%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP345-1 : 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 10:13:42 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.28s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 48
% Syntax : Number of formulae : 296 ( 18 unt; 19 def)
% Number of atoms : 932 ( 270 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1182 ( 546 ~; 617 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 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(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c4,sk_c6) = 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_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = 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
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = 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_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = 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
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = 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_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = 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(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
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(f59,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
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
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(X3) != sk_c6 ),
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_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c5 != inverse(sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( sk_c5 != inverse(sk_c6)
| spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl0_3
<=> ! [X2] :
( sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c6 != multiply(X2,sk_c7) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
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,f75,f71,f68]) ).
fof(f93,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = 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(f100,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f64,f97,f93]) ).
fof(f102,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f62,f97,f102]) ).
fof(f106,plain,
( spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f97,f71]) ).
fof(f108,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f110,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f113,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f115,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f113]) ).
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(f122,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f119,f93]) ).
fof(f123,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f119,f102]) ).
fof(f124,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f119,f71]) ).
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_2
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f129,f71]) ).
fof(f135,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f129,f108]) ).
fof(f136,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f129,f113]) ).
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_2
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f139,f71]) ).
fof(f145,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f139,f108]) ).
fof(f146,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f139,f113]) ).
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_2
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f88,f71]) ).
fof(f151,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f88,f108]) ).
fof(f153,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f88,f78]) ).
fof(f154,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_2 ),
inference(superposition,[],[f3,f72]) ).
fof(f156,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f110]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f104]) ).
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_2 ),
inference(superposition,[],[f4,f154]) ).
fof(f167,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f166,f1]) ).
fof(f170,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f156]) ).
fof(f171,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f170,f1]) ).
fof(f176,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f167,f79]) ).
fof(f209,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f163,f156]) ).
fof(f213,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f163,f176]) ).
fof(f214,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f163,f115]) ).
fof(f216,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f163,f104]) ).
fof(f221,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f216,f95]) ).
fof(f223,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f214,f110]) ).
fof(f224,plain,
( identity = sk_c7
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f213,f3]) ).
fof(f231,plain,
( sk_c6 = sk_c7
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f221,f79]) ).
fof(f247,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f223,f231]) ).
fof(f248,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c5,sk_c6)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f162,f247]) ).
fof(f253,plain,
( identity = multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f248,f154]) ).
fof(f254,plain,
( identity = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f253,f104]) ).
fof(f255,plain,
( sk_c7 = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f254,f224]) ).
fof(f256,plain,
( sk_c6 = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f255,f231]) ).
fof(f258,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f209,f224]) ).
fof(f259,plain,
( identity = sk_c3
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f3]) ).
fof(f260,plain,
( sk_c7 = sk_c3
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f259,f224]) ).
fof(f261,plain,
( sk_c6 = sk_c3
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f260,f231]) ).
fof(f308,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f171,f261]) ).
fof(f309,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c6,X0)) = X0
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f308,f231]) ).
fof(f346,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f309,f79]) ).
fof(f356,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f346,f90]) ).
fof(f357,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f365,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f83,f256]) ).
fof(f374,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f365,f110]) ).
fof(f377,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f374,f231]) ).
fof(f382,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f377,f261]) ).
fof(f387,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f382,f247]) ).
fof(f388,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f399,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f141]) ).
fof(f406,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f163,f89]) ).
fof(f407,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f89]) ).
fof(f410,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f163,f99]) ).
fof(f412,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f410,f121]) ).
fof(f413,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f163,f131]) ).
fof(f415,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f413,f141]) ).
fof(f423,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f83,f72]) ).
fof(f436,definition,
( spl0_17
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f437,plain,
( sk_c6 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f446,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f423,f79]) ).
fof(f449,definition,
( spl0_19
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f450,plain,
( sk_c6 = sk_c5
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f452,plain,
( ~ spl0_19
| ~ spl0_17
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f446,f82,f78,f71,f436,f449]) ).
fof(f456,plain,
( sk_c7 != sk_c5
| sk_c6 != multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f76,f72]) ).
fof(f458,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f76,f110]) ).
fof(f462,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f458]) ).
fof(f465,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f462,f115]) ).
fof(f466,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f465]) ).
fof(f467,plain,
( sk_c6 != sk_c5
| sk_c7 != sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f456,f89]) ).
fof(f470,definition,
( spl0_20
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f471,plain,
( sk_c7 = sk_c5
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f472,plain,
( sk_c7 != sk_c5
| spl0_20 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f473,plain,
( ~ spl0_20
| ~ spl0_19
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f467,f88,f75,f71,f449,f470]) ).
fof(f475,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f69,f72]) ).
fof(f490,definition,
( spl0_22
<=> sk_c5 = multiply(sk_c6,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f491,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f493,plain,
( ~ spl0_22
| ~ spl0_19
| ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f475,f71,f68,f449,f490]) ).
fof(f530,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f407,f223]) ).
fof(f532,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f223]) ).
fof(f534,plain,
( identity = sk_c6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f532,f3]) ).
fof(f536,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f530,f154]) ).
fof(f537,plain,
( identity = sk_c5
| ~ spl0_2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f536,f89]) ).
fof(f545,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f86,f110]) ).
fof(f546,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f86,f141]) ).
fof(f548,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_6
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f546]) ).
fof(f549,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_6
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f545]) ).
fof(f551,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f548,f131]) ).
fof(f552,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f551]) ).
fof(f553,plain,
( sk_c7 != multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f549,f260]) ).
fof(f561,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f553,f223]) ).
fof(f562,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f561]) ).
fof(f568,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f80,f471]) ).
fof(f569,plain,
( sk_c7 != sk_c5
| spl0_4
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f568,f89]) ).
fof(f570,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f569,f471]) ).
fof(f571,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f570]) ).
fof(f574,plain,
( sk_c6 = sk_c5
| ~ spl0_2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f537,f534]) ).
fof(f577,plain,
( spl0_19
| ~ spl0_2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f574,f113,f108,f88,f71,f449]) ).
fof(f646,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_15 ),
inference(superposition,[],[f163,f399]) ).
fof(f669,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f407,f415]) ).
fof(f674,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f669,f491]) ).
fof(f700,plain,
( spl0_22
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f412,f119,f97,f490]) ).
fof(f702,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f89,f437]) ).
fof(f708,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f702,f436,f88,f490]) ).
fof(f713,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_22 ),
inference(superposition,[],[f163,f491]) ).
fof(f836,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f163,f674]) ).
fof(f838,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f836,f3]) ).
fof(f849,plain,
( sk_c6 = sk_c7
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f406,f713]) ).
fof(f857,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f849,f490,f88,f436]) ).
fof(f862,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f646,f437]) ).
fof(f864,plain,
( sk_c1 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f862,f838]) ).
fof(f866,plain,
( sk_c1 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f864,f437]) ).
fof(f868,plain,
( identity = sk_c1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f866,f3]) ).
fof(f869,plain,
( sk_c7 = sk_c1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f868,f838]) ).
fof(f870,plain,
( sk_c6 = sk_c1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f869,f437]) ).
fof(f873,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f141,f870]) ).
fof(f874,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f399,f870]) ).
fof(f878,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f874,f437]) ).
fof(f879,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f873,f437]) ).
fof(f882,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f878,f491]) ).
fof(f883,plain,
( sk_c7 = sk_c5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f882,f838]) ).
fof(f884,plain,
( $false
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f883,f472]) ).
fof(f885,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f884]) ).
fof(f893,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f883,f437]) ).
fof(f900,plain,
( spl0_19
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f893,f490,f436,f139,f129,f88,f449]) ).
fof(f954,plain,
( sk_c6 != sk_c5
| spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f73,f879]) ).
fof(f958,plain,
( $false
| spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f954,f450]) ).
fof(f959,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f958]) ).
fof(f986,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f231,f102,f93,f78,f436]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f100]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
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_2
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_12
| 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_2
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s24,plain,
( spl0_12
| 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_2
| spl0_7 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f151]) ).
cnf(s31,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f357]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f388]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f452]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f466]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f473]) ).
cnf(s46,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f493]) ).
cnf(s52,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f552]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f562]) ).
cnf(s56,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_20 ),
inference(sat_conversion,[],[f571]) ).
cnf(s58,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f577]) ).
cnf(s64,plain,
( ~ spl0_9
| ~ spl0_13
| spl0_22 ),
inference(sat_conversion,[],[f700]) ).
cnf(s67,plain,
( ~ spl0_7
| ~ spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f708]) ).
cnf(s74,plain,
( ~ spl0_7
| spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f857]) ).
cnf(s77,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f885]) ).
cnf(s83,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f900]) ).
cnf(s86,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f959]) ).
cnf(s88,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f986]) ).
cnf(s96,plain,
( ~ spl0_22
| ~ spl0_7
| ~ spl0_17
| ~ spl0_15
| ~ spl0_14
| spl0_2 ),
inference(rat,[],[s83,s86]) ).
cnf(s97,plain,
spl0_2,
inference(rat,[],[s96,s74,s64,s4,s10,s16,s22,s28]) ).
cnf(s98,plain,
( ~ spl0_17
| ~ spl0_15
| ~ spl0_14
| ~ spl0_7
| spl0_1 ),
inference(rat,[],[s1,s41,s43,s56,s83,s77,s67,s52,s97]) ).
cnf(s99,plain,
( spl0_8
| spl0_22 ),
inference(rat,[],[s64,s2,s8]) ).
cnf(s100,plain,
( spl0_10
| spl0_22 ),
inference(rat,[],[s64,s3,s9]) ).
cnf(s101,plain,
( spl0_17
| ~ spl0_7 ),
inference(rat,[],[s64,s7,s13,s88,s100,s99,s74]) ).
cnf(s102,plain,
( spl0_15
| ~ spl0_7
| spl0_1 ),
inference(rat,[],[s1,s36,s55,s42,s20,s21,s23,s24,s25,s97]) ).
cnf(s103,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_1
| ~ spl0_7 ),
inference(rat,[],[s1,s36,s55,s42,s14,s15,s17,s18,s19,s98,s97]) ).
cnf(s104,plain,
( ~ spl0_7
| spl0_1 ),
inference(rat,[],[s103,s102,s101]) ).
cnf(s105,plain,
spl0_7,
inference(rat,[],[s32,s26,s27,s29,s31,s97]) ).
cnf(s106,plain,
spl0_17,
inference(rat,[],[s101,s105]) ).
cnf(s107,plain,
spl0_1,
inference(rat,[],[s104,s105]) ).
cnf(s108,plain,
spl0_22,
inference(rat,[],[s67,s105,s106]) ).
cnf(s109,plain,
~ spl0_19,
inference(rat,[],[s46,s108,s97,s107]) ).
cnf(s111,plain,
spl0_14,
inference(rat,[],[s58,s17,s18,s97,s109,s105]) ).
cnf(s112,plain,
~ spl0_15,
inference(rat,[],[s83,s108,s106,s109,s105,s111]) ).
cnf(s115,plain,
spl0_12,
inference(rat,[],[s24,s112]) ).
cnf(s116,plain,
spl0_11,
inference(rat,[],[s23,s112]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s58,s105,s109,s97,s115,s116]) ).
fof(f1009,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:56:53 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.74/1.28 % (2089271)Input is clausal, will run a generic CNF schedule.
% 2.74/1.28 % (2089276)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=1787125787:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.28 % (2089278)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3828262516:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.28 % (2089281)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=597904403:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.28 % (2089277)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3734984886:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.28 % (2089279)lrs+10_1_sil=8000:sp=occurrence:random_seed=2769681785:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.28 % (2089282)dis-21_1_sil=8000:lcm=predicate:random_seed=626604278: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)
% 2.74/1.28 % (2089280)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=973863415:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.28 % (2089282)Refutation not found, incomplete strategy
% 2.74/1.28 % (2089282)------------------------------
% 2.74/1.28 % (2089282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2089282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2089282)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2089282)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.28 % (2089282)Time elapsed: 0.002 s
% 2.74/1.28 % (2089282)Peak memory usage: 88 MB
% 2.74/1.28 % (2089282)Instructions burned: 1 (million)
% 2.74/1.28 % (2089279)Refutation not found, incomplete strategy
% 2.74/1.28 % (2089279)------------------------------
% 2.74/1.28 % (2089279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2089279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2089279)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2089279)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.28 % (2089279)Time elapsed: 0.002 s
% 2.74/1.28 % (2089279)Peak memory usage: 88 MB
% 2.74/1.28 % (2089279)Instructions burned: 3 (million)
% 2.74/1.28 % (2089281)First to succeed.
% 2.74/1.28 % (2089281)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2089271"
% 2.74/1.28 % (2089280)Instruction limit reached!
% 2.74/1.28 % (2089280)------------------------------
% 2.74/1.28 % (2089280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2089280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2089280)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2089280)Termination reason: Instruction limit
% 2.74/1.28 % (2089280)Termination phase: Saturation
% 2.74/1.28 % (2089280)Time elapsed: 0.067 s
% 2.74/1.28 % (2089280)Peak memory usage: 89 MB
% 2.74/1.28 % (2089280)Instructions burned: 115 (million)
% 2.74/1.28 % (2089290)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=2017552685:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.74/1.28 % (2089290)Refutation not found, incomplete strategy
% 2.74/1.28 % (2089290)------------------------------
% 2.74/1.28 % (2089290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2089290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2089290)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2089290)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.28 % (2089290)Time elapsed: 0.003 s
% 2.74/1.28 % (2089290)Peak memory usage: 88 MB
% 2.74/1.28 % (2089290)Instructions burned: 3 (million)
% 2.74/1.28 % (2089282)------------------------------
% 2.74/1.28 % (2089282)------------------------------
% 2.74/1.28 % (2089279)------------------------------
% 2.74/1.28 % (2089279)------------------------------
% 2.74/1.28 % (2089281)Refutation found. Thanks to Tanya!
% 2.74/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.38 % (2089281)------------------------------
% 3.48/1.38 % (2089281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.38 % (2089281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.38 % (2089281)CaDiCaL version: 2.1.3
% 3.48/1.38 % (2089281)Termination reason: Refutation
% 3.48/1.38 % (2089281)Time elapsed: 0.025 s
% 3.48/1.38 % (2089281)Peak memory usage: 89 MB
% 3.48/1.38 % (2089281)Instructions burned: 35 (million)
% 3.48/1.38 % (2089281)------------------------------
% 3.48/1.38 % (2089281)------------------------------
% 3.48/1.38 % (2089271)Success in time 0.425 s
% 3.48/1.38 % Vampire exiting
%------------------------------------------------------------------------------