%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP347-1 : 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 : n003.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 10:13:42 AM UTC 2026
% Result : Unsatisfiable 2.15s 1.30s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 47
% Syntax : Number of formulae : 306 ( 20 unt; 21 def)
% Number of atoms : 927 ( 271 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1156 ( 535 ~; 600 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 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_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c6
| multiply(X3,sk_c7) != sk_c5
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c7 != multiply(sk_c6,sk_c5)
| sk_c5 != inverse(sk_c6)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c5 != multiply(X3,sk_c7) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( sk_c5 != inverse(sk_c6)
| spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_4
<=> sk_c7 = multiply(sk_c6,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( sk_c7 != multiply(sk_c6,sk_c5)
| spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_5
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_7
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f89,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f66,f88,f85,f82,f78,f74,f71,f68]) ).
fof(f93,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f102,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f107,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f109,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f97,f107]) ).
fof(f112,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f97,f74]) ).
fof(f117,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f54,f97,f78]) ).
fof(f119,definition,
( spl0_13
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f124,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f119,f107]) ).
fof(f126,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f119,f74]) ).
fof(f127,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f119,f78]) ).
fof(f129,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f131,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f129,f93]) ).
fof(f133,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f129,f102]) ).
fof(f134,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f129,f107]) ).
fof(f136,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f129,f74]) ).
fof(f137,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f129,f78]) ).
fof(f139,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f141,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f139,f93]) ).
fof(f143,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f139,f102]) ).
fof(f144,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f139,f107]) ).
fof(f146,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f139,f74]) ).
fof(f147,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f139,f78]) ).
fof(f148,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f88,f93]) ).
fof(f149,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f88,f102]) ).
fof(f150,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f88,f107]) ).
fof(f151,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f88,f112]) ).
fof(f152,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f88,f74]) ).
fof(f153,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f88,f78]) ).
fof(f154,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f3,f75]) ).
fof(f156,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f109]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = multiply(sk_c7,X0)
| ~ spl0_4 ),
inference(superposition,[],[f4,f79]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f166,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f154]) ).
fof(f167,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f166,f1]) ).
fof(f176,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f167,f79]) ).
fof(f177,plain,
( sk_c3 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f167,f156]) ).
fof(f188,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f160,f176]) ).
fof(f190,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f188,f79]) ).
fof(f212,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl0_3 ),
inference(superposition,[],[f163,f154]) ).
fof(f213,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f163,f176]) ).
fof(f214,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f163,f114]) ).
fof(f216,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f163,f104]) ).
fof(f221,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f216,f95]) ).
fof(f223,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f214,f109]) ).
fof(f224,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f213,f3]) ).
fof(f228,plain,
( sk_c3 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f177,f224]) ).
fof(f230,plain,
( sk_c5 = sk_c3
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f228,f176]) ).
fof(f232,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f163,f221]) ).
fof(f234,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f232,f3]) ).
fof(f236,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f234,f224]) ).
fof(f246,plain,
( sk_c6 != sk_c5
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f90,f223]) ).
fof(f254,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f246,f236]) ).
fof(f265,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f212,f224]) ).
fof(f266,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f265,f236]) ).
fof(f267,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f266,f3]) ).
fof(f268,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f267,f224]) ).
fof(f275,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f268,f254]) ).
fof(f276,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f275]) ).
fof(f314,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f89,f223]) ).
fof(f330,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f121]) ).
fof(f334,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f141]) ).
fof(f342,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f163,f131]) ).
fof(f343,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f131]) ).
fof(f344,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f342,f141]) ).
fof(f388,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f163,f89]) ).
fof(f390,plain,
( sk_c7 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f388,f75]) ).
fof(f395,plain,
( sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f113,f230]) ).
fof(f396,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f395,f154]) ).
fof(f397,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f396,f224]) ).
fof(f398,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f412,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f83,f75]) ).
fof(f420,definition,
( spl0_16
<=> sk_c6 = multiply(sk_c1,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f421,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f424,definition,
( spl0_17
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f425,plain,
( sk_c6 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f426,plain,
( sk_c6 != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f434,definition,
( spl0_18
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f435,plain,
( sk_c6 = sk_c5
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f436,plain,
( sk_c6 != sk_c5
| spl0_18 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f440,definition,
( spl0_19
<=> sk_c6 = multiply(sk_c6,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f441,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f443,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f412,f82,f74,f434,f440]) ).
fof(f444,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f163,f99]) ).
fof(f446,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f444,f121]) ).
fof(f448,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_13 ),
inference(superposition,[],[f163,f330]) ).
fof(f451,plain,
( sk_c2 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_13 ),
inference(forward_demodulation,[],[f448,f75]) ).
fof(f453,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_15 ),
inference(superposition,[],[f163,f334]) ).
fof(f486,plain,
( sk_c6 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f167,f446]) ).
fof(f487,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f163,f446]) ).
fof(f500,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f390,f486]) ).
fof(f508,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f500,f119,f97,f88,f74,f424]) ).
fof(f513,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f344,f425]) ).
fof(f524,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f453,f425]) ).
fof(f525,plain,
( sk_c1 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f524,f75]) ).
fof(f526,plain,
( sk_c1 = sk_c2
| ~ spl0_3
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f525,f451]) ).
fof(f538,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f99,f526]) ).
fof(f540,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f538,f424,f139,f119,f97,f74,f420]) ).
fof(f542,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c5,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f421]) ).
fof(f549,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f542,f486]) ).
fof(f556,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f549,f131]) ).
fof(f562,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f556,f80]) ).
fof(f563,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f562]) ).
fof(f566,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f79,f425]) ).
fof(f574,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f86,f425]) ).
fof(f577,plain,
( spl0_19
| ~ spl0_4
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f566,f424,f78,f440]) ).
fof(f579,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f574,f425]) ).
fof(f588,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f579,f75]) ).
fof(f589,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f579,f141]) ).
fof(f593,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f589,f425]) ).
fof(f597,plain,
( sk_c6 != sk_c7
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f593,f131]) ).
fof(f601,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f597,f425]) ).
fof(f602,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f603,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_demodulation,[],[f72,f425]) ).
fof(f618,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f603,f75]) ).
fof(f633,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f69,f425]) ).
fof(f634,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f633,f425]) ).
fof(f644,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f634,f75]) ).
fof(f660,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_19 ),
inference(superposition,[],[f163,f441]) ).
fof(f662,plain,
( identity = sk_c5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f660,f3]) ).
fof(f685,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c7,sk_c6)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f343,f513]) ).
fof(f689,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c6)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f685,f425]) ).
fof(f694,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f689,f446]) ).
fof(f695,plain,
( sk_c7 = sk_c5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f694,f131]) ).
fof(f696,plain,
( sk_c6 = sk_c5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f695,f425]) ).
fof(f697,plain,
( $false
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f696,f436]) ).
fof(f698,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f697]) ).
fof(f748,plain,
( sk_c6 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f487,f388]) ).
fof(f754,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f748,f426]) ).
fof(f755,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f754]) ).
fof(f756,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f190,f344]) ).
fof(f773,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f756,f426]) ).
fof(f774,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f773]) ).
fof(f786,definition,
( spl0_20
<=> sk_c6 = multiply(sk_c6,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f789,plain,
( ~ spl0_20
| ~ spl0_18
| ~ spl0_3
| ~ spl0_6
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f588,f424,f85,f74,f434,f786]) ).
fof(f791,plain,
( spl0_18
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f314,f112,f107,f88,f434]) ).
fof(f792,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f268,f102,f93,f78,f74,f424]) ).
fof(f797,definition,
( spl0_21
<=> sk_c5 = multiply(sk_c6,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f800,plain,
( ~ spl0_21
| ~ spl0_18
| ~ spl0_1
| ~ spl0_3
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f644,f424,f74,f68,f434,f797]) ).
fof(f805,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f89,f425]) ).
fof(f814,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f805,f424,f88,f797]) ).
fof(f816,plain,
( ~ spl0_20
| ~ spl0_18
| ~ spl0_2
| ~ spl0_3
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f618,f424,f74,f71,f434,f786]) ).
fof(f830,plain,
( sk_c6 != inverse(sk_c6)
| spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f76,f435]) ).
fof(f831,plain,
( sk_c7 != multiply(sk_c6,sk_c6)
| spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f80,f435]) ).
fof(f837,plain,
( spl0_20
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f513,f424,f139,f129,f786]) ).
fof(f839,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f141,f425]) ).
fof(f840,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f831,f425]) ).
fof(f843,plain,
( ~ spl0_20
| spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f840,f434,f424,f78,f786]) ).
fof(f854,plain,
( identity = sk_c6
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f662,f435]) ).
fof(f868,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f3,f839]) ).
fof(f869,plain,
( sk_c6 = multiply(sk_c6,sk_c1)
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f868,f854]) ).
fof(f870,plain,
( sk_c6 = multiply(sk_c3,sk_c6)
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f114,f425]) ).
fof(f877,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_12
| ~ spl0_17 ),
inference(superposition,[],[f163,f870]) ).
fof(f879,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f877,f109]) ).
fof(f880,plain,
( spl0_20
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f879,f424,f112,f107,f786]) ).
fof(f881,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f441,f435]) ).
fof(f882,plain,
( spl0_20
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f881,f440,f434,f786]) ).
fof(f916,plain,
( sk_c1 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f163,f869]) ).
fof(f918,plain,
( identity = sk_c1
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f916,f3]) ).
fof(f919,plain,
( sk_c6 = sk_c1
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f918,f854]) ).
fof(f923,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f839,f919]) ).
fof(f925,plain,
( $false
| spl0_3
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f923,f830]) ).
fof(f926,plain,
( spl0_3
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f925]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f110]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s10,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s12,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s16,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s18,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f142]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s22,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s24,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s25,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s26,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f151]) ).
cnf(s30,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f152]) ).
cnf(s31,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f276]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f398]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f443]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f508]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f540]) ).
cnf(s48,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f563]) ).
cnf(s50,plain,
( ~ spl0_4
| ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f577]) ).
cnf(s55,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f602]) ).
cnf(s67,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f698]) ).
cnf(s71,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f755]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f774]) ).
cnf(s83,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f789]) ).
cnf(s87,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f791]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f792]) ).
cnf(s92,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f800]) ).
cnf(s93,plain,
( ~ spl0_7
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f814]) ).
cnf(s94,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f816]) ).
cnf(s97,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f837]) ).
cnf(s100,plain,
( spl0_4
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f843]) ).
cnf(s110,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f880]) ).
cnf(s111,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f882]) ).
cnf(s114,plain,
( spl0_3
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f926]) ).
cnf(s115,plain,
spl0_3,
inference(rat,[],[s100,s50,s97,s114,s67,s71,s6,s12,s18,s24,s30]) ).
cnf(s116,plain,
spl0_4,
inference(rat,[],[s47,s45,s48,s7,s13,s19,s25,s31,s115]) ).
cnf(s117,plain,
spl0_7,
inference(rat,[],[s33,s26,s27,s28,s29,s115,s116]) ).
cnf(s118,plain,
( ~ spl0_11
| ~ spl0_17
| ~ spl0_6 ),
inference(rat,[],[s83,s110,s87,s36,s115,s117,s116]) ).
cnf(s119,plain,
( ~ spl0_17
| ~ spl0_6 ),
inference(rat,[],[s55,s16,s22,s118]) ).
cnf(s120,plain,
( spl0_10
| spl0_17 ),
inference(rat,[],[s77,s15,s21,s115,s116]) ).
cnf(s121,plain,
( ~ spl0_10
| spl0_17 ),
inference(rat,[],[s77,s14,s20,s88,s116,s115]) ).
cnf(s122,plain,
spl0_17,
inference(rat,[],[s121,s120]) ).
cnf(s123,plain,
spl0_21,
inference(rat,[],[s93,s117,s122]) ).
cnf(s124,plain,
spl0_19,
inference(rat,[],[s50,s116,s122]) ).
cnf(s125,plain,
~ spl0_6,
inference(rat,[],[s119,s122]) ).
cnf(s126,plain,
( ~ spl0_11
| spl0_18 ),
inference(rat,[],[s87,s36,s117,s115,s116]) ).
cnf(s127,plain,
spl0_18,
inference(rat,[],[s16,s67,s4,s10,s22,s126,s122]) ).
cnf(s128,plain,
spl0_20,
inference(rat,[],[s111,s124,s127]) ).
cnf(s129,plain,
~ spl0_5,
inference(rat,[],[s42,s124,s115,s127]) ).
cnf(s130,plain,
~ spl0_2,
inference(rat,[],[s94,s122,s127,s115,s128]) ).
cnf(s131,plain,
spl0_1,
inference(rat,[],[s1,s125,s116,s115,s117,s129,s130]) ).
cnf(s132,plain,
$false,
inference(rat,[],[s92,s123,s127,s115,s122,s131]) ).
fof(f927,plain,
$false,
inference(avatar_sat_refutation,[],[s132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP347-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:56:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 2.15/1.30 % (262418)Input is clausal, will run a generic CNF schedule.
% 2.15/1.30 % (262429)dis-21_1_sil=8000:lcm=predicate:random_seed=3329242452: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)
% 2.15/1.30 % (262429)Refutation not found, incomplete strategy
% 2.15/1.30 % (262429)------------------------------
% 2.15/1.30 % (262429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/1.30 % (262429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/1.30 % (262429)CaDiCaL version: 2.1.3
% 2.15/1.30 % (262429)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.30 % (262429)Time elapsed: 0.001 s
% 2.15/1.30 % (262429)Peak memory usage: 88 MB
% 2.15/1.30 % (262429)Instructions burned: 1 (million)
% 2.15/1.30 % (262426)lrs+10_1_sil=8000:sp=occurrence:random_seed=1841338049:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.15/1.30 % (262423)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=820480740:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.15/1.30 % (262425)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2707057181:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.15/1.30 % (262424)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1943105181:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.15/1.30 % (262427)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1290796081:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.15/1.30 % (262426)Refutation not found, incomplete strategy
% 2.15/1.30 % (262426)------------------------------
% 2.15/1.30 % (262426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/1.30 % (262426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/1.30 % (262426)CaDiCaL version: 2.1.3
% 2.15/1.30 % (262426)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.30 % (262426)Time elapsed: 0.003 s
% 2.15/1.30 % (262426)Peak memory usage: 88 MB
% 2.15/1.30 % (262426)Instructions burned: 3 (million)
% 2.15/1.30 % (262428)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=901945793:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.15/1.30 % (262428)First to succeed.
% 2.15/1.30 % (262428)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-262418"
% 2.15/1.30 % (262427)Instruction limit reached!
% 2.15/1.30 % (262427)------------------------------
% 2.15/1.30 % (262427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/1.30 % (262427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/1.30 % (262427)CaDiCaL version: 2.1.3
% 2.15/1.30 % (262427)Termination reason: Instruction limit
% 2.15/1.30 % (262427)Termination phase: Saturation
% 2.15/1.30 % (262427)Time elapsed: 0.067 s
% 2.15/1.30 % (262427)Peak memory usage: 89 MB
% 2.15/1.30 % (262427)Instructions burned: 115 (million)
% 2.15/1.30 % (262429)------------------------------
% 2.15/1.30 % (262429)------------------------------
% 2.15/1.30 % (262437)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=3435871795:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.15/1.30 % (262437)Refutation not found, incomplete strategy
% 2.15/1.30 % (262437)------------------------------
% 2.15/1.30 % (262437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/1.30 % (262437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/1.30 % (262437)CaDiCaL version: 2.1.3
% 2.15/1.30 % (262437)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.30 % (262437)Time elapsed: 0.003 s
% 2.15/1.30 % (262437)Peak memory usage: 88 MB
% 2.15/1.30 % (262437)Instructions burned: 3 (million)
% 2.15/1.30 % (262438)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1510724833:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.15/1.30 % (262438)Refutation not found, incomplete strategy
% 2.15/1.30 % (262438)------------------------------
% 2.15/1.30 % (262438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/1.30 % (262438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/1.30 % (262438)CaDiCaL version: 2.1.3
% 2.15/1.30 % (262438)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.30 % (262438)Time elapsed: 0.002 s
% 2.15/1.30 % (262438)Peak memory usage: 88 MB
% 2.15/1.30 % (262438)Instructions burned: 3 (million)
% 2.15/1.30 % (262426)------------------------------
% 2.15/1.30 % (262426)------------------------------
% 2.15/1.30 % (262428)Refutation found. Thanks to Tanya!
% 2.15/1.30 % SZS status Unsatisfiable for theBenchmark
% 2.15/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.50 % (262428)------------------------------
% 4.02/1.50 % (262428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.50 % (262428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.50 % (262428)CaDiCaL version: 2.1.3
% 4.02/1.50 % (262428)Termination reason: Refutation
% 4.02/1.50 % (262428)Time elapsed: 0.026 s
% 4.02/1.50 % (262428)Peak memory usage: 89 MB
% 4.02/1.50 % (262428)Instructions burned: 34 (million)
% 4.02/1.50 % (262428)------------------------------
% 4.02/1.50 % (262428)------------------------------
% 4.02/1.50 % (262418)Success in time 0.477 s
% 4.02/1.50 % Vampire exiting
%------------------------------------------------------------------------------