%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 10:13:44 AM UTC 2026
% Result : Unsatisfiable 2.85s 1.28s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 49
% Syntax : Number of formulae : 308 ( 22 unt; 18 def)
% Number of atoms : 1058 ( 308 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1444 ( 694 ~; 732 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl0_5
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f82,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( sk_c6 != inverse(sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| 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,f81,f78,f75,f72,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c8 = inverse(sk_c1)
| ~ 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_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c6 = 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_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = inverse(sk_c4)
| ~ 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_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f114,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f114]) ).
fof(f119,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f94,f119]) ).
fof(f124,definition,
( spl0_14
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f126,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f124,f90]) ).
fof(f128,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f124,f99]) ).
fof(f129,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f124,f104]) ).
fof(f130,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f124,f109]) ).
fof(f131,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f124,f114]) ).
fof(f132,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f124,f119]) ).
fof(f134,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f136,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f134,f90]) ).
fof(f139,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f134,f104]) ).
fof(f140,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f134,f109]) ).
fof(f143,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f81,f90]) ).
fof(f144,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f81,f99]) ).
fof(f145,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f81,f104]) ).
fof(f146,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f22,f81,f109]) ).
fof(f147,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f81,f114]) ).
fof(f148,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f81,f119]) ).
fof(f149,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f85,f90]) ).
fof(f150,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f99]) ).
fof(f151,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f85,f104]) ).
fof(f152,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f109]) ).
fof(f153,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f114]) ).
fof(f154,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f119]) ).
fof(f155,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f160,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f163,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f92]) ).
fof(f164,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f160,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f155]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f177,plain,
( sk_c8 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f168,f92]) ).
fof(f204,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f164,f155]) ).
fof(f208,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f164,f121]) ).
fof(f210,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f164,f111]) ).
fof(f213,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c5),multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f164,f163]) ).
fof(f216,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c6,multiply(sk_c6,X0))
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f213,f101]) ).
fof(f219,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f210,f106]) ).
fof(f221,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f208,f116]) ).
fof(f223,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f164,f219]) ).
fof(f225,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f223,f3]) ).
fof(f229,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f164,f221]) ).
fof(f231,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f229,f3]) ).
fof(f236,plain,
( sk_c7 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f231,f225]) ).
fof(f239,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f204,f225]) ).
fof(f240,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f3]) ).
fof(f241,plain,
( sk_c6 = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f240,f225]) ).
fof(f244,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f155,f241]) ).
fof(f246,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f101,f241]) ).
fof(f247,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f244,f177]) ).
fof(f249,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f247,f231]) ).
fof(f250,plain,
( sk_c6 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f247,f225]) ).
fof(f355,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f216,f236]) ).
fof(f356,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f355,f249]) ).
fof(f409,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f246,f236]) ).
fof(f410,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f409,f249]) ).
fof(f412,plain,
( sk_c6 != sk_c8
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f83,f410]) ).
fof(f416,plain,
( $false
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f412,f250]) ).
fof(f417,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f422,plain,
( sk_c7 != sk_c8
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f87,f219]) ).
fof(f423,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f422,f249]) ).
fof(f424,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f425,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(sk_c8,multiply(X1,sk_c8)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f79,f249]) ).
fof(f426,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f86,f236]) ).
fof(f427,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f426,f249]) ).
fof(f443,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f425,f410]) ).
fof(f446,plain,
( sk_c6 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f425,f101]) ).
fof(f448,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f443]) ).
fof(f449,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f446,f250]) ).
fof(f453,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f448,f356]) ).
fof(f454,plain,
( sk_c8 != multiply(sk_c8,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f449,f92]) ).
fof(f456,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f453,f427]) ).
fof(f457,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f458,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f454,f236]) ).
fof(f461,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f458,f221]) ).
fof(f462,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f463,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f70,f236]) ).
fof(f464,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f463,f249]) ).
fof(f465,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f464,f236]) ).
fof(f466,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f465,f249]) ).
fof(f467,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f466,f410]) ).
fof(f472,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f467]) ).
fof(f476,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f472,f427]) ).
fof(f477,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f476]) ).
fof(f487,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f73,f249]) ).
fof(f488,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f487,f236]) ).
fof(f489,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f488,f249]) ).
fof(f490,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f489,f249]) ).
fof(f491,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f490,f410]) ).
fof(f496,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f491]) ).
fof(f500,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f496,f427]) ).
fof(f501,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f500]) ).
fof(f562,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f164,f126]) ).
fof(f564,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f562,f96]) ).
fof(f583,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,sk_c8))
| sk_c8 != inverse(multiply(X0,X1)) )
| ~ spl0_3 ),
inference(superposition,[],[f76,f4]) ).
fof(f585,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f76,f121]) ).
fof(f587,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f585]) ).
fof(f600,plain,
( ~ spl0_12
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f587,f119,f75,f114]) ).
fof(f603,definition,
( spl0_16
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f604,plain,
( sk_c7 = sk_c8
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f621,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f82]) ).
fof(f624,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f219,f86]) ).
fof(f627,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f86]) ).
fof(f632,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f624,f109,f104,f85,f603]) ).
fof(f633,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f86,f604]) ).
fof(f681,plain,
( sk_c7 = sk_c8
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f136,f564]) ).
fof(f693,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c6,X0))
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f627,f604]) ).
fof(f706,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f164,f633]) ).
fof(f708,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f706,f3]) ).
fof(f717,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f164,f693]) ).
fof(f720,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f717,f164]) ).
fof(f735,plain,
( ! [X0,X1] :
( sk_c8 != multiply(X0,multiply(X1,sk_c8))
| sk_c8 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f583,f604]) ).
fof(f755,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(multiply(sk_c8,sk_c6))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f735,f693]) ).
fof(f763,plain,
( sk_c8 != inverse(sk_c8)
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f755,f633]) ).
fof(f778,plain,
( sk_c6 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f763,f82]) ).
fof(f787,definition,
( spl0_20
<=> sk_c8 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f791,definition,
( spl0_21
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f792,plain,
( sk_c6 = sk_c8
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f794,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f778,f603,f85,f81,f75,f791,f787]) ).
fof(f817,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f720,f621]) ).
fof(f838,plain,
( spl0_16
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f681,f134,f124,f94,f603]) ).
fof(f872,plain,
( sk_c6 = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f708,f817]) ).
fof(f879,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f73,f604]) ).
fof(f880,plain,
( spl0_21
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f872,f603,f85,f81,f791]) ).
fof(f881,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c6 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f879,f604]) ).
fof(f882,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_21 ),
inference(superposition,[],[f86,f792]) ).
fof(f893,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f882,f604]) ).
fof(f896,plain,
( spl0_20
| ~ spl0_6
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f893,f791,f603,f85,f787]) ).
fof(f899,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f881,f792]) ).
fof(f900,plain,
( sk_c6 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f899,f82]) ).
fof(f908,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f900,f792]) ).
fof(f909,plain,
( ~ spl0_20
| ~ spl0_2
| ~ spl0_5
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f908,f791,f603,f81,f72,f787]) ).
fof(f910,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(sk_c8,multiply(X1,sk_c8)) )
| ~ spl0_4
| ~ spl0_16 ),
inference(forward_demodulation,[],[f79,f604]) ).
fof(f915,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f910,f96]) ).
fof(f916,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f915]) ).
fof(f917,plain,
( sk_c8 != multiply(sk_c8,sk_c2)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f916,f126]) ).
fof(f921,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f917,f564]) ).
fof(f922,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f921]) ).
fof(f923,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f70,f792]) ).
fof(f924,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f923,f792]) ).
fof(f926,plain,
( sk_c6 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(superposition,[],[f924,f82]) ).
fof(f934,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f926,f792]) ).
fof(f935,plain,
( ~ spl0_20
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f934,f791,f81,f69,f787]) ).
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_8
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s8,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s9,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s10,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s11,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s12,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s13,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s14,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f137]) ).
cnf(s16,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s17,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f140]) ).
cnf(s20,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f143]) ).
cnf(s21,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f144]) ).
cnf(s22,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f417]) ).
cnf(s33,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f424]) ).
cnf(s35,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f457]) ).
cnf(s37,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f462]) ).
cnf(s38,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f477]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f501]) ).
cnf(s51,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f600]) ).
cnf(s56,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f632]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f794]) ).
cnf(s64,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f838]) ).
cnf(s74,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f880]) ).
cnf(s78,plain,
( ~ spl0_6
| ~ spl0_16
| spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f896]) ).
cnf(s79,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_16
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f909]) ).
cnf(s80,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f922]) ).
cnf(s81,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f935]) ).
cnf(s82,plain,
spl0_5,
inference(rat,[],[s32,s20,s21,s22,s23,s24,s25]) ).
cnf(s83,plain,
spl0_6,
inference(rat,[],[s33,s26,s27,s28,s29,s30,s31]) ).
cnf(s84,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s35,s3,s4,s5,s6,s7,s83]) ).
cnf(s85,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s37,s12,s13,s80,s56,s84,s83]) ).
cnf(s86,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s80,s64,s11,s17]) ).
cnf(s87,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s80,s64,s10,s16]) ).
cnf(s88,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s80,s9,s56,s85,s87,s86,s84,s83]) ).
cnf(s89,plain,
~ spl0_4,
inference(rat,[],[s80,s64,s2,s8,s14,s88]) ).
cnf(s90,plain,
( ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s59,s78,s74,s83,s82]) ).
cnf(s91,plain,
( spl0_11
| ~ spl0_8
| spl0_16 ),
inference(rat,[],[s64,s11,s17]) ).
cnf(s92,plain,
( ~ spl0_8
| spl0_16 ),
inference(rat,[],[s64,s10,s16,s56,s91,s83]) ).
cnf(s93,plain,
~ spl0_3,
inference(rat,[],[s51,s6,s7,s92,s90]) ).
cnf(s94,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s79,s78,s74,s82,s83]) ).
cnf(s95,plain,
~ spl0_2,
inference(rat,[],[s42,s4,s5,s2,s3,s6,s7,s92,s94,s83]) ).
cnf(s96,plain,
spl0_1,
inference(rat,[],[s1,s82,s89,s83,s93,s95]) ).
cnf(s97,plain,
( ~ spl0_16
| ~ spl0_21 ),
inference(rat,[],[s81,s78,s83,s96,s82]) ).
cnf(s98,plain,
~ spl0_16,
inference(rat,[],[s97,s74,s82,s83]) ).
cnf(s99,plain,
~ spl0_8,
inference(rat,[],[s92,s98]) ).
cnf(s100,plain,
spl0_13,
inference(rat,[],[s7,s99]) ).
cnf(s101,plain,
spl0_12,
inference(rat,[],[s6,s99]) ).
cnf(s102,plain,
spl0_9,
inference(rat,[],[s3,s99]) ).
cnf(s103,plain,
spl0_7,
inference(rat,[],[s2,s99]) ).
cnf(s104,plain,
spl0_11,
inference(rat,[],[s5,s99]) ).
cnf(s105,plain,
spl0_10,
inference(rat,[],[s4,s99]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s38,s104,s105,s102,s96,s83,s100,s103,s101]) ).
fof(f936,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:57:53 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.85/1.27 % (2090906)Input is clausal, will run a generic CNF schedule.
% 2.85/1.27 % (2090915)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4084778303:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.85/1.27 % (2090915)Instruction limit reached!
% 2.85/1.27 % (2090915)------------------------------
% 2.85/1.27 % (2090915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.27 % (2090915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.27 % (2090915)CaDiCaL version: 2.1.3
% 2.85/1.27 % (2090915)Termination reason: Instruction limit
% 2.85/1.27 % (2090915)Termination phase: Saturation
% 2.85/1.27 % (2090915)Time elapsed: 0.036 s
% 2.85/1.27 % (2090915)Peak memory usage: 89 MB
% 2.85/1.27 % (2090915)Instructions burned: 114 (million)
% 2.85/1.27 % (2090916)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=59113035:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.85/1.27 % (2090914)lrs+10_1_sil=8000:sp=occurrence:random_seed=256781871:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.85/1.27 % (2090912)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3614028072:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.85/1.28 % (2090911)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=341275681:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.85/1.28 % (2090913)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3213324182:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.85/1.28 % (2090914)Refutation not found, incomplete strategy
% 2.85/1.28 % (2090914)------------------------------
% 2.85/1.28 % (2090914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2090914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2090914)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2090914)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.28 % (2090914)Time elapsed: 0.002 s
% 2.85/1.28 % (2090914)Peak memory usage: 88 MB
% 2.85/1.28 % (2090914)Instructions burned: 3 (million)
% 2.85/1.28 % (2090917)dis-21_1_sil=8000:lcm=predicate:random_seed=476172213:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.85/1.28 % (2090917)Refutation not found, incomplete strategy
% 2.85/1.28 % (2090917)------------------------------
% 2.85/1.28 % (2090917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2090917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2090917)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2090917)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.28 % (2090917)Time elapsed: 0.002 s
% 2.85/1.28 % (2090917)Peak memory usage: 88 MB
% 2.85/1.28 % (2090917)Instructions burned: 2 (million)
% 2.85/1.28 % (2090916)First to succeed.
% 2.85/1.28 % (2090916)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2090906"
% 2.85/1.28 % (2090919)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2722514086:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.85/1.28 % (2090919)Refutation not found, incomplete strategy
% 2.85/1.28 % (2090919)------------------------------
% 2.85/1.28 % (2090919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2090919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2090919)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2090919)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.28 % (2090919)Time elapsed: 0.001 s
% 2.85/1.28 % (2090919)Peak memory usage: 88 MB
% 2.85/1.28 % (2090919)Instructions burned: 3 (million)
% 2.85/1.28 % (2090919)------------------------------
% 2.85/1.28 % (2090919)------------------------------
% 2.85/1.28 % (2090914)------------------------------
% 2.85/1.28 % (2090914)------------------------------
% 2.85/1.28 % (2090917)------------------------------
% 2.85/1.28 % (2090917)------------------------------
% 2.85/1.28 % (2090916)Refutation found. Thanks to Tanya!
% 2.85/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.85/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.37 % (2090916)------------------------------
% 3.48/1.37 % (2090916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (2090916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (2090916)CaDiCaL version: 2.1.3
% 3.48/1.37 % (2090916)Termination reason: Refutation
% 3.48/1.37 % (2090916)Time elapsed: 0.022 s
% 3.48/1.37 % (2090916)Peak memory usage: 89 MB
% 3.48/1.37 % (2090916)Instructions burned: 31 (million)
% 3.48/1.37 % (2090916)------------------------------
% 3.48/1.37 % (2090916)------------------------------
% 3.48/1.37 % (2090906)Success in time 0.425 s
% 3.48/1.37 % Vampire exiting
%------------------------------------------------------------------------------