%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP339-1 : 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 : n004.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 10:13:41 AM UTC 2026
% Result : Unsatisfiable 1.90s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 43
% Syntax : Number of formulae : 299 ( 25 unt; 20 def)
% Number of atoms : 932 ( 271 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1241 ( 608 ~; 613 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 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_c8,sk_c9) = sk_c7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f10]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f28]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f70]) ).
fof(f78,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != X5
| inverse(X5) != sk_c9
| multiply(X4,sk_c9) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| inverse(X4) != X5
| sk_c9 != inverse(X5)
| multiply(X4,sk_c9) != X5 ),
inference(reorient_equations,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) ),
inference(equality_resolution,[],[f79]) ).
fof(f82,definition,
( spl0_1
<=> ! [X4] :
( sk_c9 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f83,plain,
( ! [X4] :
( sk_c9 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_3
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_4
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( sk_c7 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_5
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f97,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_6
<=> ! [X1] :
( sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f100,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_7
<=> ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f103,plain,
( ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_8
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f106,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f80,f105,f102,f99,f96,f92,f88,f85,f82]) ).
fof(f114,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f129,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f131,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_13
| spl0_10 ),
inference(avatar_split_clause,[],[f71,f114,f129]) ).
fof(f134,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f136,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_14
| spl0_10 ),
inference(avatar_split_clause,[],[f69,f114,f134]) ).
fof(f138,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f67,f114,f88]) ).
fof(f139,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f65,f114,f92]) ).
fof(f141,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f143,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_15
| spl0_10 ),
inference(avatar_split_clause,[],[f63,f114,f141]) ).
fof(f146,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f148,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_16
| spl0_10 ),
inference(avatar_split_clause,[],[f61,f114,f146]) ).
fof(f151,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f153,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f157,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f53,f151,f129]) ).
fof(f158,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f51,f151,f134]) ).
fof(f159,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f49,f151,f88]) ).
fof(f160,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f47,f151,f92]) ).
fof(f161,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f45,f151,f141]) ).
fof(f162,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f43,f151,f146]) ).
fof(f164,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f166,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f173,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f29,f164,f92]) ).
fof(f174,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f27,f164,f141]) ).
fof(f175,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f25,f164,f146]) ).
fof(f177,definition,
( spl0_19
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f179,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f186,plain,
( spl0_4
| spl0_19 ),
inference(avatar_split_clause,[],[f11,f177,f92]) ).
fof(f187,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f9,f177,f141]) ).
fof(f188,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f7,f177,f146]) ).
fof(f189,plain,
spl0_8,
inference(avatar_split_clause,[],[f5,f105]) ).
fof(f190,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c9)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f86,f89]) ).
fof(f191,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f86,f131]) ).
fof(f192,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f191]) ).
fof(f193,plain,
( sk_c8 != inverse(sk_c9)
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f190]) ).
fof(f194,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f192,f136]) ).
fof(f195,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f202,definition,
( spl0_21
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f203,plain,
( sk_c8 = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f206,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f93]) ).
fof(f207,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f179]) ).
fof(f212,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f116]) ).
fof(f219,definition,
( spl0_23
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f220,plain,
( identity = sk_c8
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( identity != sk_c8
| spl0_23 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f225,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f226,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c9,X0)) = multiply(sk_c7,X0)
| ~ spl0_8 ),
inference(superposition,[],[f4,f106]) ).
fof(f228,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f206]) ).
fof(f234,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f228,f1]) ).
fof(f235,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f225,f1]) ).
fof(f258,plain,
( sk_c9 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f234,f106]) ).
fof(f270,plain,
( sk_c8 != sk_c9
| sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f86,f258]) ).
fof(f273,definition,
( spl0_24
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f275,plain,
( sk_c8 != inverse(sk_c7)
| spl0_24 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f277,definition,
( spl0_25
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f278,plain,
( sk_c8 = sk_c9
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f280,plain,
( ~ spl0_24
| ~ spl0_25
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f270,f105,f92,f85,f277,f273]) ).
fof(f364,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_8 ),
inference(superposition,[],[f235,f226]) ).
fof(f365,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f235,f106]) ).
fof(f378,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_18 ),
inference(superposition,[],[f235,f166]) ).
fof(f380,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f235,f148]) ).
fof(f385,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f235,f153]) ).
fof(f392,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f385,f116]) ).
fof(f397,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f380,f143]) ).
fof(f399,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f378,f179]) ).
fof(f407,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f106,f392]) ).
fof(f416,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f407,f151,f114,f105,f202]) ).
fof(f428,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_21
| spl0_24 ),
inference(superposition,[],[f275,f203]) ).
fof(f429,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(forward_demodulation,[],[f428,f93]) ).
fof(f433,plain,
( $false
| ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f429,f203]) ).
fof(f434,plain,
( ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f437,plain,
( sk_c8 != inverse(sk_c8)
| spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f94,f203]) ).
fof(f439,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f365,f203]) ).
fof(f440,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f364,f203]) ).
fof(f442,plain,
( identity = sk_c9
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f439,f3]) ).
fof(f443,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f440,f235]) ).
fof(f455,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f235,f397]) ).
fof(f457,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f455,f3]) ).
fof(f461,plain,
( $false
| ~ spl0_15
| ~ spl0_16
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f457,f221]) ).
fof(f462,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f489,plain,
( sk_c8 = sk_c9
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(superposition,[],[f399,f443]) ).
fof(f491,plain,
( identity = sk_c1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21 ),
inference(superposition,[],[f207,f443]) ).
fof(f501,plain,
( sk_c9 = sk_c1
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f491,f442]) ).
fof(f510,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f489,f202,f177,f164,f105,f277]) ).
fof(f514,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_23 ),
inference(superposition,[],[f1,f220]) ).
fof(f538,plain,
( sk_c9 = sk_c7
| ~ spl0_8
| ~ spl0_23 ),
inference(superposition,[],[f514,f106]) ).
fof(f544,plain,
( sk_c8 = sk_c9
| ~ spl0_10
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f392,f514]) ).
fof(f547,plain,
( identity = sk_c2
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f212,f514]) ).
fof(f555,plain,
( sk_c9 = sk_c2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[],[f547,f442]) ).
fof(f558,plain,
( spl0_25
| ~ spl0_10
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f544,f219,f151,f114,f277]) ).
fof(f572,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21 ),
inference(superposition,[],[f179,f501]) ).
fof(f584,plain,
( sk_c8 = inverse(sk_c9)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(superposition,[],[f116,f555]) ).
fof(f585,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f584,f193]) ).
fof(f586,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f585]) ).
fof(f593,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f90,f443]) ).
fof(f600,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f593,f203]) ).
fof(f601,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f614,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_8
| ~ spl0_25 ),
inference(superposition,[],[f106,f278]) ).
fof(f631,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f614,f514]) ).
fof(f666,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f572,f278]) ).
fof(f667,plain,
( $false
| spl0_4
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f666,f437]) ).
fof(f668,plain,
( spl0_4
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f669,plain,
( ! [X4] :
( sk_c8 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) )
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f83,f278]) ).
fof(f670,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f93,f203]) ).
fof(f676,plain,
( ! [X4] :
( sk_c8 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f669,f278]) ).
fof(f688,plain,
( sk_c8 != inverse(sk_c8)
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f676,f670]) ).
fof(f691,plain,
( sk_c8 != inverse(sk_c8)
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_25 ),
inference(superposition,[],[f676,f116]) ).
fof(f692,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f691,f670]) ).
fof(f694,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f688,f670]) ).
fof(f695,plain,
( sk_c8 != sk_c9
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_17
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f692,f153]) ).
fof(f697,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f694,f514]) ).
fof(f698,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f697]) ).
fof(f699,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_17
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f695,f278]) ).
fof(f700,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_17
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f699]) ).
fof(f703,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c9 != multiply(X0,sk_c8) )
| ~ spl0_7
| ~ spl0_25 ),
inference(forward_demodulation,[],[f103,f278]) ).
fof(f704,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c8) )
| ~ spl0_7
| ~ spl0_25 ),
inference(forward_demodulation,[],[f703,f278]) ).
fof(f709,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f704,f670]) ).
fof(f712,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_25 ),
inference(superposition,[],[f704,f116]) ).
fof(f713,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f712]) ).
fof(f714,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_21
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f709]) ).
fof(f715,plain,
( sk_c8 != sk_c9
| ~ spl0_7
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f713,f153]) ).
fof(f726,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f714,f514]) ).
fof(f727,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f726]) ).
fof(f728,plain,
( $false
| ~ spl0_7
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f715,f278]) ).
fof(f729,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f733,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c8)
| sk_c9 != inverse(X2) )
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f97,f278]) ).
fof(f734,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f733,f278]) ).
fof(f736,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f734,f670]) ).
fof(f739,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_25 ),
inference(superposition,[],[f734,f116]) ).
fof(f740,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f739]) ).
fof(f741,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f736]) ).
fof(f742,plain,
( sk_c8 != sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f740,f153]) ).
fof(f745,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f741,f514]) ).
fof(f746,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f745]) ).
fof(f747,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f742,f278]) ).
fof(f748,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f747]) ).
fof(f752,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(X1,sk_c8) )
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_demodulation,[],[f100,f278]) ).
fof(f753,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f752,f670]) ).
fof(f756,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_25 ),
inference(superposition,[],[f752,f116]) ).
fof(f757,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f756]) ).
fof(f758,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_21
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f753]) ).
fof(f759,plain,
( sk_c8 != sk_c9
| ~ spl0_6
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f757,f153]) ).
fof(f762,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f758,f514]) ).
fof(f763,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f764,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f759,f278]) ).
fof(f765,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f764]) ).
fof(f808,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_3
| ~ spl0_25 ),
inference(forward_demodulation,[],[f89,f278]) ).
fof(f811,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f631,f277,f219,f105,f202]) ).
fof(f827,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f808,f514]) ).
fof(f832,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f827,f277,f219,f88,f202]) ).
fof(f851,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f136]) ).
fof(f852,plain,
( identity = sk_c4
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f851,f514]) ).
fof(f854,plain,
( sk_c8 = sk_c4
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f852,f220]) ).
fof(f861,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f131,f538]) ).
fof(f862,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f861,f854]) ).
fof(f863,plain,
( sk_c8 = sk_c9
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f862,f514]) ).
fof(f864,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f863,f219,f134,f129,f105,f277]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f108]) ).
cnf(s5,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s6,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s7,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f139]) ).
cnf(s9,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s10,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f149]) ).
cnf(s14,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f157]) ).
cnf(s15,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f158]) ).
cnf(s16,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f159]) ).
cnf(s17,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f160]) ).
cnf(s18,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f161]) ).
cnf(s19,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f162]) ).
cnf(s26,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f173]) ).
cnf(s27,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f174]) ).
cnf(s28,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f175]) ).
cnf(s35,plain,
( spl0_4
| spl0_19 ),
inference(sat_conversion,[],[f186]) ).
cnf(s36,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f187]) ).
cnf(s37,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f188]) ).
cnf(s38,plain,
spl0_8,
inference(sat_conversion,[],[f189]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f195]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f280]) ).
cnf(s44,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f416]) ).
cnf(s46,plain,
( ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(sat_conversion,[],[f434]) ).
cnf(s49,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_23 ),
inference(sat_conversion,[],[f462]) ).
cnf(s52,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| spl0_25 ),
inference(sat_conversion,[],[f510]) ).
cnf(s57,plain,
( ~ spl0_10
| ~ spl0_17
| ~ spl0_23
| spl0_25 ),
inference(sat_conversion,[],[f558]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f586]) ).
cnf(s64,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(sat_conversion,[],[f601]) ).
cnf(s70,plain,
( spl0_4
| ~ spl0_8
| ~ spl0_19
| ~ spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f668]) ).
cnf(s72,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f698]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_17
| ~ spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f700]) ).
cnf(s77,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f727]) ).
cnf(s78,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(sat_conversion,[],[f729]) ).
cnf(s81,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f746]) ).
cnf(s82,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(sat_conversion,[],[f748]) ).
cnf(s85,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f763]) ).
cnf(s86,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_17
| ~ spl0_25 ),
inference(sat_conversion,[],[f765]) ).
cnf(s90,plain,
( ~ spl0_8
| spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f811]) ).
cnf(s99,plain,
( ~ spl0_3
| spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f832]) ).
cnf(s103,plain,
( ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_25 ),
inference(sat_conversion,[],[f864]) ).
cnf(s104,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(rat,[],[s1,s38]) ).
cnf(s105,plain,
spl0_3,
inference(rat,[],[s44,s7,s16,s64,s38]) ).
cnf(s106,plain,
spl0_4,
inference(rat,[],[s70,s52,s44,s8,s17,s26,s35,s38]) ).
cnf(s108,plain,
( spl0_19
| spl0_23 ),
inference(rat,[],[s49,s36,s37]) ).
cnf(s109,plain,
( ~ spl0_17
| ~ spl0_10
| ~ spl0_7 ),
inference(rat,[],[s49,s27,s28,s52,s108,s57,s78,s44,s38]) ).
cnf(s110,plain,
( spl0_17
| ~ spl0_7 ),
inference(rat,[],[s77,s99,s103,s49,s14,s15,s18,s19,s106,s105,s38]) ).
cnf(s111,plain,
( ~ spl0_17
| ~ spl0_7 ),
inference(rat,[],[s77,s99,s103,s49,s5,s6,s9,s10,s109,s38,s105,s106]) ).
cnf(s112,plain,
~ spl0_7,
inference(rat,[],[s111,s110]) ).
cnf(s113,plain,
( ~ spl0_17
| ~ spl0_10
| ~ spl0_6 ),
inference(rat,[],[s49,s27,s28,s52,s108,s57,s86,s44,s38]) ).
cnf(s114,plain,
( spl0_17
| ~ spl0_6 ),
inference(rat,[],[s85,s99,s103,s49,s14,s15,s18,s19,s106,s105,s38]) ).
cnf(s115,plain,
( ~ spl0_17
| ~ spl0_6 ),
inference(rat,[],[s85,s99,s103,s49,s5,s6,s9,s10,s113,s38,s105,s106]) ).
cnf(s116,plain,
~ spl0_6,
inference(rat,[],[s115,s114]) ).
cnf(s117,plain,
( ~ spl0_17
| ~ spl0_10
| ~ spl0_5 ),
inference(rat,[],[s49,s27,s28,s52,s108,s57,s82,s44,s38]) ).
cnf(s118,plain,
( spl0_17
| ~ spl0_5 ),
inference(rat,[],[s81,s99,s103,s49,s14,s15,s18,s19,s106,s105,s38]) ).
cnf(s119,plain,
( ~ spl0_17
| ~ spl0_5 ),
inference(rat,[],[s81,s99,s103,s49,s5,s6,s9,s10,s117,s38,s105,s106]) ).
cnf(s120,plain,
~ spl0_5,
inference(rat,[],[s119,s118]) ).
cnf(s121,plain,
( ~ spl0_21
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s49,s27,s28,s52,s108,s42,s62,s46,s38,s106,s105]) ).
cnf(s122,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s39,s14,s15]) ).
cnf(s123,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s44,s121,s122,s38]) ).
cnf(s124,plain,
~ spl0_2,
inference(rat,[],[s39,s5,s6,s123]) ).
cnf(s125,plain,
spl0_1,
inference(rat,[],[s104,s116,s106,s120,s105,s112,s124]) ).
cnf(s126,plain,
( ~ spl0_21
| ~ spl0_17
| ~ spl0_10 ),
inference(rat,[],[s49,s27,s28,s52,s108,s57,s73,s125,s106,s38]) ).
cnf(s127,plain,
( ~ spl0_17
| ~ spl0_10 ),
inference(rat,[],[s126,s44,s38]) ).
cnf(s128,plain,
( ~ spl0_25
| ~ spl0_23 ),
inference(rat,[],[s72,s90,s38,s125,s106]) ).
cnf(s129,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(rat,[],[s128,s103,s38]) ).
cnf(s130,plain,
spl0_17,
inference(rat,[],[s129,s49,s14,s15,s18,s19]) ).
cnf(s131,plain,
~ spl0_10,
inference(rat,[],[s127,s130]) ).
cnf(s132,plain,
spl0_16,
inference(rat,[],[s10,s131]) ).
cnf(s133,plain,
spl0_15,
inference(rat,[],[s9,s131]) ).
cnf(s134,plain,
spl0_14,
inference(rat,[],[s6,s131]) ).
cnf(s135,plain,
spl0_13,
inference(rat,[],[s5,s131]) ).
cnf(s139,plain,
spl0_23,
inference(rat,[],[s49,s132,s133]) ).
cnf(s140,plain,
$false,
inference(rat,[],[s129,s139,s134,s135]) ).
fof(f865,plain,
$false,
inference(avatar_sat_refutation,[],[s140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP339-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:54:22 UTC 2026
% 0.10/0.37 % 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
% 1.90/1.30 % (3260967)Input is clausal, will run a generic CNF schedule.
% 1.90/1.30 % (3260974)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2042338677:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.90/1.30 % (3260972)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=197051530:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.90/1.30 % (3260975)lrs+10_1_sil=8000:sp=occurrence:random_seed=1910650698:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.90/1.30 % (3260976)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1669103010:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.90/1.30 % (3260977)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=913425825:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.90/1.30 % (3260978)dis-21_1_sil=8000:lcm=predicate:random_seed=1581476763: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)
% 1.90/1.30 % (3260973)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1298119205:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.90/1.30 % (3260978)Refutation not found, incomplete strategy
% 1.90/1.30 % (3260978)------------------------------
% 1.90/1.30 % (3260978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.90/1.30 % (3260978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/1.30 % (3260978)CaDiCaL version: 2.1.3
% 1.90/1.30 % (3260978)Termination reason: Refutation not found, incomplete strategy
% 1.90/1.30 % (3260978)Time elapsed: 0.002 s
% 1.90/1.30 % (3260978)Peak memory usage: 88 MB
% 1.90/1.30 % (3260978)Instructions burned: 2 (million)
% 1.90/1.30 % (3260977)First to succeed.
% 1.90/1.30 % (3260977)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3260967"
% 1.90/1.30 % (3260975)Instruction limit reached!
% 1.90/1.30 % (3260975)------------------------------
% 1.90/1.30 % (3260975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.90/1.30 % (3260975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/1.30 % (3260975)CaDiCaL version: 2.1.3
% 1.90/1.30 % (3260975)Termination reason: Instruction limit
% 1.90/1.30 % (3260975)Termination phase: Saturation
% 1.90/1.30 % (3260975)Time elapsed: 0.059 s
% 1.90/1.30 % (3260975)Peak memory usage: 89 MB
% 1.90/1.30 % (3260975)Instructions burned: 108 (million)
% 1.90/1.30 % (3260976)Instruction limit reached!
% 1.90/1.30 % (3260976)------------------------------
% 1.90/1.30 % (3260976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.90/1.30 % (3260976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/1.30 % (3260976)CaDiCaL version: 2.1.3
% 1.90/1.30 % (3260976)Termination reason: Instruction limit
% 1.90/1.30 % (3260976)Termination phase: Saturation
% 1.90/1.30 % (3260976)Time elapsed: 0.065 s
% 1.90/1.30 % (3260976)Peak memory usage: 89 MB
% 1.90/1.30 % (3260976)Instructions burned: 114 (million)
% 1.90/1.30 % (3260987)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2105296035: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)
% 1.90/1.30 % (3260986)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=1208382286:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.90/1.30 % (3260978)------------------------------
% 1.90/1.30 % (3260978)------------------------------
% 1.90/1.30 % (3260977)Refutation found. Thanks to Tanya!
% 1.90/1.30 % SZS status Unsatisfiable for theBenchmark
% 1.90/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3260977)------------------------------
% 0.17/1.50 % (3260977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3260977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3260977)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3260977)Termination reason: Refutation
% 0.17/1.50 % (3260977)Time elapsed: 0.019 s
% 0.17/1.50 % (3260977)Peak memory usage: 89 MB
% 0.17/1.50 % (3260977)Instructions burned: 28 (million)
% 0.17/1.50 % (3260977)------------------------------
% 0.17/1.50 % (3260977)------------------------------
% 0.17/1.50 % (3260967)Success in time 0.444 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------