%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n007.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 10:17:15 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 54
% Syntax : Number of formulae : 335 ( 19 unt; 23 def)
% Number of atoms : 1000 ( 325 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1247 ( 582 ~; 642 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',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(f23,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f29]) ).
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(f37,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f43]) ).
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(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(f83,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f85]) ).
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 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3) )
| ~ 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(f123,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f115,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(f128,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f115,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(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(f176,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f172,f120]) ).
fof(f177,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f172,f125]) ).
fof(f178,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f172,f130]) ).
fof(f179,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f38,f172,f135]) ).
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(f187,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f183,f120]) ).
fof(f188,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f183,f125]) ).
fof(f189,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f183,f130]) ).
fof(f190,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f183,f135]) ).
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(f206,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(sk_c9,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f142]) ).
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(f222,plain,
( multiply(sk_c9,sk_c5) = multiply(sk_c4,identity)
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f206,f201]) ).
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(f314,plain,
( sk_c8 != inverse(identity)
| spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f108,f294]) ).
fof(f315,plain,
( identity != inverse(identity)
| spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f314,f286]) ).
fof(f323,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f268,f294]) ).
fof(f324,plain,
( identity = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f323,f3]) ).
fof(f328,plain,
( sk_c9 = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f147,f324]) ).
fof(f329,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f328,f294]) ).
fof(f374,plain,
( multiply(sk_c9,sk_c5) = multiply(identity,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f222,f324]) ).
fof(f375,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f374,f1]) ).
fof(f417,plain,
( $false
| spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f315,f329]) ).
fof(f418,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f420,plain,
( identity = inverse(sk_c9)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f107,f286]) ).
fof(f422,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f420,f294]) ).
fof(f446,plain,
( identity = inverse(sk_c2)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f117,f294]) ).
fof(f450,plain,
( identity = inverse(sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f185,f294]) ).
fof(f455,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f375,f294]) ).
fof(f462,plain,
( identity = sk_c5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f455,f1]) ).
fof(f484,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f3,f446]) ).
fof(f485,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f484,f1]) ).
fof(f489,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f3,f450]) ).
fof(f490,plain,
( identity = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f489,f1]) ).
fof(f497,plain,
( sk_c9 = multiply(identity,sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f137,f462]) ).
fof(f498,plain,
( sk_c8 = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f132,f462]) ).
fof(f499,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f498,f329]) ).
fof(f500,plain,
( sk_c9 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f497,f1]) ).
fof(f534,plain,
( identity = multiply(sk_c8,sk_c9)
| ~ spl0_5 ),
inference(superposition,[],[f3,f107]) ).
fof(f539,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f212,f152]) ).
fof(f541,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f539,f117]) ).
fof(f543,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f212,f163]) ).
fof(f545,plain,
( sk_c3 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f543,f107]) ).
fof(f546,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f212,f174]) ).
fof(f548,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f546,f185]) ).
fof(f557,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f101,f142]) ).
fof(f559,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f101,f174]) ).
fof(f560,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f559]) ).
fof(f562,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f557]) ).
fof(f563,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f560,f185]) ).
fof(f564,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f563]) ).
fof(f565,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f562,f147]) ).
fof(f566,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f572,definition,
( spl0_21
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f573,plain,
( identity = sk_c9
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f577,definition,
( spl0_22
<=> sk_c9 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f581,definition,
( spl0_23
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f582,plain,
( sk_c9 = sk_c8
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f590,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| sk_c9 != inverse(identity)
| ~ spl0_4 ),
inference(superposition,[],[f104,f1]) ).
fof(f595,plain,
( sk_c8 != multiply(sk_c9,sk_c3)
| sk_c9 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f104,f152]) ).
fof(f596,plain,
( sk_c9 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f595,f163]) ).
fof(f602,definition,
( spl0_25
<=> sk_c8 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f603,plain,
( sk_c8 = multiply(sk_c9,sk_c8)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f604,plain,
( sk_c8 != multiply(sk_c9,sk_c8)
| spl0_25 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f617,definition,
( spl0_28
<=> sk_c8 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f618,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f621,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f596,f117]) ).
fof(f622,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f629,plain,
( sk_c8 != multiply(sk_c8,sk_c9)
| sk_c8 != multiply(sk_c9,sk_c8)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f95,f107]) ).
fof(f633,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f95,f117]) ).
fof(f636,plain,
( sk_c8 != sk_c3
| sk_c8 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f633,f152]) ).
fof(f647,plain,
( identity != sk_c8
| sk_c8 != multiply(sk_c9,sk_c8)
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f629,f534]) ).
fof(f649,definition,
( spl0_31
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f650,plain,
( identity = sk_c8
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f654,definition,
( spl0_32
<=> sk_c8 = sk_c3 ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f656,plain,
( sk_c8 != sk_c3
| spl0_32 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f657,plain,
( ~ spl0_28
| ~ spl0_32
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f636,f150,f115,f94,f654,f617]) ).
fof(f658,plain,
( ~ spl0_25
| ~ spl0_31
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f647,f106,f94,f649,f602]) ).
fof(f661,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f292,f145,f140,f617]) ).
fof(f678,plain,
( sk_c9 = sk_c8
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f163,f541]) ).
fof(f681,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f212,f541]) ).
fof(f683,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f681,f3]) ).
fof(f686,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f678,f161,f150,f115,f581]) ).
fof(f693,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_23
| spl0_25 ),
inference(superposition,[],[f604,f582]) ).
fof(f694,plain,
( sk_c9 != sk_c8
| ~ spl0_23
| spl0_25
| ~ spl0_28 ),
inference(forward_demodulation,[],[f693,f618]) ).
fof(f695,plain,
( $false
| ~ spl0_23
| spl0_25
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f694,f582]) ).
fof(f696,plain,
( ~ spl0_23
| spl0_25
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f697,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f603,f582]) ).
fof(f707,plain,
( sk_c3 = multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f545,f582]) ).
fof(f708,plain,
( sk_c8 = sk_c3
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23
| ~ spl0_28 ),
inference(forward_demodulation,[],[f707,f618]) ).
fof(f709,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23
| ~ spl0_28
| spl0_32 ),
inference(forward_subsumption_resolution,[],[f708,f656]) ).
fof(f710,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_23
| ~ spl0_28
| spl0_32 ),
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f716,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_23
| ~ spl0_25 ),
inference(superposition,[],[f212,f697]) ).
fof(f718,plain,
( identity = sk_c9
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f716,f3]) ).
fof(f729,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c9)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_23 ),
inference(forward_demodulation,[],[f98,f582]) ).
fof(f731,plain,
( spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f718,f602,f581,f572]) ).
fof(f737,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c9)
| sk_c9 != inverse(X4) )
| ~ spl0_2
| ~ spl0_23 ),
inference(forward_demodulation,[],[f729,f582]) ).
fof(f743,plain,
( identity != sk_c9
| sk_c9 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_23 ),
inference(superposition,[],[f737,f534]) ).
fof(f745,plain,
( sk_c9 != sk_c3
| sk_c9 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_23 ),
inference(superposition,[],[f737,f152]) ).
fof(f747,plain,
( sk_c9 != sk_c3
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f745,f117]) ).
fof(f749,plain,
( sk_c9 != inverse(sk_c9)
| identity != sk_c9
| ~ spl0_2
| ~ spl0_5
| ~ spl0_23 ),
inference(forward_demodulation,[],[f743,f582]) ).
fof(f752,plain,
( identity != sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f747,f683]) ).
fof(f754,plain,
( sk_c9 != sk_c8
| identity != sk_c9
| ~ spl0_2
| ~ spl0_5
| ~ spl0_23 ),
inference(forward_demodulation,[],[f749,f107]) ).
fof(f756,plain,
( ~ spl0_21
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f752,f581,f150,f115,f97,f572]) ).
fof(f757,plain,
( identity != sk_c9
| ~ spl0_2
| ~ spl0_5
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f754,f582]) ).
fof(f759,plain,
( ~ spl0_21
| ~ spl0_2
| ~ spl0_5
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f757,f581,f106,f97,f572]) ).
fof(f763,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f231,f534]) ).
fof(f764,plain,
( spl0_21
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f294,f135,f130,f572]) ).
fof(f765,plain,
( spl0_31
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f499,f145,f140,f135,f130,f649]) ).
fof(f766,plain,
( spl0_23
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f500,f145,f140,f135,f130,f581]) ).
fof(f770,plain,
( spl0_28
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f548,f183,f172,f617]) ).
fof(f771,plain,
( spl0_31
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f763,f135,f130,f106,f649]) ).
fof(f773,plain,
( ~ spl0_22
| ~ spl0_28
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f590,f103,f617,f577]) ).
fof(f780,plain,
( sk_c9 = inverse(identity)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f117,f485]) ).
fof(f781,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f780,f135,f130,f115,f577]) ).
fof(f784,plain,
( sk_c9 = multiply(identity,sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f174,f490]) ).
fof(f787,plain,
( sk_c9 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f784,f1]) ).
fof(f789,plain,
( spl0_23
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f787,f183,f172,f135,f130,f581]) ).
fof(f868,plain,
( ! [X2] :
( sk_c8 != multiply(identity,multiply(X2,identity))
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f104,f573]) ).
fof(f869,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f868,f1]) ).
fof(f870,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_21
| ~ spl0_31 ),
inference(forward_demodulation,[],[f869,f650]) ).
fof(f871,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_21
| ~ spl0_31 ),
inference(forward_demodulation,[],[f870,f573]) ).
fof(f874,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_21
| ~ spl0_31 ),
inference(superposition,[],[f871,f3]) ).
fof(f878,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_21
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f874]) ).
fof(f881,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21
| ~ spl0_31 ),
inference(forward_demodulation,[],[f878,f422]) ).
fof(f885,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f881,f422]) ).
fof(f886,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f885]) ).
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(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f123]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f128]) ).
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(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s25,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s26,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f178]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f179]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f180]) ).
cnf(s30,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f181]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s33,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s34,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s35,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
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,[],[f418]) ).
cnf(s53,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f564]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f566]) ).
cnf(s60,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f622]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_28
| ~ spl0_32 ),
inference(sat_conversion,[],[f657]) ).
cnf(s66,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_25
| ~ spl0_31 ),
inference(sat_conversion,[],[f658]) ).
cnf(s68,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_28 ),
inference(sat_conversion,[],[f661]) ).
cnf(s69,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| spl0_23 ),
inference(sat_conversion,[],[f686]) ).
cnf(s71,plain,
( ~ spl0_23
| spl0_25
| ~ spl0_28 ),
inference(sat_conversion,[],[f696]) ).
cnf(s73,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_23
| ~ spl0_28
| spl0_32 ),
inference(sat_conversion,[],[f710]) ).
cnf(s76,plain,
( spl0_21
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f731]) ).
cnf(s81,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f756]) ).
cnf(s82,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f759]) ).
cnf(s86,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_21 ),
inference(sat_conversion,[],[f764]) ).
cnf(s87,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_31 ),
inference(sat_conversion,[],[f765]) ).
cnf(s88,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_23 ),
inference(sat_conversion,[],[f766]) ).
cnf(s93,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_28 ),
inference(sat_conversion,[],[f770]) ).
cnf(s94,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| spl0_31 ),
inference(sat_conversion,[],[f771]) ).
cnf(s96,plain,
( ~ spl0_4
| ~ spl0_22
| ~ spl0_28 ),
inference(sat_conversion,[],[f773]) ).
cnf(s102,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f781]) ).
cnf(s104,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_23 ),
inference(sat_conversion,[],[f789]) ).
cnf(s109,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21
| ~ spl0_31 ),
inference(sat_conversion,[],[f886]) ).
cnf(s111,plain,
spl0_5,
inference(rat,[],[s45,s39,s40,s41,s42,s44]) ).
cnf(s112,plain,
( ~ spl0_11
| ~ spl0_31
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(rat,[],[s86,s109,s111]) ).
cnf(s113,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s112,s87,s4,s5,s6,s7,s8,s9]) ).
cnf(s114,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s60,s14,s21,s113]) ).
cnf(s115,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s60,s13,s20,s113]) ).
cnf(s116,plain,
( spl0_9
| spl0_28 ),
inference(rat,[],[s93,s26,s33]) ).
cnf(s117,plain,
~ spl0_4,
inference(rat,[],[s93,s25,s32,s112,s116,s96,s102,s94,s115,s114,s113,s111]) ).
cnf(s119,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s53,s30,s37]) ).
cnf(s120,plain,
( ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s53,s29,s36,s54]) ).
cnf(s121,plain,
~ spl0_3,
inference(rat,[],[s120,s119]) ).
cnf(s122,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s76,s71,s81,s69,s93,s7,s14,s21,s28,s35]) ).
cnf(s123,plain,
( spl0_17
| spl0_23
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s88,s36,s37]) ).
cnf(s124,plain,
( ~ spl0_17
| ~ spl0_10
| ~ spl0_11
| spl0_23 ),
inference(rat,[],[s88,s29,s30,s104]) ).
cnf(s125,plain,
( spl0_23
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s124,s123]) ).
cnf(s126,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s125,s82,s86,s122,s111]) ).
cnf(s127,plain,
~ spl0_2,
inference(rat,[],[s76,s71,s81,s69,s93,s6,s13,s20,s27,s34,s126]) ).
cnf(s128,plain,
spl0_1,
inference(rat,[],[s2,s117,s121,s111,s127]) ).
cnf(s129,plain,
spl0_11,
inference(rat,[],[s73,s65,s69,s93,s7,s14,s21,s28,s35,s111,s128]) ).
cnf(s130,plain,
( spl0_16
| spl0_28 ),
inference(rat,[],[s68,s29,s30]) ).
cnf(s131,plain,
( ~ spl0_16
| spl0_28 ),
inference(rat,[],[s68,s36,s37,s93]) ).
cnf(s132,plain,
spl0_28,
inference(rat,[],[s131,s130]) ).
cnf(s134,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_7 ),
inference(rat,[],[s73,s65,s69,s128,s132,s111]) ).
cnf(s135,plain,
spl0_10,
inference(rat,[],[s134,s6,s13,s20]) ).
cnf(s136,plain,
spl0_31,
inference(rat,[],[s94,s129,s111,s135]) ).
cnf(s138,plain,
spl0_23,
inference(rat,[],[s125,s129,s135]) ).
cnf(s140,plain,
~ spl0_25,
inference(rat,[],[s66,s128,s111,s136]) ).
cnf(s141,plain,
$false,
inference(rat,[],[s71,s132,s138,s140]) ).
fof(f890,plain,
$false,
inference(avatar_sat_refutation,[],[s141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:36:55 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.49 % (1163197)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (1163204)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3632408615:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (1163203)% WARNING: option uhcvi not known.
% 0.16/0.49 % (1163202)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=737438792_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (1163203)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2040003785:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (1163205)dis+10_1_sil=32000:sp=arity:random_seed=2141125728:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (1163206)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2493597018:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (1163207)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=90046450:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % (1163208)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1912160629:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % (1163205) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1163197-1163205"...
% 0.16/0.49 % (1163206) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1163197-1163206"...
% 0.16/0.49 % TRYING [5]
% 0.16/0.49 % (1163205)...printing done.
% 0.16/0.49 % (1163206)...printing done.
% 0.16/0.49 % (1163205)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (1163205)------------------------------
% 0.16/0.50 % (1163205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (1163205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (1163205)CaDiCaL version: 2.1.3
% 0.16/0.50 % (1163205)Termination reason: Refutation
% 0.16/0.50 % (1163205)Time elapsed: 0.019 s
% 0.16/0.50 % (1163205)Peak memory usage: 12 MB
% 0.16/0.50 % (1163205)Instructions burned: 30 (million)
% 0.16/0.50 % (1163197)Success in time 0.059 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------