%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP367-1 : 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 : n001.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 10:17:36 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 53
% Syntax : Number of formulae : 409 ( 22 unt; 19 def)
% Number of atoms : 1648 ( 377 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 2429 (1190 ~;1220 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 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_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| multiply(X2,sk_c6) != sk_c8
| inverse(X2) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c6,sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1,X4] :
( multiply(sk_c6,sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c7,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c6,sk_c8) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f75,f72,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f94,f90]) ).
fof(f99,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f94,f99]) ).
fof(f104,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f105,plain,
( sk_c8 != multiply(sk_c4,sk_c7)
| spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f94,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f113,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f75]) ).
fof(f115,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f115,f90]) ).
fof(f119,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f115,f99]) ).
fof(f120,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f115,f104]) ).
fof(f121,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f115,f109]) ).
fof(f122,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f115,f75]) ).
fof(f124,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f124,f90]) ).
fof(f128,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f124,f99]) ).
fof(f129,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f124,f104]) ).
fof(f130,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f124,f109]) ).
fof(f131,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f124,f75]) ).
fof(f133,definition,
( spl0_14
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f133,f90]) ).
fof(f137,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f133,f99]) ).
fof(f138,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f133,f104]) ).
fof(f139,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f133,f109]) ).
fof(f140,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f133,f75]) ).
fof(f142,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f142,f90]) ).
fof(f146,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f142,f99]) ).
fof(f147,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f142,f104]) ).
fof(f148,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f142,f109]) ).
fof(f149,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f142,f75]) ).
fof(f150,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f90]) ).
fof(f151,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f85,f99]) ).
fof(f152,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f104]) ).
fof(f153,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f109]) ).
fof(f154,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f75]) ).
fof(f155,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f111]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f76]) ).
fof(f161,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f155]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f106]) ).
fof(f164,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f161,f1]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f168,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f156]) ).
fof(f169,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f168,f1]) ).
fof(f174,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f164,f92]) ).
fof(f177,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f162,f76]) ).
fof(f178,plain,
( multiply(sk_c8,sk_c5) = multiply(sk_c4,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f162,f155]) ).
fof(f191,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f169,f106]) ).
fof(f200,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f165,f3]) ).
fof(f201,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f165,f165]) ).
fof(f202,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f165,f156]) ).
fof(f203,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_11 ),
inference(superposition,[],[f165,f169]) ).
fof(f206,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f165,f76]) ).
fof(f220,plain,
( sk_c4 = multiply(sk_c4,identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f202,f203]) ).
fof(f221,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f200,f201]) ).
fof(f229,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f160,f191]) ).
fof(f233,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f229,f174]) ).
fof(f238,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f87,f233]) ).
fof(f240,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f165,f233]) ).
fof(f242,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f240,f3]) ).
fof(f252,plain,
( sk_c6 = multiply(inverse(sk_c4),multiply(sk_c8,sk_c8))
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f165,f177]) ).
fof(f255,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f252,f191]) ).
fof(f257,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f255,f111]) ).
fof(f260,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f242]) ).
fof(f264,plain,
( sk_c4 = multiply(sk_c8,sk_c5)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f220,f178]) ).
fof(f266,plain,
( identity = multiply(inverse(sk_c4),multiply(sk_c8,sk_c5))
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f165,f178]) ).
fof(f269,plain,
( identity = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f266,f260]) ).
fof(f271,plain,
( sk_c4 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f264,f260]) ).
fof(f275,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f269,f111]) ).
fof(f277,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f275,f260]) ).
fof(f278,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f277,f271]) ).
fof(f279,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f278,f242]) ).
fof(f282,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f155,f271]) ).
fof(f283,plain,
( sk_c7 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f92,f271]) ).
fof(f284,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f101,f271]) ).
fof(f285,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f284,f111]) ).
fof(f286,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f283,f279]) ).
fof(f287,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f282,f279]) ).
fof(f290,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f286,f260]) ).
fof(f291,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f76]) ).
fof(f294,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f290,f238]) ).
fof(f295,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f296,plain,
( sk_c6 = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f291,f242]) ).
fof(f299,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c8)
| sk_c6 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f80,f296]) ).
fof(f302,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f299,f296]) ).
fof(f308,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f302,f191]) ).
fof(f312,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f308,f285]) ).
fof(f319,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f111,f279]) ).
fof(f333,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f319,f312]) ).
fof(f334,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f345,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f96]) ).
fof(f347,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f126]) ).
fof(f352,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_12 ),
inference(superposition,[],[f165,f117]) ).
fof(f354,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f352,f96]) ).
fof(f355,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f354,f86]) ).
fof(f356,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f86,f355]) ).
fof(f358,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f117,f355]) ).
fof(f361,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f206,f355]) ).
fof(f362,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f361,f3]) ).
fof(f364,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f165,f135]) ).
fof(f366,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f364,f126]) ).
fof(f368,plain,
( sk_c4 = multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f220,f362]) ).
fof(f369,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f1,f362]) ).
fof(f372,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f165,f144]) ).
fof(f373,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c2,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f144]) ).
fof(f374,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c2,X0)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f373,f369]) ).
fof(f375,plain,
( multiply(sk_c4,sk_c7) = sk_c2
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f372,f203]) ).
fof(f381,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f165,f345]) ).
fof(f384,plain,
( sk_c3 = inverse(sk_c6)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f381,f221]) ).
fof(f387,plain,
( sk_c3 = inverse(sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f384,f355]) ).
fof(f394,plain,
( sk_c8 != sk_c8
| sk_c6 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f80,f117]) ).
fof(f395,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f394]) ).
fof(f397,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f395,f96]) ).
fof(f398,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f414,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f83,f369]) ).
fof(f418,plain,
( identity = multiply(sk_c3,sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f3,f387]) ).
fof(f419,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f418,f358]) ).
fof(f423,plain,
( identity != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f414,f3]) ).
fof(f431,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f423,f362]) ).
fof(f436,definition,
( spl0_16
<=> sk_c8 = inverse(inverse(sk_c8)) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f438,plain,
( sk_c8 != inverse(inverse(sk_c8))
| spl0_16 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f440,definition,
( spl0_17
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f441,plain,
( sk_c8 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f442,plain,
( sk_c8 != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f445,definition,
( spl0_18
<=> sk_c8 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f446,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f452,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_13 ),
inference(superposition,[],[f165,f347]) ).
fof(f455,plain,
( sk_c1 = multiply(sk_c4,identity)
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f452,f203]) ).
fof(f457,plain,
( sk_c4 = sk_c1
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f455,f220]) ).
fof(f461,plain,
( sk_c2 = multiply(sk_c4,sk_c8)
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f135,f457]) ).
fof(f463,plain,
( sk_c4 = sk_c2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f461,f368]) ).
fof(f464,plain,
( ! [X0] : multiply(inverse(sk_c2),multiply(sk_c7,X0)) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f165,f374]) ).
fof(f466,plain,
( sk_c7 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f414,f374]) ).
fof(f467,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f466,f356]) ).
fof(f469,plain,
( ! [X0] : multiply(inverse(sk_c4),multiply(sk_c7,X0)) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f464,f463]) ).
fof(f470,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f467,f463]) ).
fof(f471,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f469,f111]) ).
fof(f472,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f470,f111]) ).
fof(f473,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f474,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f471,f369]) ).
fof(f475,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f70,f355]) ).
fof(f484,plain,
( identity != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f475,f3]) ).
fof(f486,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f475,f374]) ).
fof(f488,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f486,f474]) ).
fof(f490,plain,
( sk_c8 != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f484,f362]) ).
fof(f492,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f488,f463]) ).
fof(f494,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f492,f111]) ).
fof(f497,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f144,f463]) ).
fof(f498,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f497,f369]) ).
fof(f543,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f490,f441]) ).
fof(f544,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f494,f441]) ).
fof(f545,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f544]) ).
fof(f546,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f543,f387]) ).
fof(f547,plain,
( sk_c6 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f546,f96]) ).
fof(f548,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f547,f355]) ).
fof(f549,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f550,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_demodulation,[],[f73,f441]) ).
fof(f553,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_17 ),
inference(superposition,[],[f550,f3]) ).
fof(f555,plain,
( sk_c6 != sk_c8
| sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f550,f76]) ).
fof(f557,plain,
( sk_c8 != sk_c2
| sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f550,f135]) ).
fof(f559,plain,
( sk_c8 != sk_c2
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f557,f126]) ).
fof(f563,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f553,f362]) ).
fof(f565,plain,
( sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f559,f463]) ).
fof(f569,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f563,f440,f115,f94,f85,f75,f72,f436]) ).
fof(f571,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f565,f498]) ).
fof(f578,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f571,f441]) ).
fof(f579,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f580,plain,
( ! [X1] :
( sk_c8 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f83,f441]) ).
fof(f585,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f319,f109,f104,f99,f90,f75,f445]) ).
fof(f594,plain,
( sk_c3 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f384,f296]) ).
fof(f603,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f580,f260]) ).
fof(f652,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f603,f3]) ).
fof(f653,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f603,f86]) ).
fof(f659,plain,
( sk_c8 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f653,f441]) ).
fof(f660,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f652,f242]) ).
fof(f665,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f659,f296]) ).
fof(f666,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f660,f594]) ).
fof(f671,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f665,f446]) ).
fof(f672,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f673,plain,
( sk_c6 != sk_c8
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f666,f96]) ).
fof(f674,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f673,f296]) ).
fof(f675,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f674]) ).
fof(f679,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f257,f260]) ).
fof(f691,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f679,f296]) ).
fof(f702,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f691,f442]) ).
fof(f703,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f711,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f555,f296]) ).
fof(f713,definition,
( spl0_19
<=> sk_c8 = sk_c2 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f714,plain,
( sk_c8 = sk_c2
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f715,plain,
( sk_c8 != sk_c2
| spl0_19 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f731,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f711,f441]) ).
fof(f741,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f731,f446]) ).
fof(f742,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f745,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f70,f441]) ).
fof(f746,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f745,f296]) ).
fof(f747,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f746,f441]) ).
fof(f772,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f747,f3]) ).
fof(f780,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f772,f242]) ).
fof(f785,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f780,f446]) ).
fof(f792,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f785,f446]) ).
fof(f793,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f792]) ).
fof(f794,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f77,f441]) ).
fof(f796,plain,
( sk_c6 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f355,f441]) ).
fof(f802,plain,
( sk_c3 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f387,f441]) ).
fof(f895,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f1,f419]) ).
fof(f985,plain,
( sk_c8 = sk_c7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f366,f144]) ).
fof(f989,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f165,f366]) ).
fof(f992,plain,
( identity = sk_c2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f989,f3]) ).
fof(f997,plain,
( $false
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f985,f442]) ).
fof(f998,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f997]) ).
fof(f1000,plain,
( sk_c8 = sk_c2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f992,f419]) ).
fof(f1003,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f1000,f715]) ).
fof(f1004,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f1003]) ).
fof(f1005,plain,
( sk_c8 != sk_c2
| spl0_10
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f105,f375]) ).
fof(f1006,plain,
( sk_c6 != sk_c8
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f794,f895]) ).
fof(f1023,plain,
( $false
| spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1005,f714]) ).
fof(f1024,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1023]) ).
fof(f1025,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1006,f796]) ).
fof(f1026,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1025]) ).
fof(f1052,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f431,f441]) ).
fof(f1064,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f438,f802]) ).
fof(f1080,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1052,f802]) ).
fof(f1082,plain,
( sk_c6 != sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1064,f96]) ).
fof(f1092,plain,
( sk_c6 != sk_c8
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1080,f96]) ).
fof(f1093,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1082,f796]) ).
fof(f1094,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1093]) ).
fof(f1097,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1092,f796]) ).
fof(f1098,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1097]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s22,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f295]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f334]) ).
cnf(s34,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f398]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f473]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f545]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f549]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f569]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f579]) ).
cnf(s49,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f585]) ).
cnf(s53,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f672]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f675]) ).
cnf(s60,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f703]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f742]) ).
cnf(s72,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f793]) ).
cnf(s78,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f998]) ).
cnf(s79,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f1004]) ).
cnf(s80,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f1024]) ).
cnf(s81,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f1026]) ).
cnf(s87,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1094]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f1098]) ).
cnf(s89,plain,
spl0_3,
inference(rat,[],[s78,s81,s6,s11,s16,s21,s26,s31]) ).
cnf(s90,plain,
spl0_6,
inference(rat,[],[s32,s27,s28,s29,s30,s89]) ).
cnf(s91,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(rat,[],[s60,s54,s89]) ).
cnf(s92,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s88,s78,s10,s15,s20,s25,s89,s90]) ).
cnf(s93,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s39,s9,s14,s19,s24,s92,s89,s90]) ).
cnf(s94,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_11
| ~ spl0_5
| ~ spl0_7 ),
inference(rat,[],[s39,s8,s13,s18,s23,s91,s90,s89]) ).
cnf(s95,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s94,s93,s92]) ).
cnf(s96,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s53,s49,s60,s3,s4,s5,s95,s90,s89]) ).
cnf(s97,plain,
~ spl0_5,
inference(rat,[],[s88,s78,s2,s7,s12,s17,s22,s96,s89,s90]) ).
cnf(s98,plain,
( spl0_12
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s33,s8,s9,s10,s89]) ).
cnf(s99,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s33,s3,s4,s5,s34,s98,s89]) ).
cnf(s100,plain,
~ spl0_4,
inference(rat,[],[s34,s2,s7,s99]) ).
cnf(s101,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_10
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s66,s49,s60,s89]) ).
cnf(s102,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s48,s78,s8,s13,s18,s23,s101,s89,s90]) ).
cnf(s103,plain,
( ~ spl0_12
| ~ spl0_17
| ~ spl0_2
| ~ spl0_8 ),
inference(rat,[],[s87,s43,s89,s90]) ).
cnf(s104,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s103,s78,s10,s15,s20,s25]) ).
cnf(s105,plain,
( ~ spl0_11
| ~ spl0_8
| ~ spl0_2
| ~ spl0_7 ),
inference(rat,[],[s79,s80,s9,s14,s19,s24,s102,s90]) ).
cnf(s106,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s105,s104]) ).
cnf(s107,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s101,s3,s4,s5,s106]) ).
cnf(s108,plain,
~ spl0_2,
inference(rat,[],[s103,s78,s2,s7,s12,s17,s22,s107]) ).
cnf(s109,plain,
spl0_1,
inference(rat,[],[s1,s90,s97,s89,s100,s108]) ).
cnf(s110,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_7
| ~ spl0_11 ),
inference(rat,[],[s72,s49,s60,s109,s89]) ).
cnf(s111,plain,
( spl0_9
| ~ spl0_11
| ~ spl0_8 ),
inference(rat,[],[s41,s78,s8,s13,s18,s23,s89,s90,s109]) ).
cnf(s112,plain,
( ~ spl0_11
| ~ spl0_7
| ~ spl0_8 ),
inference(rat,[],[s79,s80,s9,s14,s19,s24,s110,s111,s90]) ).
cnf(s113,plain,
( spl0_11
| ~ spl0_8 ),
inference(rat,[],[s42,s78,s10,s15,s20,s25,s89,s90,s109]) ).
cnf(s114,plain,
( ~ spl0_11
| ~ spl0_8 ),
inference(rat,[],[s41,s78,s7,s12,s17,s22,s112,s109,s90,s89]) ).
cnf(s115,plain,
~ spl0_8,
inference(rat,[],[s114,s113]) ).
cnf(s116,plain,
spl0_11,
inference(rat,[],[s5,s115]) ).
cnf(s117,plain,
spl0_10,
inference(rat,[],[s4,s115]) ).
cnf(s118,plain,
spl0_9,
inference(rat,[],[s3,s115]) ).
cnf(s119,plain,
spl0_7,
inference(rat,[],[s2,s115]) ).
cnf(s120,plain,
$false,
inference(rat,[],[s110,s116,s119,s117,s118]) ).
fof(f1099,plain,
$false,
inference(avatar_sat_refutation,[],[s120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP367-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:03:45 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.46 % (3318700)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3318709)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3938554173:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (3318706)% WARNING: option uhcvi not known.
% 0.16/0.46 % (3318707)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=23407019:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (3318705)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1255322225_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (3318706)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2329374320:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (3318710)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=639156033:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3318708)dis+10_1_sil=32000:sp=arity:random_seed=502422302:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3318711)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=853837749:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (3318709) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3318700-3318709"...
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (3318709)...printing done.
% 0.16/0.46 % (3318709)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3318709)------------------------------
% 0.16/0.47 % (3318709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3318709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3318709)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3318709)Termination reason: Refutation
% 0.16/0.47 % (3318709)Time elapsed: 0.012 s
% 0.16/0.47 % (3318709)Peak memory usage: 12 MB
% 0.16/0.47 % (3318709)Instructions burned: 35 (million)
% 0.16/0.47 % (3318700)Success in time 0.045 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------