%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP331-1 : 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 : n017.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 10:13:40 AM UTC 2026
% Result : Unsatisfiable 3.17s 1.07s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 45
% Syntax : Number of formulae : 299 ( 21 unt; 19 def)
% Number of atoms : 979 ( 256 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1325 ( 645 ~; 661 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f66,f83,f80,f77,f74,f71,f68]) ).
fof(f88,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f90,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f97,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f102,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f92,f102]) ).
fof(f107,definition,
( spl0_11
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f109,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f92,f107]) ).
fof(f112,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f92,f112]) ).
fof(f117,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f92,f117]) ).
fof(f122,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f124,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f127,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f122,f102]) ).
fof(f128,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f122,f107]) ).
fof(f129,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f122,f112]) ).
fof(f130,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f122,f117]) ).
fof(f132,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f134,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f137,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f132,f102]) ).
fof(f138,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f132,f107]) ).
fof(f139,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f132,f112]) ).
fof(f140,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f132,f117]) ).
fof(f142,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f147,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f142,f102]) ).
fof(f148,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f142,f107]) ).
fof(f149,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f142,f112]) ).
fof(f150,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f18,f142,f117]) ).
fof(f151,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f83,f88]) ).
fof(f152,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f83,f97]) ).
fof(f153,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f83,f102]) ).
fof(f154,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f83,f107]) ).
fof(f155,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f83,f112]) ).
fof(f156,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f83,f117]) ).
fof(f157,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f99]) ).
fof(f158,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f104]) ).
fof(f162,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f166,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f162,f1]) ).
fof(f204,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f166,f158]) ).
fof(f207,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f166,f157]) ).
fof(f210,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f166,f119]) ).
fof(f212,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f166,f109]) ).
fof(f221,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f212,f104]) ).
fof(f223,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f210,f114]) ).
fof(f225,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f166,f221]) ).
fof(f227,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f225,f3]) ).
fof(f231,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f166,f223]) ).
fof(f233,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f231,f3]) ).
fof(f238,plain,
( sk_c7 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f233,f227]) ).
fof(f248,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f207,f227]) ).
fof(f249,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f3]) ).
fof(f250,plain,
( sk_c6 = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f249,f227]) ).
fof(f251,plain,
( sk_c7 = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f250,f238]) ).
fof(f255,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f90,f251]) ).
fof(f258,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f255,f85]) ).
fof(f259,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f265,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f84,f238]) ).
fof(f268,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f166,f265]) ).
fof(f270,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f268,f3]) ).
fof(f272,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f270,f233]) ).
fof(f300,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f204,f233]) ).
fof(f303,plain,
( identity = sk_c4
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f300,f3]) ).
fof(f304,plain,
( sk_c7 = sk_c4
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f303,f233]) ).
fof(f324,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f166,f144]) ).
fof(f326,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f324,f134]) ).
fof(f328,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f75,f114]) ).
fof(f331,plain,
( sk_c7 != sk_c8
| sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f75,f134]) ).
fof(f333,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f328]) ).
fof(f339,definition,
( spl0_18
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f340,plain,
( sk_c7 = sk_c8
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f344,definition,
( spl0_19
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f345,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f346,plain,
( sk_c7 != multiply(sk_c1,sk_c8)
| spl0_19 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f347,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f331,f132,f74,f339,f344]) ).
fof(f350,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f333,f119]) ).
fof(f351,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f350]) ).
fof(f358,definition,
( spl0_21
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f359,plain,
( sk_c7 = sk_c6
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f383,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f84,f326]) ).
fof(f384,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f166,f326]) ).
fof(f386,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f384,f3]) ).
fof(f391,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f383,f142,f132,f83,f358]) ).
fof(f393,plain,
( sk_c7 = multiply(sk_c2,sk_c7)
| ~ spl0_8
| ~ spl0_21 ),
inference(superposition,[],[f94,f359]) ).
fof(f397,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_8
| ~ spl0_21 ),
inference(superposition,[],[f166,f393]) ).
fof(f399,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_14
| ~ spl0_21 ),
inference(forward_demodulation,[],[f397,f124]) ).
fof(f429,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_14
| ~ spl0_21 ),
inference(superposition,[],[f166,f399]) ).
fof(f431,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_21 ),
inference(forward_demodulation,[],[f429,f3]) ).
fof(f453,plain,
( sk_c7 = sk_c8
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f386,f431]) ).
fof(f460,plain,
( spl0_18
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f453,f358,f142,f132,f122,f92,f339]) ).
fof(f479,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c7) )
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f81,f340]) ).
fof(f481,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_18
| spl0_19 ),
inference(forward_demodulation,[],[f346,f340]) ).
fof(f482,plain,
( sk_c7 != sk_c8
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(forward_demodulation,[],[f481,f144]) ).
fof(f483,plain,
( $false
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f482,f340]) ).
fof(f484,plain,
( ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f485,plain,
( sk_c7 = multiply(sk_c1,sk_c7)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f345,f340]) ).
fof(f486,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f479,f104]) ).
fof(f487,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f479,f134]) ).
fof(f490,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f487]) ).
fof(f491,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f486]) ).
fof(f494,plain,
( sk_c7 != sk_c8
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f490,f144]) ).
fof(f495,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f494,f340]) ).
fof(f496,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f495]) ).
fof(f497,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f78,f359]) ).
fof(f499,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f497,f104]) ).
fof(f500,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f497,f134]) ).
fof(f503,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f500]) ).
fof(f504,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f499]) ).
fof(f507,plain,
( sk_c7 != sk_c8
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f503,f144]) ).
fof(f508,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f507,f340]) ).
fof(f509,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f510,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_21 ),
inference(forward_demodulation,[],[f72,f359]) ).
fof(f518,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_21 ),
inference(superposition,[],[f510,f124]) ).
fof(f519,plain,
( sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f518]) ).
fof(f522,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f519,f393]) ).
fof(f523,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f522]) ).
fof(f526,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f69,f359]) ).
fof(f527,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f526,f340]) ).
fof(f528,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f527,f359]) ).
fof(f529,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f528,f104]) ).
fof(f530,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f528,f134]) ).
fof(f531,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f528,f124]) ).
fof(f532,plain,
( sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f531]) ).
fof(f533,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f530]) ).
fof(f534,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_18
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f529]) ).
fof(f535,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f532,f393]) ).
fof(f536,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f537,plain,
( $false
| ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f533,f485]) ).
fof(f538,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f552,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f265,f340]) ).
fof(f593,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f534,f304]) ).
fof(f594,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f593,f552]) ).
fof(f595,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f599,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_demodulation,[],[f504,f304]) ).
fof(f602,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f599,f552]) ).
fof(f603,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f602]) ).
fof(f606,plain,
( spl0_18
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f272,f117,f112,f107,f102,f83,f339]) ).
fof(f655,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f510,f104]) ).
fof(f656,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f655]) ).
fof(f659,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_demodulation,[],[f656,f304]) ).
fof(f663,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f659,f552]) ).
fof(f664,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f668,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f491,f304]) ).
fof(f671,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f668,f552]) ).
fof(f672,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f684,plain,
( spl0_21
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f238,f117,f112,f107,f102,f358]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f110]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s11,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s12,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s13,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f137]) ).
cnf(s17,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f138]) ).
cnf(s18,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s19,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f140]) ).
cnf(s22,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f147]) ).
cnf(s23,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f148]) ).
cnf(s24,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f149]) ).
cnf(s25,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f150]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f151]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f152]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f153]) ).
cnf(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f155]) ).
cnf(s31,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f156]) ).
cnf(s32,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f259]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f347]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f351]) ).
cnf(s43,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f391]) ).
cnf(s48,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f460]) ).
cnf(s52,plain,
( ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f484]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f496]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f509]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_21 ),
inference(sat_conversion,[],[f523]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f536]) ).
cnf(s60,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(sat_conversion,[],[f538]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f595]) ).
cnf(s65,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f603]) ).
cnf(s67,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f606]) ).
cnf(s72,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f664]) ).
cnf(s74,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f672]) ).
cnf(s75,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_21 ),
inference(sat_conversion,[],[f684]) ).
cnf(s84,plain,
spl0_6,
inference(rat,[],[s32,s26,s27,s28,s29,s30,s31]) ).
cnf(s85,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s74,s67,s4,s5,s6,s7,s84]) ).
cnf(s86,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_5 ),
inference(rat,[],[s74,s67,s84]) ).
cnf(s87,plain,
( spl0_13
| ~ spl0_5 ),
inference(rat,[],[s48,s54,s43,s13,s19,s25,s85,s84]) ).
cnf(s88,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s48,s54,s43,s12,s18,s24,s85,s84]) ).
cnf(s89,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s48,s54,s43,s11,s17,s23,s85,s84]) ).
cnf(s90,plain,
~ spl0_5,
inference(rat,[],[s48,s54,s43,s10,s16,s22,s86,s89,s88,s87,s85,s84]) ).
cnf(s91,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_4 ),
inference(rat,[],[s65,s67,s75,s84]) ).
cnf(s92,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s48,s56,s43,s7,s13,s19,s25,s84]) ).
cnf(s93,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s48,s56,s43,s6,s12,s18,s24,s84]) ).
cnf(s94,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s48,s56,s43,s5,s11,s17,s23,s84]) ).
cnf(s95,plain,
( ~ spl0_11
| ~ spl0_4
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s48,s56,s43,s4,s10,s16,s22,s91,s84]) ).
cnf(s96,plain,
~ spl0_4,
inference(rat,[],[s95,s94,s93,s92]) ).
cnf(s97,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s35,s52,s48,s43,s7,s13,s19,s25,s84]) ).
cnf(s98,plain,
( ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s35,s52,s48,s43,s6,s12,s18,s24,s36,s84]) ).
cnf(s99,plain,
~ spl0_3,
inference(rat,[],[s98,s97]) ).
cnf(s100,plain,
( spl0_14
| ~ spl0_21
| ~ spl0_18
| ~ spl0_13
| ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s72,s10,s11,s84]) ).
cnf(s101,plain,
( ~ spl0_21
| ~ spl0_18
| ~ spl0_2
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s72,s4,s5,s57,s100,s84]) ).
cnf(s103,plain,
( spl0_11
| spl0_21 ),
inference(rat,[],[s43,s17,s23,s84]) ).
cnf(s104,plain,
( ~ spl0_11
| spl0_21
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s43,s16,s22,s75,s84]) ).
cnf(s105,plain,
( spl0_21
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s104,s103]) ).
cnf(s106,plain,
( spl0_11
| spl0_18
| ~ spl0_21 ),
inference(rat,[],[s48,s5,s11,s17,s23]) ).
cnf(s107,plain,
( ~ spl0_21
| ~ spl0_13
| ~ spl0_2
| ~ spl0_12 ),
inference(rat,[],[s48,s4,s10,s16,s22,s67,s106,s101,s84]) ).
cnf(s108,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s107,s105]) ).
cnf(s109,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s57,s43,s7,s13,s19,s25,s84]) ).
cnf(s110,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s57,s43,s6,s12,s18,s24,s108,s84]) ).
cnf(s111,plain,
~ spl0_2,
inference(rat,[],[s110,s109]) ).
cnf(s112,plain,
spl0_1,
inference(rat,[],[s1,s84,s96,s90,s99,s111]) ).
cnf(s113,plain,
( spl0_11
| ~ spl0_18
| ~ spl0_21 ),
inference(rat,[],[s60,s52,s17,s23,s112]) ).
cnf(s114,plain,
( ~ spl0_11
| ~ spl0_18
| ~ spl0_12
| ~ spl0_21
| ~ spl0_13 ),
inference(rat,[],[s60,s52,s16,s22,s63,s84,s112]) ).
cnf(s115,plain,
( ~ spl0_18
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s114,s113,s105]) ).
cnf(s116,plain,
( ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s48,s4,s10,s16,s22,s67,s106,s115,s105,s84]) ).
cnf(s117,plain,
( ~ spl0_8
| ~ spl0_21
| ~ spl0_15
| ~ spl0_16
| ~ spl0_14 ),
inference(rat,[],[s59,s48,s112]) ).
cnf(s118,plain,
spl0_13,
inference(rat,[],[s117,s43,s7,s13,s19,s25,s84]) ).
cnf(s119,plain,
~ spl0_12,
inference(rat,[],[s116,s118]) ).
cnf(s120,plain,
spl0_16,
inference(rat,[],[s24,s119]) ).
cnf(s121,plain,
spl0_15,
inference(rat,[],[s18,s119]) ).
cnf(s122,plain,
spl0_14,
inference(rat,[],[s12,s119]) ).
cnf(s123,plain,
spl0_8,
inference(rat,[],[s6,s119]) ).
cnf(s124,plain,
spl0_21,
inference(rat,[],[s43,s120,s84,s121]) ).
cnf(s125,plain,
$false,
inference(rat,[],[s117,s122,s120,s121,s124,s123]) ).
fof(f697,plain,
$false,
inference(avatar_sat_refutation,[],[s125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP331-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:49:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.17/1.07 % (2294547)Input is clausal, will run a generic CNF schedule.
% 3.17/1.07 % (2294575)lrs+10_1_sil=8000:sp=occurrence:random_seed=3553056002:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.17/1.07 % (2294575)Refutation not found, incomplete strategy
% 3.17/1.07 % (2294575)------------------------------
% 3.17/1.07 % (2294575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.07 % (2294575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.07 % (2294575)CaDiCaL version: 2.1.3
% 3.17/1.07 % (2294575)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.07 % (2294575)Time elapsed: 0.001 s
% 3.17/1.07 % (2294575)Peak memory usage: 88 MB
% 3.17/1.07 % (2294575)Instructions burned: 2 (million)
% 3.17/1.07 % (2294576)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2896670193:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.17/1.07 % (2294574)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3633674303:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.17/1.07 % (2294572)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=2028004254:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.17/1.07 % (2294573)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2490755706:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.17/1.07 % (2294578)dis-21_1_sil=8000:lcm=predicate:random_seed=869615332: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)
% 3.17/1.07 % (2294577)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2307669437:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.17/1.07 % (2294578)Refutation not found, incomplete strategy
% 3.17/1.07 % (2294578)------------------------------
% 3.17/1.07 % (2294578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.07 % (2294578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.07 % (2294578)CaDiCaL version: 2.1.3
% 3.17/1.07 % (2294578)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.07 % (2294578)Time elapsed: 0.002 s
% 3.17/1.07 % (2294578)Peak memory usage: 88 MB
% 3.17/1.07 % (2294578)Instructions burned: 1 (million)
% 3.17/1.07 % (2294577)First to succeed.
% 3.17/1.07 % (2294577)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2294547"
% 3.17/1.07 % (2294576)Instruction limit reached!
% 3.17/1.07 % (2294576)------------------------------
% 3.17/1.07 % (2294576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.07 % (2294576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.07 % (2294576)CaDiCaL version: 2.1.3
% 3.17/1.07 % (2294576)Termination reason: Instruction limit
% 3.17/1.07 % (2294576)Termination phase: Saturation
% 3.17/1.07 % (2294576)Time elapsed: 0.067 s
% 3.17/1.07 % (2294576)Peak memory usage: 89 MB
% 3.17/1.07 % (2294576)Instructions burned: 115 (million)
% 3.17/1.07 % (2294575)------------------------------
% 3.17/1.07 % (2294575)------------------------------
% 3.17/1.07 % (2294612)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=126801105:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.17/1.07 % (2294612)Refutation not found, incomplete strategy
% 3.17/1.07 % (2294612)------------------------------
% 3.17/1.07 % (2294612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.07 % (2294612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.07 % (2294612)CaDiCaL version: 2.1.3
% 3.17/1.07 % (2294612)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.07 % (2294612)Time elapsed: 0.003 s
% 3.17/1.07 % (2294612)Peak memory usage: 88 MB
% 3.17/1.07 % (2294612)Instructions burned: 2 (million)
% 3.17/1.07 % (2294634)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3233854417: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)
% 3.17/1.07 % (2294634)Refutation not found, incomplete strategy
% 3.17/1.07 % (2294634)------------------------------
% 3.17/1.07 % (2294634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.07 % (2294634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.07 % (2294634)CaDiCaL version: 2.1.3
% 3.17/1.07 % (2294634)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.07 % (2294634)Time elapsed: 0.001 s
% 3.17/1.07 % (2294634)Peak memory usage: 88 MB
% 3.17/1.07 % (2294634)Instructions burned: 3 (million)
% 3.17/1.07 % (2294578)------------------------------
% 3.17/1.07 % (2294578)------------------------------
% 3.17/1.07 % (2294577)Refutation found. Thanks to Tanya!
% 3.17/1.07 % SZS status Unsatisfiable for theBenchmark
% 3.17/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.27 % (2294577)------------------------------
% 3.66/1.27 % (2294577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.27 % (2294577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.27 % (2294577)CaDiCaL version: 2.1.3
% 3.66/1.27 % (2294577)Termination reason: Refutation
% 3.66/1.27 % (2294577)Time elapsed: 0.017 s
% 3.66/1.27 % (2294577)Peak memory usage: 89 MB
% 3.66/1.27 % (2294577)Instructions burned: 25 (million)
% 3.66/1.27 % (2294577)------------------------------
% 3.66/1.27 % (2294577)------------------------------
% 3.66/1.27 % (2294547)Success in time 0.462 s
% 3.66/1.27 % Vampire exiting
%------------------------------------------------------------------------------