f796]) ).
fof(f936,plain,
( ~ spl0_18
| ~ spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f934,f452,f191,f109,f203]) ).
fof(f965,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_13
| ~ spl0_27 ),
inference(forward_demodulation,[],[f159,f584]) ).
fof(f989,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_13
| spl0_21
| ~ spl0_27 ),
inference(superposition,[],[f450,f965]) ).
fof(f992,plain,
( $false
| ~ spl0_13
| spl0_21
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f989,f965]) ).
fof(f993,plain,
( ~ spl0_13
| spl0_21
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f992]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f149]) ).
cnf(s7,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f154]) ).
cnf(s9,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s10,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s14,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f173]) ).
cnf(s15,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f174]) ).
cnf(s16,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f175]) ).
cnf(s17,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f176]) ).
cnf(s18,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f177]) ).
cnf(s22,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f185]) ).
cnf(s23,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f186]) ).
cnf(s24,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s25,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s26,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f189]) ).
cnf(s30,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f197]) ).
cnf(s31,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f198]) ).
cnf(s32,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f199]) ).
cnf(s33,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s34,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s36,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f207]) ).
cnf(s37,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f208]) ).
cnf(s38,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s40,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s41,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s42,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s44,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f215]) ).
cnf(s45,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f216]) ).
cnf(s46,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f217]) ).
cnf(s47,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f218]) ).
cnf(s48,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f219]) ).
cnf(s49,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f220]) ).
cnf(s50,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f221]) ).
cnf(s51,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f388]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f462]) ).
cnf(s58,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f518]) ).
cnf(s60,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f561]) ).
cnf(s61,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f565]) ).
cnf(s63,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f569]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f609]) ).
cnf(s68,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f632]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f640]) ).
cnf(s72,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f648]) ).
cnf(s75,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f691]) ).
cnf(s80,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_22 ),
inference(sat_conversion,[],[f703]) ).
cnf(s81,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f721]) ).
cnf(s83,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_21
| ~ spl0_22
| ~ spl0_27 ),
inference(sat_conversion,[],[f768]) ).
cnf(s84,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| spl0_27 ),
inference(sat_conversion,[],[f769]) ).
cnf(s85,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f772]) ).
cnf(s92,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f933]) ).
cnf(s93,plain,
( ~ spl0_2
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f936]) ).
cnf(s95,plain,
( ~ spl0_13
| spl0_21
| ~ spl0_27 ),
inference(sat_conversion,[],[f993]) ).
cnf(s96,plain,
spl0_3,
inference(rat,[],[s80,s75,s16,s24,s32,s40,s48]) ).
cnf(s97,plain,
spl0_6,
inference(rat,[],[s51,s44,s45,s46,s47,s49,s50,s96]) ).
cnf(s98,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(rat,[],[s58,s63]) ).
cnf(s99,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_5
| ~ spl0_11 ),
inference(rat,[],[s80,s81,s18,s26,s34,s42,s98,s97,s96]) ).
cnf(s100,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s60,s80,s17,s25]) ).
cnf(s101,plain,
( spl0_12
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s60,s80,s15,s23]) ).
cnf(s102,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_5 ),
inference(rat,[],[s80,s72,s14,s22,s30,s38,s99]) ).
cnf(s103,plain,
( ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s102,s101,s100]) ).
cnf(s104,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(rat,[],[s58,s61]) ).
cnf(s105,plain,
~ spl0_5,
inference(rat,[],[s104,s6,s7,s9,s10,s103]) ).
cnf(s106,plain,
( ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s80,s81,s18,s26,s34,s42,s56,s97,s96]) ).
cnf(s107,plain,
~ spl0_4,
inference(rat,[],[s80,s92,s17,s25,s33,s41,s106,s96,s97]) ).
cnf(s108,plain,
( spl0_22
| ~ spl0_13 ),
inference(rat,[],[s80,s18,s26,s58]) ).
cnf(s109,plain,
( ~ spl0_27
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s83,s95,s108]) ).
cnf(s111,plain,
( spl0_18
| spl0_27
| ~ spl0_13 ),
inference(rat,[],[s84,s36,s37,s96,s97]) ).
cnf(s112,plain,
( ~ spl0_18
| ~ spl0_22
| ~ spl0_2
| ~ spl0_13 ),
inference(rat,[],[s85,s31,s30,s67]) ).
cnf(s113,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s112,s111,s109,s108]) ).
cnf(s114,plain,
~ spl0_2,
inference(rat,[],[s80,s93,s17,s25,s33,s41,s113]) ).
cnf(s115,plain,
spl0_1,
inference(rat,[],[s2,s97,s105,s96,s107,s114]) ).
cnf(s116,plain,
( ~ spl0_11
| ~ spl0_18
| ~ spl0_22
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s81,s71,s85,s115,s97,s96]) ).
cnf(s117,plain,
( ~ spl0_18
| ~ spl0_12
| ~ spl0_22
| ~ spl0_13 ),
inference(rat,[],[s72,s30,s116]) ).
cnf(s118,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(rat,[],[s71,s38,s42,s117,s115,s97]) ).
cnf(s119,plain,
( ~ spl0_13
| ~ spl0_22 ),
inference(rat,[],[s68,s7,s15,s23,s118,s97,s115]) ).
cnf(s120,plain,
~ spl0_13,
inference(rat,[],[s119,s108]) ).
cnf(s123,plain,
spl0_16,
inference(rat,[],[s25,s120]) ).
cnf(s124,plain,
spl0_15,
inference(rat,[],[s17,s120]) ).
cnf(s125,plain,
spl0_8,
inference(rat,[],[s9,s120]) ).
cnf(s126,plain,
spl0_22,
inference(rat,[],[s80,s123,s124]) ).
cnf(s127,plain,
$false,
inference(rat,[],[s68,s97,s123,s126,s115,s125,s124]) ).
fof(f994,plain,
$false,
inference(avatar_sat_refutation,[],[s127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP336-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:52:55 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.18/0.49 % (990028)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (990033)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2882853372_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % TRYING [1]
% 0.18/0.49 % (990034)% WARNING: option uhcvi not known.
% 0.18/0.49 % TRYING [2]
% 0.18/0.49 % TRYING [3]
% 0.18/0.49 % TRYING [4]
% 0.18/0.49 % (990034)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2449184318:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (990035)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4243652133:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (990036)dis+10_1_sil=32000:sp=arity:random_seed=3021415549:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (990037)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3295366738:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (990038)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1045660548:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (990039)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=576659940:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % TRYING [5]
% 0.18/0.49 % TRYING [6]
% 0.18/0.49 % (990036) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-990028-990036"...
% 0.18/0.49 % (990037) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-990028-990037"...
% 0.18/0.49 % (990036)...printing done.
% 0.18/0.49 % (990036)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (990036)------------------------------
% 0.18/0.50 % (990036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (990036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (990036)CaDiCaL version: 2.1.3
% 0.18/0.50 % (990036)Termination reason: Refutation
% 0.18/0.50 % (990036)Time elapsed: 0.023 s
% 0.18/0.50 % (990036)Peak memory usage: 12 MB
% 0.18/0.50 % (990036)Instructions burned: 38 (million)
% 0.18/0.50 % (990028)Success in time 0.057 s
% 0.18/0.50 % Vampire exiting
%------------------------------------------------------------------------------