%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:41 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.33s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 52
% Syntax : Number of formulae : 297 ( 20 unt; 21 def)
% Number of atoms : 858 ( 279 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1024 ( 463 ~; 540 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = inverse(sk_c2)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f71,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(equality_resolution,[],[f78]) ).
fof(f81,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_2
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( sk_c6 != inverse(sk_c8)
| spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,definition,
( spl0_4
<=> sk_c8 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( sk_c8 != multiply(sk_c7,sk_c6)
| spl0_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f95,definition,
( spl0_5
<=> ! [X1] :
( sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f96,plain,
( ! [X1] :
( sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c7 != multiply(X1,inverse(X1)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_6
<=> ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f99,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_7
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f102,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f79,f101,f98,f95,f91,f88,f84,f81]) ).
fof(f106,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f110,f106]) ).
fof(f115,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f117,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f74,f110,f115]) ).
fof(f119,plain,
( spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f110,f84]) ).
fof(f121,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f123,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f126,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f132,definition,
( spl0_13
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f64,f132,f106]) ).
fof(f136,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f62,f132,f115]) ).
fof(f137,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f60,f132,f84]) ).
fof(f138,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f58,f132,f121]) ).
fof(f139,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f56,f132,f126]) ).
fof(f140,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f132,f91]) ).
fof(f142,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f142,f106]) ).
fof(f146,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f142,f115]) ).
fof(f147,plain,
( spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f142,f84]) ).
fof(f148,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f142,f121]) ).
fof(f149,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f142,f126]) ).
fof(f150,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f142,f91]) ).
fof(f152,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f154,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f157,plain,
( spl0_2
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f152,f84]) ).
fof(f158,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f152,f121]) ).
fof(f159,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f152,f126]) ).
fof(f162,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f167,plain,
( spl0_2
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f162,f84]) ).
fof(f168,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f162,f121]) ).
fof(f169,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f162,f126]) ).
fof(f171,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f101,f106]) ).
fof(f172,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f101,f115]) ).
fof(f173,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f101,f84]) ).
fof(f174,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f101,f121]) ).
fof(f175,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f101,f126]) ).
fof(f176,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f101,f91]) ).
fof(f177,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f3,f85]) ).
fof(f178,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f108]) ).
fof(f179,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f123]) ).
fof(f181,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f128]) ).
fof(f185,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f117]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f181,f1]) ).
fof(f189,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_2 ),
inference(superposition,[],[f4,f177]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c8,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f189,f1]) ).
fof(f195,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c4,identity)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f183,f179]) ).
fof(f199,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f190,f179]) ).
fof(f213,plain,
( multiply(sk_c7,sk_c8) = multiply(sk_c5,identity)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f185,f177]) ).
fof(f237,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f187,f128]) ).
fof(f240,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f187,f117]) ).
fof(f242,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f187,f178]) ).
fof(f246,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f240,f108]) ).
fof(f247,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f237,f123]) ).
fof(f252,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f187,f246]) ).
fof(f254,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f252,f3]) ).
fof(f259,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f187,f247]) ).
fof(f261,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f259,f3]) ).
fof(f263,plain,
( sk_c4 = multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f199,f254]) ).
fof(f265,plain,
( sk_c6 = sk_c4
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f263,f246]) ).
fof(f272,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f123,f265]) ).
fof(f275,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f242,f254]) ).
fof(f280,plain,
( sk_c5 = multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f275,f272]) ).
fof(f281,plain,
( sk_c8 = sk_c5
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f280,f247]) ).
fof(f288,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c4,sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f195,f254]) ).
fof(f289,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f288,f265]) ).
fof(f290,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f289,f246]) ).
fof(f291,plain,
( sk_c8 = sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f290,f92]) ).
fof(f300,plain,
( sk_c4 = multiply(sk_c8,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f199,f291]) ).
fof(f303,plain,
( sk_c4 = multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f300,f254]) ).
fof(f309,plain,
( sk_c8 = sk_c4
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f303,f247]) ).
fof(f315,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f179,f309]) ).
fof(f318,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f315,f254]) ).
fof(f326,plain,
( multiply(sk_c7,sk_c8) = multiply(sk_c5,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f213,f254]) ).
fof(f327,plain,
( multiply(sk_c7,sk_c8) = multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f326,f281]) ).
fof(f328,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f327,f247]) ).
fof(f329,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f103,f328]) ).
fof(f332,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f329,f291]) ).
fof(f333,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f332]) ).
fof(f342,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f96,f108]) ).
fof(f348,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f342,f117]) ).
fof(f362,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f348,f177]) ).
fof(f366,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f362,f254]) ).
fof(f367,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f366]) ).
fof(f381,definition,
( spl0_21
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f382,plain,
( identity = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f387,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| sk_c7 != multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f96,f134]) ).
fof(f390,plain,
( ~ spl0_14
| ~ spl0_9
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f387,f132,f95,f110,f142]) ).
fof(f393,plain,
( spl0_21
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f261,f126,f121,f381]) ).
fof(f395,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f164]) ).
fof(f397,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_21 ),
inference(superposition,[],[f1,f382]) ).
fof(f401,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f112]) ).
fof(f402,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f187,f144]) ).
fof(f404,plain,
( sk_c3 = multiply(sk_c3,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f402,f134]) ).
fof(f405,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f187,f154]) ).
fof(f407,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f405,f164]) ).
fof(f423,plain,
( sk_c8 = sk_c6
| ~ spl0_7
| ~ spl0_21 ),
inference(superposition,[],[f397,f102]) ).
fof(f434,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21 ),
inference(superposition,[],[f82,f423]) ).
fof(f446,plain,
( spl0_3
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f434,f381,f101,f81,f88]) ).
fof(f467,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f187,f404]) ).
fof(f469,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f467,f3]) ).
fof(f472,plain,
( spl0_21
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f469,f142,f132,f381]) ).
fof(f473,plain,
( sk_c8 != sk_c6
| sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f99,f85]) ).
fof(f475,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f99,f164]) ).
fof(f483,definition,
( spl0_26
<=> sk_c8 = sk_c3 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f484,plain,
( sk_c8 = sk_c3
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f494,definition,
( spl0_28
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f495,plain,
( sk_c8 = sk_c6
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f499,definition,
( spl0_29
<=> sk_c8 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f503,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_21 ),
inference(superposition,[],[f1,f382]) ).
fof(f504,plain,
( sk_c8 != sk_c6
| sk_c7 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f89,f85]) ).
fof(f520,definition,
( spl0_32
<=> sk_c7 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f521,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f523,plain,
( ~ spl0_32
| ~ spl0_28
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f504,f88,f84,f494,f520]) ).
fof(f526,plain,
( spl0_28
| ~ spl0_7
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f423,f381,f101,f494]) ).
fof(f529,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_28 ),
inference(superposition,[],[f177,f495]) ).
fof(f537,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_21
| ~ spl0_28 ),
inference(forward_demodulation,[],[f529,f382]) ).
fof(f539,plain,
( spl0_32
| ~ spl0_2
| ~ spl0_21
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f537,f494,f381,f84,f520]) ).
fof(f540,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| spl0_4
| ~ spl0_28 ),
inference(forward_demodulation,[],[f93,f495]) ).
fof(f541,plain,
( sk_c8 != sk_c6
| spl0_4
| ~ spl0_7
| ~ spl0_28 ),
inference(forward_demodulation,[],[f540,f102]) ).
fof(f542,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f541,f495]) ).
fof(f543,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f544,plain,
( sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_6
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f475]) ).
fof(f546,plain,
( spl0_32
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f318,f126,f121,f115,f106,f91,f84,f520]) ).
fof(f548,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f473,f495]) ).
fof(f550,plain,
( ~ spl0_15
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f544,f162,f98,f152]) ).
fof(f561,plain,
( spl0_29
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f247,f126,f121,f499]) ).
fof(f563,plain,
( ~ spl0_29
| ~ spl0_2
| ~ spl0_6
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f548,f494,f98,f84,f499]) ).
fof(f570,plain,
( sk_c8 != inverse(sk_c8)
| spl0_2
| ~ spl0_28 ),
inference(forward_demodulation,[],[f86,f495]) ).
fof(f572,plain,
( spl0_32
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f407,f162,f152,f520]) ).
fof(f596,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c8,X0)) = X0
| ~ spl0_9
| ~ spl0_21 ),
inference(forward_demodulation,[],[f401,f503]) ).
fof(f600,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_9
| ~ spl0_21
| ~ spl0_32 ),
inference(superposition,[],[f596,f521]) ).
fof(f601,plain,
( sk_c1 = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f596,f395]) ).
fof(f605,plain,
( sk_c1 = multiply(sk_c3,sk_c7)
| ~ spl0_9
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f601,f382]) ).
fof(f606,plain,
( sk_c1 = sk_c3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f605,f404]) ).
fof(f609,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f164,f606]) ).
fof(f652,plain,
( sk_c8 = sk_c3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_21
| ~ spl0_32 ),
inference(superposition,[],[f404,f600]) ).
fof(f663,plain,
( spl0_26
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_21
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f652,f520,f381,f142,f132,f110,f483]) ).
fof(f670,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_21
| ~ spl0_26 ),
inference(superposition,[],[f609,f484]) ).
fof(f673,plain,
( $false
| spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_21
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f670,f570]) ).
fof(f674,plain,
( spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_21
| ~ spl0_26
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f673]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s16,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s22,plain,
( spl0_2
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s28,plain,
( spl0_2
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s29,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s30,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f169]) ).
cnf(s32,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f171]) ).
cnf(s33,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f172]) ).
cnf(s34,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f173]) ).
cnf(s35,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f174]) ).
cnf(s36,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f175]) ).
cnf(s37,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f176]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f333]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f367]) ).
cnf(s45,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f390]) ).
cnf(s47,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_21 ),
inference(sat_conversion,[],[f393]) ).
cnf(s50,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_7
| ~ spl0_21 ),
inference(sat_conversion,[],[f446]) ).
cnf(s54,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f472]) ).
cnf(s61,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_28
| ~ spl0_32 ),
inference(sat_conversion,[],[f523]) ).
cnf(s63,plain,
( ~ spl0_7
| ~ spl0_21
| spl0_28 ),
inference(sat_conversion,[],[f526]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_21
| ~ spl0_28
| spl0_32 ),
inference(sat_conversion,[],[f539]) ).
cnf(s67,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_28 ),
inference(sat_conversion,[],[f543]) ).
cnf(s68,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_32 ),
inference(sat_conversion,[],[f546]) ).
cnf(s75,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f550]) ).
cnf(s78,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_29 ),
inference(sat_conversion,[],[f561]) ).
cnf(s79,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_28
| ~ spl0_29 ),
inference(sat_conversion,[],[f563]) ).
cnf(s88,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_32 ),
inference(sat_conversion,[],[f572]) ).
cnf(s97,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_21
| spl0_26
| ~ spl0_32 ),
inference(sat_conversion,[],[f663]) ).
cnf(s99,plain,
( spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_21
| ~ spl0_26
| ~ spl0_28 ),
inference(sat_conversion,[],[f674]) ).
cnf(s100,plain,
spl0_2,
inference(rat,[],[s99,s97,s63,s54,s88,s4,s10,s16,s22,s28,s34]) ).
cnf(s101,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s38,s32,s33,s35,s36,s100]) ).
cnf(s102,plain,
( spl0_12
| ~ spl0_6 ),
inference(rat,[],[s75,s24,s30]) ).
cnf(s103,plain,
( spl0_11
| ~ spl0_6 ),
inference(rat,[],[s75,s23,s29]) ).
cnf(s104,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(rat,[],[s63,s79,s47,s78,s103,s102,s100]) ).
cnf(s106,plain,
( spl0_14
| ~ spl0_5 ),
inference(rat,[],[s40,s14,s15,s100]) ).
cnf(s107,plain,
( spl0_13
| ~ spl0_5 ),
inference(rat,[],[s40,s8,s9,s100]) ).
cnf(s108,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_5 ),
inference(rat,[],[s40,s2,s3,s45,s100]) ).
cnf(s109,plain,
~ spl0_5,
inference(rat,[],[s108,s107,s106]) ).
cnf(s111,plain,
spl0_4,
inference(rat,[],[s63,s54,s67,s13,s19,s37]) ).
cnf(s112,plain,
spl0_7,
inference(rat,[],[s101,s111]) ).
cnf(s113,plain,
~ spl0_6,
inference(rat,[],[s104,s112]) ).
cnf(s114,plain,
( spl0_14
| ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s61,s63,s68,s47,s14,s15,s17,s100,s112,s111]) ).
cnf(s115,plain,
( ~ spl0_21
| ~ spl0_3 ),
inference(rat,[],[s66,s61,s63,s100,s112]) ).
cnf(s116,plain,
( ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s11,s54,s47,s114,s115]) ).
cnf(s117,plain,
~ spl0_3,
inference(rat,[],[s54,s12,s18,s116,s115]) ).
cnf(s118,plain,
spl0_1,
inference(rat,[],[s1,s100,s109,s111,s112,s117,s113]) ).
cnf(s119,plain,
~ spl0_21,
inference(rat,[],[s50,s117,s112,s118]) ).
cnf(s120,plain,
spl0_11,
inference(rat,[],[s54,s11,s17,s119]) ).
cnf(s121,plain,
~ spl0_12,
inference(rat,[],[s47,s119,s120]) ).
cnf(s124,plain,
spl0_14,
inference(rat,[],[s18,s121]) ).
cnf(s125,plain,
spl0_13,
inference(rat,[],[s12,s121]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s54,s119,s124,s125]) ).
fof(f677,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:57:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.74/1.33 % (3304014)Input is clausal, will run a generic CNF schedule.
% 2.74/1.33 % (3304054)lrs+10_1_sil=8000:sp=occurrence:random_seed=2203607471:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.33 % (3304054)Refutation not found, incomplete strategy
% 2.74/1.33 % (3304054)------------------------------
% 2.74/1.33 % (3304054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.33 % (3304054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.33 % (3304054)CaDiCaL version: 2.1.3
% 2.74/1.33 % (3304054)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.33 % (3304054)Time elapsed: 0.002 s
% 2.74/1.33 % (3304054)Peak memory usage: 88 MB
% 2.74/1.33 % (3304054)Instructions burned: 3 (million)
% 2.74/1.33 % (3304052)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2172190009:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.33 % (3304049)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=2838019931:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.33 % (3304050)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=181871861:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.33 % (3304058)dis-21_1_sil=8000:lcm=predicate:random_seed=1247398083:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.74/1.33 % (3304055)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1792524170:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.33 % (3304058)Refutation not found, incomplete strategy
% 2.74/1.33 % (3304058)------------------------------
% 2.74/1.33 % (3304058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.33 % (3304058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.33 % (3304058)CaDiCaL version: 2.1.3
% 2.74/1.33 % (3304058)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.33 % (3304058)Time elapsed: 0.002 s
% 2.74/1.33 % (3304058)Peak memory usage: 88 MB
% 2.74/1.33 % (3304058)Instructions burned: 2 (million)
% 2.74/1.33 % (3304056)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3591517928:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.33 % (3304056)First to succeed.
% 2.74/1.33 % (3304056)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3304014"
% 2.74/1.33 % (3304055)Instruction limit reached!
% 2.74/1.33 % (3304055)------------------------------
% 2.74/1.33 % (3304055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.33 % (3304055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.33 % (3304055)CaDiCaL version: 2.1.3
% 2.74/1.33 % (3304055)Termination reason: Instruction limit
% 2.74/1.33 % (3304055)Termination phase: Saturation
% 2.74/1.33 % (3304055)Time elapsed: 0.066 s
% 2.74/1.33 % (3304055)Peak memory usage: 89 MB
% 2.74/1.33 % (3304055)Instructions burned: 114 (million)
% 2.74/1.33 % (3304054)------------------------------
% 2.74/1.33 % (3304054)------------------------------
% 2.74/1.33 % (3304140)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=476973603: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)
% 2.74/1.33 % (3304140)Refutation not found, incomplete strategy
% 2.74/1.33 % (3304140)------------------------------
% 2.74/1.33 % (3304140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.33 % (3304140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.33 % (3304140)CaDiCaL version: 2.1.3
% 2.74/1.33 % (3304140)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.33 % (3304140)Time elapsed: 0.002 s
% 2.74/1.33 % (3304140)Peak memory usage: 88 MB
% 2.74/1.33 % (3304140)Instructions burned: 4 (million)
% 2.74/1.33 % (3304133)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=2474186224:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.74/1.33 % (3304133)Refutation not found, incomplete strategy
% 2.74/1.33 % (3304133)------------------------------
% 2.74/1.33 % (3304133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.33 % (3304133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.33 % (3304133)CaDiCaL version: 2.1.3
% 2.74/1.33 % (3304133)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.33 % (3304133)Time elapsed: 0.003 s
% 2.74/1.33 % (3304133)Peak memory usage: 88 MB
% 2.74/1.33 % (3304133)Instructions burned: 3 (million)
% 2.74/1.33 % (3304058)------------------------------
% 2.74/1.33 % (3304058)------------------------------
% 2.74/1.33 % (3304056)Refutation found. Thanks to Tanya!
% 2.74/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.53 % (3304056)------------------------------
% 3.91/1.53 % (3304056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.53 % (3304056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.53 % (3304056)CaDiCaL version: 2.1.3
% 3.91/1.53 % (3304056)Termination reason: Refutation
% 3.91/1.53 % (3304056)Time elapsed: 0.017 s
% 3.91/1.53 % (3304056)Peak memory usage: 89 MB
% 3.91/1.53 % (3304056)Instructions burned: 25 (million)
% 3.91/1.53 % (3304056)------------------------------
% 3.91/1.53 % (3304056)------------------------------
% 3.91/1.53 % (3304014)Success in time 0.456 s
% 3.91/1.53 % Vampire exiting
%------------------------------------------------------------------------------