%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP239-1 : 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 : n016.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 10:13:25 AM UTC 2026
% Result : Unsatisfiable 2.58s 1.29s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 44
% Syntax : Number of formulae : 264 ( 18 unt; 21 def)
% Number of atoms : 800 ( 261 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1022 ( 486 ~; 515 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 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,
( inverse(sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f9,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c9) = sk_c8
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c9) = sk_c8
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c9) = sk_c8
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f51,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(X5,X6) != sk_c8
| inverse(X5) != X6
| multiply(X6,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c8 != multiply(X6,sk_c9) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c8 != multiply(X6,sk_c9) ),
inference(equality_resolution,[],[f90]) ).
fof(f92,plain,
! [X2,X3,X0,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,inverse(X5))
| sk_c8 != multiply(inverse(X5),sk_c9) ),
inference(equality_resolution,[],[f91]) ).
fof(f94,definition,
( spl0_1
<=> ! [X5] :
( sk_c8 != multiply(X5,inverse(X5))
| sk_c8 != multiply(inverse(X5),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f95,plain,
( ! [X5] :
( sk_c8 != multiply(inverse(X5),sk_c9)
| sk_c8 != multiply(X5,inverse(X5)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f98,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f101,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,definition,
( spl0_4
<=> ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f104,plain,
( ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,definition,
( spl0_5
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f107,plain,
( inverse(sk_c9) = sk_c8
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f108,plain,
( inverse(sk_c9) != sk_c8
| spl0_5 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f92,f106,f100,f103,f100,f97,f94]) ).
fof(f115,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f117,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f120,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f122,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f125,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f127,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f130,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f132,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f115,f130]) ).
fof(f135,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f137,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f80,f115,f135]) ).
fof(f140,definition,
( spl0_12
<=> sk_c9 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f142,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f78,f115,f140]) ).
fof(f145,definition,
( spl0_13
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f147,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f115,f145]) ).
fof(f150,definition,
( spl0_14
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f152,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f156,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f150,f130]) ).
fof(f157,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f150,f135]) ).
fof(f158,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f150,f140]) ).
fof(f159,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f150,f145]) ).
fof(f161,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f163,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f167,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f161,f130]) ).
fof(f168,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f161,f135]) ).
fof(f172,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f174,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f180,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f36,f172,f140]) ).
fof(f181,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f34,f172,f145]) ).
fof(f183,definition,
( spl0_17
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f185,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f191,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f183,f140]) ).
fof(f192,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f183,f145]) ).
fof(f194,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f106,f120]) ).
fof(f195,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f106,f125]) ).
fof(f196,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f106,f130]) ).
fof(f197,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f106,f135]) ).
fof(f199,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f106,f145]) ).
fof(f200,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f122]) ).
fof(f201,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f132]) ).
fof(f202,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f147]) ).
fof(f205,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f210,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f200]) ).
fof(f211,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f210,f1]) ).
fof(f212,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f205,f1]) ).
fof(f215,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f201]) ).
fof(f216,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f215,f1]) ).
fof(f219,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f211,f127]) ).
fof(f231,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f216,f137]) ).
fof(f268,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_13 ),
inference(superposition,[],[f212,f202]) ).
fof(f270,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f212,f231]) ).
fof(f273,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_12 ),
inference(superposition,[],[f212,f142]) ).
fof(f282,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f212,f219]) ).
fof(f286,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f282,f3]) ).
fof(f292,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f273,f147]) ).
fof(f294,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f270,f3]) ).
fof(f300,plain,
( sk_c9 = sk_c8
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f294,f286]) ).
fof(f303,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f268,f286]) ).
fof(f346,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f303,f300]) ).
fof(f347,plain,
( identity = sk_c4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f346,f3]) ).
fof(f348,plain,
( sk_c8 = sk_c4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f347,f286]) ).
fof(f349,plain,
( sk_c9 = sk_c4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f348,f300]) ).
fof(f353,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f147,f349]) ).
fof(f386,plain,
( sk_c9 != sk_c8
| spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f108,f353]) ).
fof(f390,plain,
( $false
| spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f386,f300]) ).
fof(f391,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f417,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f268,f294]) ).
fof(f422,plain,
( identity = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f417,f3]) ).
fof(f423,plain,
( sk_c9 = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f422,f294]) ).
fof(f425,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f202,f423]) ).
fof(f428,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f425,f292]) ).
fof(f429,plain,
( sk_c9 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f428,f294]) ).
fof(f431,plain,
( identity = multiply(sk_c8,sk_c9)
| ~ spl0_5 ),
inference(superposition,[],[f3,f107]) ).
fof(f432,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f431,f231]) ).
fof(f433,plain,
( sk_c9 = sk_c8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f432,f294]) ).
fof(f458,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f212,f152]) ).
fof(f460,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f458,f117]) ).
fof(f524,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f212,f174]) ).
fof(f526,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f524,f185]) ).
fof(f535,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f101,f147]) ).
fof(f537,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f101,f185]) ).
fof(f540,plain,
( sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f537]) ).
fof(f541,plain,
( sk_c9 != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f535]) ).
fof(f542,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f540,f174]) ).
fof(f543,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f549,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f541,f142]) ).
fof(f550,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f549]) ).
fof(f556,definition,
( spl0_22
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f557,plain,
( sk_c9 = sk_c8
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f568,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_1
| ~ spl0_17 ),
inference(superposition,[],[f95,f185]) ).
fof(f570,plain,
( identity != sk_c8
| sk_c8 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_1 ),
inference(superposition,[],[f95,f3]) ).
fof(f577,definition,
( spl0_23
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f579,plain,
( identity != sk_c8
| spl0_23 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f581,definition,
( spl0_24
<=> sk_c8 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f583,plain,
( sk_c8 != multiply(sk_c9,sk_c8)
| spl0_24 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f603,plain,
( sk_c9 = sk_c8
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f163,f460]) ).
fof(f611,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f603,f161,f150,f115,f556]) ).
fof(f614,plain,
( sk_c9 = multiply(sk_c1,sk_c9)
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f174,f557]) ).
fof(f618,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f431,f557]) ).
fof(f619,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f618,f292]) ).
fof(f620,plain,
( $false
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f619,f579]) ).
fof(f621,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f623,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_22
| spl0_24 ),
inference(forward_demodulation,[],[f583,f557]) ).
fof(f625,plain,
( sk_c9 != sk_c8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_24 ),
inference(forward_demodulation,[],[f623,f292]) ).
fof(f626,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f625,f557]) ).
fof(f627,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f628,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c9)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f98,f557]) ).
fof(f630,plain,
( ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c9) )
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f628,f557]) ).
fof(f632,plain,
( sk_c9 != sk_c8
| sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f630,f107]) ).
fof(f635,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f630,f185]) ).
fof(f638,plain,
( sk_c9 != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f635]) ).
fof(f642,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f632,f557]) ).
fof(f643,plain,
( sk_c9 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f642,f292]) ).
fof(f644,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f643,f557]) ).
fof(f645,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f644]) ).
fof(f646,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(sk_c9,multiply(X2,sk_c9)) )
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f104,f557]) ).
fof(f647,plain,
( sk_c9 != sk_c8
| sk_c9 != multiply(sk_c9,multiply(sk_c9,sk_c9))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f646,f107]) ).
fof(f651,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f646,f117]) ).
fof(f652,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f651]) ).
fof(f655,plain,
( sk_c9 != multiply(sk_c9,sk_c3)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f652,f152]) ).
fof(f661,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c9,sk_c9))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f647,f557]) ).
fof(f662,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f655,f460]) ).
fof(f663,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f662]) ).
fof(f664,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f661,f292]) ).
fof(f665,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f664,f557]) ).
fof(f666,plain,
( sk_c9 != sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f665,f292]) ).
fof(f667,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f666,f557]) ).
fof(f668,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f701,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f614,f638]) ).
fof(f702,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f701]) ).
fof(f718,definition,
( spl0_27
<=> sk_c9 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f719,plain,
( sk_c9 = multiply(sk_c1,sk_c9)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f740,plain,
( spl0_27
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f614,f556,f172,f718]) ).
fof(f766,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f429,f145,f140,f135,f130,f556]) ).
fof(f767,plain,
( spl0_22
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f433,f135,f130,f106,f556]) ).
fof(f773,definition,
( spl0_30
<=> sk_c8 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f779,plain,
( spl0_30
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f526,f183,f172,f773]) ).
fof(f780,plain,
( sk_c9 != sk_c8
| sk_c8 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_27 ),
inference(forward_demodulation,[],[f568,f719]) ).
fof(f781,plain,
( sk_c8 != multiply(sk_c9,sk_c8)
| identity != sk_c8
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f570,f107]) ).
fof(f786,plain,
( ~ spl0_30
| ~ spl0_22
| ~ spl0_1
| ~ spl0_17
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f780,f718,f183,f94,f556,f773]) ).
fof(f787,plain,
( ~ spl0_23
| ~ spl0_24
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f781,f106,f94,f581,f577]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f109]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f143]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s15,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s16,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f159]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f180]) ).
cnf(s30,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f181]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f192]) ).
cnf(s39,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f194]) ).
cnf(s40,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f195]) ).
cnf(s41,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f196]) ).
cnf(s42,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f197]) ).
cnf(s44,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f199]) ).
cnf(s45,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(sat_conversion,[],[f391]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f543]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f550]) ).
cnf(s62,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f611]) ).
cnf(s64,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f621]) ).
cnf(s65,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_24 ),
inference(sat_conversion,[],[f627]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f645]) ).
cnf(s69,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f663]) ).
cnf(s70,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f668]) ).
cnf(s74,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f702]) ).
cnf(s80,plain,
( ~ spl0_16
| ~ spl0_22
| spl0_27 ),
inference(sat_conversion,[],[f740]) ).
cnf(s101,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_22 ),
inference(sat_conversion,[],[f766]) ).
cnf(s102,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f767]) ).
cnf(s105,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_30 ),
inference(sat_conversion,[],[f779]) ).
cnf(s109,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_22
| ~ spl0_27
| ~ spl0_30 ),
inference(sat_conversion,[],[f786]) ).
cnf(s110,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f787]) ).
cnf(s112,plain,
spl0_5,
inference(rat,[],[s45,s39,s40,s41,s42,s44]) ).
cnf(s113,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s101,s70,s6,s7,s8,s9,s112]) ).
cnf(s114,plain,
( ~ spl0_22
| ~ spl0_4
| ~ spl0_7 ),
inference(rat,[],[s70,s15,s16,s69,s112]) ).
cnf(s115,plain,
( spl0_14
| spl0_22 ),
inference(rat,[],[s102,s13,s14,s112]) ).
cnf(s116,plain,
( ~ spl0_14
| ~ spl0_7
| spl0_22 ),
inference(rat,[],[s102,s20,s21,s62,s112]) ).
cnf(s117,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(rat,[],[s116,s115,s114]) ).
cnf(s118,plain,
~ spl0_4,
inference(rat,[],[s117,s113]) ).
cnf(s121,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s56,s30,s37]) ).
cnf(s122,plain,
( ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s56,s29,s36,s58]) ).
cnf(s123,plain,
~ spl0_3,
inference(rat,[],[s122,s121]) ).
cnf(s124,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s67,s115,s15,s16,s112]) ).
cnf(s125,plain,
( spl0_22
| ~ spl0_14 ),
inference(rat,[],[s102,s6,s7,s116,s112]) ).
cnf(s126,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s74,s30,s37,s125,s124]) ).
cnf(s127,plain,
( ~ spl0_13
| ~ spl0_22
| ~ spl0_2 ),
inference(rat,[],[s74,s29,s36,s67,s112]) ).
cnf(s128,plain,
~ spl0_2,
inference(rat,[],[s127,s126,s125,s124]) ).
cnf(s129,plain,
spl0_1,
inference(rat,[],[s2,s112,s118,s123,s128]) ).
cnf(s130,plain,
spl0_22,
inference(rat,[],[s125,s115]) ).
cnf(s131,plain,
( ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s110,s65,s64,s130,s129,s112]) ).
cnf(s132,plain,
( ~ spl0_16
| ~ spl0_17 ),
inference(rat,[],[s109,s80,s105,s130,s129]) ).
cnf(s133,plain,
spl0_13,
inference(rat,[],[s132,s30,s37]) ).
cnf(s134,plain,
~ spl0_12,
inference(rat,[],[s131,s133]) ).
cnf(s135,plain,
spl0_17,
inference(rat,[],[s36,s134]) ).
cnf(s136,plain,
spl0_16,
inference(rat,[],[s29,s134]) ).
cnf(s140,plain,
$false,
inference(rat,[],[s132,s135,s136]) ).
fof(f789,plain,
$false,
inference(avatar_sat_refutation,[],[s140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n016.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 09:43:47 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 2.58/1.29 % (2378833)Input is clausal, will run a generic CNF schedule.
% 2.58/1.29 % (2378840)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3726392636:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.58/1.29 % (2378841)lrs+10_1_sil=8000:sp=occurrence:random_seed=3941442066:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.58/1.29 % (2378843)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1930751349:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.58/1.29 % (2378839)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=51777073:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.58/1.29 % (2378838)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=242870916:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.58/1.29 % (2378841)Refutation not found, incomplete strategy
% 2.58/1.29 % (2378841)------------------------------
% 2.58/1.29 % (2378841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2378841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2378841)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2378841)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.29 % (2378841)Time elapsed: 0.003 s
% 2.58/1.29 % (2378841)Peak memory usage: 88 MB
% 2.58/1.29 % (2378841)Instructions burned: 4 (million)
% 2.58/1.29 % (2378844)dis-21_1_sil=8000:lcm=predicate:random_seed=2503581313: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)
% 2.58/1.29 % (2378842)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1934069131:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.58/1.29 % (2378844)Refutation not found, incomplete strategy
% 2.58/1.29 % (2378844)------------------------------
% 2.58/1.29 % (2378844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2378844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2378844)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2378844)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.29 % (2378844)Time elapsed: 0.002 s
% 2.58/1.29 % (2378844)Peak memory usage: 88 MB
% 2.58/1.29 % (2378844)Instructions burned: 2 (million)
% 2.58/1.29 % (2378843)First to succeed.
% 2.58/1.29 % (2378843)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2378833"
% 2.58/1.29 % (2378842)Instruction limit reached!
% 2.58/1.29 % (2378842)------------------------------
% 2.58/1.29 % (2378842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2378842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2378842)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2378842)Termination reason: Instruction limit
% 2.58/1.29 % (2378842)Termination phase: Saturation
% 2.58/1.29 % (2378842)Time elapsed: 0.066 s
% 2.58/1.29 % (2378842)Peak memory usage: 89 MB
% 2.58/1.29 % (2378842)Instructions burned: 115 (million)
% 2.58/1.29 % (2378852)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=1721276132:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.58/1.29 % (2378852)Refutation not found, incomplete strategy
% 2.58/1.29 % (2378852)------------------------------
% 2.58/1.29 % (2378852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2378852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2378852)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2378852)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.29 % (2378852)Time elapsed: 0.003 s
% 2.58/1.29 % (2378852)Peak memory usage: 88 MB
% 2.58/1.29 % (2378852)Instructions burned: 4 (million)
% 2.58/1.29 % (2378841)------------------------------
% 2.58/1.29 % (2378841)------------------------------
% 2.58/1.29 % (2378844)------------------------------
% 2.58/1.29 % (2378844)------------------------------
% 2.58/1.29 % (2378843)Refutation found. Thanks to Tanya!
% 2.58/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.39 % (2378843)------------------------------
% 3.41/1.39 % (2378843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.39 % (2378843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.39 % (2378843)CaDiCaL version: 2.1.3
% 3.41/1.39 % (2378843)Termination reason: Refutation
% 3.41/1.39 % (2378843)Time elapsed: 0.018 s
% 3.41/1.39 % (2378843)Peak memory usage: 90 MB
% 3.41/1.39 % (2378843)Instructions burned: 26 (million)
% 3.41/1.39 % (2378843)------------------------------
% 3.41/1.39 % (2378843)------------------------------
% 3.41/1.39 % (2378833)Success in time 0.412 s
% 3.41/1.39 % Vampire exiting
%------------------------------------------------------------------------------